ber correction in qpsk

8/12/2019 BER Correction in QPSK

1/10

US007027524B2

( 1 2 ) United S t a t e s Patent ( 1 0 ) P a t e n t N 0 . : US 7 , 0 2 7 , 5 2 4 B 2Fang ( 4 5 ) D a t e o f P a t e n t : A p r . 1 1 , 2 0 0 6

(54) METHODOFTRANSMITTINGAND 6,470,055 B1 * 10/2002 Feher . . . . . . . . . . . . . . . . . . . . . . . . . 375/259RECEIVING QPSK DIGITAL SIGNALS FOREIGN PATENT DOCUMENTS

( 7 5 ) I n v e n t o r : J u i n g F a n g , C u p e r t i n o , CA U S ) EP 0 7 1 6 5 2 9 A2 6 / 1 9 9 6E P 0 780 987 A 1 6/19977 3 A :AltlP FR( ) s s l g n e e c a 6 a n s ( ) OTHER PUBLICATIONS

( * ) N o t i c e ? subleqw a n y d i 5 C 1 a i m e r , _ t h e t e r m O f t h i s C a V a l e c - A m i s K t a l : B l o c k t u r b o c o d e s f o r s p a c e - t i m ePawnt 1 5 e x t e n d e d o r a d l u s t e d u n d e r 3 5 s y s t e m s , Globecom 00ilEEE. G l o b a l TelecommunicaU - S - C - 1 5 4 ( 1 ) ) b y 7 7 3 d a y s - t i o n s C o n f e r e n c e , N o v . 2 7 , 2 0 0 0 - D e c . 1 , 2 0 0 0 , p p . 1 0 2 1

1 0 2 5 , V 0 1 . 2 , P i s c a t a W a y , N J , USA.( 2 1 ) A p p l ' N O : 1 0 / 4 3 , 1 1 1 S a n d e e p R a j p a l e t a l : P r o d u c t Coded o d u l a t i o n P r o c e e d_ _ ings of the Global Telecommunications Conference( 2 2 ) Med J a n - 1 4 2 0 0 2 ( G l o b e c o m ) , N o v . 2 9 , 1 9 9 3 - D e c . 2 , 1 9 9 3 , p p . 7 - 1 1 , v o l . 4 ,

( 6 5 ) P r i o r P u b l i c a t i o n Data New Y o r k USAUs 2002/0133644 A 1 S e p . 1 9 , 2002 * ted by exammer

_ _ _ _ _ PrimaryExaminerilean Corrielus

( 3 0 ) F o r e l g n A p p h c a t l o n Pnonty D a t a A s s i s t a n t E x a m i n e r 4 Q u t u b G h u l a m a l iJ a n . 1 5 , 2001 (FR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0 1 00464 (70141100162 Agem, 0 r Fir mis u gh r u e M 1 9 1 1 , PLLC( 5 1 ) I n t . C l . ( 5 7 ) ABSTRACT

met 0 o transmittm 1 1 t a s1 na s 1n W c03C 1/52 (2006.01) A h d f . . g PSK dg. 1 . g 1 . h i hH 3K /06 (2006.01) . . . .5 2 Us Cl 3 7 5 / 3 0 3 _ 3 7 5 / 3 0 8 e a c h 2 - d 1 g 1 t bmary number, r e f e r r e d t o a s a s y m b o l , 1 s( ) I . . . . . . . . . . . . . . . . . ; . . . . . . . . . . . . . . . . . . . . . , assigned a phase of a C a r r i e r and Sy m bo ls are added t o( 5 8 ) Field of Classi?cation Search . . . . . . . . . . . . . . . . 375/308, enable e r r o r C o r r e c t i o n a t t h e r e c e i v e r The e r r o r C o r r e c t i o n

_ 3 7 5 / 2 9 8 2 6 0 2 6 1 2 8 3 2 8 6 2 7 9 } 2 9 5 3 1 6 c o d e i s a p r o d u c t c o d e . T o o b t a i n t r a n s p a r e n c y t o p h a s eS e e a p p l 1 c a t 1 o n ? l e f o r c o m p l e t e s e a r c h h 1 s t o r y . r o t a t i o n s , t h e : 1 b i t s ( 1 1 1 3 , e t c ) a n d h e : Q i t s ( Q 2 , Q 4 , e t c )_ of symbol t o be t r a n s m i t t e d a r e placed i n d i f f e r e n t roWs but

( 5 6 ) References Clted i n t h e same column, s o t h a t each roW c o n t a i n s o n l y one t y p eU _ S _ PATENT DOCUMENTS o f i t , I o r Q . The e r r o r c o r r e c t i o n c o d i n g i s e f f e c t e d : roW by

* / a h l l / roW ( N C - K C ) , and by p a i r s o f a d j a c e n t c o l u m n s , and t h ei * g e e g z r i l n e t a " " " " " c o d e I ( o r Q) b i t s o f tWo a s s o c i at e d a d j a c e n t c o l u m n s a r e5 : 6 9 2 : 0 0 7 A * 1 1 / 1 9 9 7 D u r r a n t e t a 1 . . . . . . . . . . 3 7 5 / 1 4 2 deduced from t h e I ( o r Q) bus Ofthe W0 Columns5,966,412 10/1999 Ramaswamy . . . . . . . . . .. 375/3416,185,259 B1 * 2/2001 Dent . . . . . . . . . . . . . . . . . . . . . . . . . . 375/261 12 Claims, 3 Drawing Sheets

5 8 ,501/7 Q 5 _ [ , I _5 0 2 ' 5 8 5 8.._.@ 5 8 35 2 1 ' ; _ 5 _ 2 i Q

75 2 J2 5 a , .

6 A 7 _ 2 E----u

4 9 9 1 I L ? ? ? Q 3 6 _ 6 7 _


2/10


3/10

U.S. Patent A p r . 1 1 , 2 0 0 6 S h e e t 2 0 f 3 U S 7 , 0 2 7 , 5 2 4 B2

5 % N 5 3 6 1 2 3 1 . __ _ _ _ KB N?

( I . X . x 0 a 0 c 0 Q X Q f2 X . X X 0 a0 X

X o

L 1 :I

Ia lI

____ _ f X i a a o p 1X 0o X I

N L K L X 0I

C 1C 1 A - - 1 : 1 A0 1 0 1 0 0 0 1 0 1 0 0 0000

O 9 1 } J r . 0 X 1 1 0 1 1 0 0 1 1 1 0 0 1000l l l r T

[ : 1 A + [ : 1 A0 1 1 1 0 0 1 1 0 1 1 0 0 0 1 0

O 9 6 O 9 %1 1 1 1 1 0 1 1 1 1 1 0 1 0 1 0


4/10


5/10

US 7 , 0 2 7 , 5 2 4 B21

METHOD F TRANSMITTING ANDRECEIVING QPSK DIGITAL SIGNALS

The i n v e n t i o n r e l a t e s t o a method o f t r a n s m i t t i n g QPSKa n d QAM-l6 d i g i t a l s i g n a l s .

BACKGROUND OF THE INVENTIONThe f o r m o f m o d u l a t i o n knoWn a s QPSK ( s h o r t f o r q u a t e m y p h a s e - s h i f t k e y i n g ) i s r o u t i n e l y u s e d t o t r a n s m i td i g i t a l s i g n a l s a n d r e p r e s e n t s a p a i r o f b i n a r y d i g i t s b y t h e

p h a s e o f a s i n u s o i d a l s i g n al r e l a t i v e t o a r e f e r e n c e p h a s e .Because a 2 - d i g i t b i n a r y number c a n t a k e f o u r v a l u e s , t h e

p h a s e s c a n d i f f e r by 3 1 / 2 r a d i a n s . F o r e x a m p l e , a s i g n a lh a v i n g a p h a s e s h i f t o f l Z / 4 r a d i a n s r e l a t i v e t o t h e r e f e r e n c ep h a s e r e p r e s e n t s t h e number 0 0 . A i g n a l W i t h a p h a s e s h i f to f 7 5 / 4 r e l a t i v e t o t h e r e f e r e n c e p h a s e r e p r e s e n t s t h e number0 1 , a s i g n a l W i t h a p h a s e s h i f t o f 5 7 5 / 4 r e l a t i v e t o t h er e f e r e n c e p h a s e r e p r e s e n t s t h e number 1 1 , a n d a s i g n a l W i t ha p h a s e s h i f t o f 7 7 5 / 4 r e l a t i v e t o t h e r e f e r e n c e p h a s e r e p r es e n t s t h e number 1 0 . T h i s k i n d o f c o r r e s p o n d e n c e betWeent h e p a i r s o f b i n a r y d i g i t s a n d t h e p h a s e s h i f t s , i n W h i c h o n l yo n e b i n a r y d i g i t i s modi?ed f o r e a c h i n c r e m e n t o f 3 1 / 2 , i sr e f e r r e d a s t h e Gray c o r r e s p o n d e n c e . O t h e r f o r m s o f c o r r es p o n d e n c e a r e p o s s i b l e , f o r e x a m p l e t h e n a t u r a l c o r r e s p o nd e n c e W i t h i n c r e a s i n g v a l u e s o f t h e n u m b e r s , i n Which c a s et h e s u c c e s s i o n o f b i n a r y n u m b e r s i s 0 0 , 0 1 , 1 0 a n d 1 1 .

The r e c e i v e r must knoW t h e r e f e r e n c e p h a s e ; i n o t h e rW o r d s , i t m u s t b e p o s s i b l e t o d i s t i n g u i s h b e t W e e n t h e f o u rp h a s e v a l u e s t r a n s m i t t e d , f o r e x a m p l e 3 1 1 / 4 , 3 7 5 / 4 , 5 3 1 3 / 4 a n d7 7 5 / 4 o r 0 , 3 1 / 2 , a t and 7 5 / 2 . The s i m p l e s t Way t o r e c o v e r t h er e f e r e n c e p h a s e , i . e . t o r e s o l v e t h e p h a s e a m b i g u i t y , i s t os e n d p e r i o d i c a l l y a knoWn s y m b o l , i . e . a s y m b o l c o n s i s t i n go f b i t s o f p r e d e t e r m i n e d v a l u e . The d i s a d v a n t a g e o f t h i smethod i s t h a t i t cannot c o r r e c t e r r o r s due t o t r a n s m i s s i o nn o i s e , Which i s i n e v i t a b l e , and a c o n s e q u e n c e o f t h i s i s t h ea p p e ar a n c e o f p h a s e j u m p s b e t W e e n s u c c e s s i v e t r a n s m i ss i o n s o f t h e knoWn s y m b o l s .

A n o t h e r , r e l a t i v e l y c o m p l e x , m e t h o d d e t e c t s d e c o d i n ge r r o r s a n d commands p h a s e r o t a t i o n s by i n c r e m e n t s o f J l Z / 4i n o r d e r t o d e t e r m i n e Which i s t h e c o r r e c t p h a s e . T h i sr e q u i r e s c o n s i d e r ab l e p r o c e s s i n g t i m e , W h i c h i s i n c o m p a ti b l e W i t h r e a l - t i m e p a c k e t t r a n s m i s s i o n , b e c a u s e t h e p r oc e s s i n g t i m e l e a d s t o l o s s o f d a t a .

The method p r o v i d i n g t h e b e s t r e s u l t s e n t a i l s a s s i g n i n gt h e t r a n s m i t t e d d a t a a n e r r o r c o r r e c t i n g code and c o r r e c t i n ge r r o r s a f t e r d e c o d i n g , r a t h e r t h a n s i m u l t a n e o u s l y W i t h t r a n sm i s s i o n , a s i n t h e p r i o r a r t m e t h o d s .

The most e f f e c t i v e e r r o r c o r r e c t i n g c o d e s a r e p r o d u c tc o d e s , Which a r e a l s o knoWn a s t u r b o c o d e s . To form ap r o d u c t c o d e , t h e b i n a r y d i g i t s t o b e t r a n s m i t t e d a r eassembled i n t o a matrix Which h a s L roWs and C columnsand t h e roWs and columns a r e coded i n b l o c k s ; i n o t h e rW o r d s , ( K - C ) e r r o r c o r r e c t i n g b i t s ( p a r i t y b i t s ) a r e a d d e d t oe a c h roW c o n t a i n i n g C a t a b i t s and ( P - L ) e r r o r c o r r e c t i n gb i t s a r e added t o each column c o n t a i n i n g L a t a b i t s . I f a roWi s c o m p l e t e l y e r r o n e o u s , i t s p a r i t y b i t s c a n n o t b e u s e d toc o r r e c t i t ; on t h e o t h e r h a n d , t h e e r r o n e o u s roW could bec o r r e c t e d by means o f t h e p a r i t y b i t s i n t h e c o l u m n s , b e c a u s eo n l y one b i t i s e r r o n e o u s i n each column.

H o W e v e r , e x i s t i n g t u r b o c o d e s c a n n o t b e u s e d f o r QPSKb e c a u s e p h a s e r o t a t i o n s a ? f e c t d e c o d i n g . I n o t h e r W o r d s ,e x i s t i n g e r r o r c o r r e c t in g t u r b o c o d e s a r e n o t t r a n s p ar e n t t op h a s e r o t a t i o n s , a n d t h e r e f o r e c a n n o t b e u s e d f o r QPSKt r a n s m i s s i o n .

1 0

20

25

30

35

40

45

50

55

60

6 5

2OBJECTS AND SUMMARY OF THE

INVENTIONThe i n v e n t i o n p r o v i d e s , f o r QPSK i g n a l s , e r r o r c o r r e c t

i n g t u r b o c o d e s ( p r o d u c t c o d e s ) Which a r e i n s e n s i t i v e t op h a s e r o t a t i o n s . The i n v e n t i o n t h e r e f o r e p r o v i d e s a t u r b oc o d e f o r QPSK m o d u l a t i o n t h a t i s t r a n s p a r e n t t o p h a s er o t a t i o n s .

I n a ? r s t embodiment o f t h e i n v e n t i o n , f o r c o d i n g , t h e Ia n d Q i t s o f a QPSK symbol to b e t r a n s m i t t e d a r e p l a c e di n d i f f e r e n t roWs but i n t h e same column, s o t h a t each roWc o n t a i n s o n l y o n e t y p e o f b i t ( I o r Q ) , t h e c o d i n g f o r e r r o rc o r r e c t i o n i s a f f e c t e d , on t h e one h a n d , roW by roW a n d , ont h e o t h e r h a n d , b y p a i r s o f a d j a c e n t c o l u m n s , t h e c o d e I b i t sof tWo a s s o c i a t e d a d j a c e n t columns a r e deduced from t h e Ib i t s i n s a i d tWo columns and h e c o d e Q i t s o f t h e a s s o c i a t e dtWo a d j a c e n t columns a r e deduced from t h e Q i t s i n s a i dtWo columns, t h e code b i t s a r e arranged i n t h e same mannera s t h e s t a r t i n g b i t s , i . e . s o t h a t each roW c o n t a i n s o n l y onet y p e o f i t ( I o r Q ) , a n d t h e p a i r s o f a d j a c e n t c o d e I a n d Qb i t s i n t h e same column a r e t r a n s m i t t e d l i k e t h e o t h e r QPSKs y m b o l s .

W i t h h i s t y p e o f c o d i n g , a n d f G r a y s y m b o l s a r e u s e d , f o re x a m p l e , a r o t a t i o n of t i n v e r t s t h e b i t s ( a 1 b i t becomes a0 b i t and a 0 b i t becomes a 1 b i t ) . Thus t h e m a t r i x r e m a i n si n t h e same f a m i l y o f roWs and c o l u m n s , Which e n a b l e se r r o r s t o be corrected i n a manner knoWn t o t h e persons k i l l e d i n t h e a r t .

I f a r o t a t i o n of 1 / 2 o c c u r s , t h e I roWs become Q oWs andt h e Q roWs become i n v e r t e d I r o W s . The roW and columnWords o b t a i n e d i n t h i s W a y With a r o t a t i o n o f 3 1 / 2 r e s p e ct i v e l y remain i n t h e roW and column c o d e s , Which meanst h a t t h e y c a n b e d e c o d e d c o r r e c t l y . S i m i l a r l y , i t c a n b eshoWn t h a t a r o t a t i o n of 3 7 5 / 2 causes t h e I roWs t o becomei n v e r t e d Q roWs and t h e Q roWs t o become I r o W s . Undert h e s e c o n d i t i o n s , t h e roW and column Words can be decodedc o r r e c t l y .

A c c o r d i n g l y , in t h e c a s e o f QPSK G r a y s y m b o l s , t h e ? r s tc o d i n g mode i s t r a n s p a r e n t t o r o t a t i o n s o f t , 3 1 / 2 a n d 3 7 5 / 2 ,i . e . t o a l l r o t a t i o n s . T h i s shoWs t h a t t h i s t y p e o f c o d i n g h a st h e same p r o p e r t i e s f o r a n a t u r a l s u c c e s s i o n o f QPSKs y m b o l s . T h e c o d i n g i s t h e r e f o r e t o t a l l y t r a n s p a r e n t t o t h ep h a s e r o t a t i o n s , W h i c h t h u s e n a b l e s c o r r e c t d e c o d i n g .

I n a second embodiment of t h e i n v e n t i o n , t o code t h es y m b o l s to b e t r a n s m i t t e d , t h e I a n d Q i t s o f a QPSKsymbol a r e both p l a c e d i n t h e same r o W , s o t h a t each o f t h eroWs i s formed o f p a i r s o f I and Q i t s ; t h e roWs and t h ecolumns a r e a r r a n g e d s o t h a t t h e I and Q its a l t e r n a t e i ne a c h c o l u m n , t h e roWs and t h e columns a r e coded bya d j a c e n t p a i r s s o t h a t t h e code b i t s a r e d e r i v e d from t h e Ib i t s o f tWo a s s o c i a te d a d j a c e n t roWs ( c o l u m n s ) and t h e c o d eQ i t s o f s a i d tWo a d j a c e n t r o W s ( c o l u m n s ) a r e d e r i v e d o n l yfrom t h e Q i t s of a i d tWo roWs ( c o l u m n s ) , t h e code i t s a r ea r r a n g e d l i k e t h e s t a r t i n g b i t s , a n d t h e p a i r s o f c o d e I a n d Qb i t s on each roWs a r e t r a n s m i t t e d l i k e t h e o t h e r QPSKs y m b o l s .

With t h i s second embodiment, With a r o t a t i o n of t r a d i a n so f s y m b o l s i n a Gray o r n a t u r a l s u c c e s s i o n , t h e I b i t s and t h eQ i t s a r e s i m p l y i n v e r t e d and t h e roW and column c o d e st h u s remain t h e s a m e , and can t h e r e f o r e be d e c o d e d .A o t a t i o n of 1 / 2 causes t h e I roWs t o become Q oWs and

t h e Q oWs t o become i n v e r t e d I r o W s . A s a g e n e r a l r u l e , i tcan be shoWn t h a t i n t h i s second embodiment t h e t u r b oc o d i n g i s t r a n s p a r e n t t o p h a s e r o t a t i o n s f o r QPSK s y m b o l s .

The e r r o r c o r r e c t i n g c o d e s a c c o r d i n g t o t h e i n v e n t i o n a r eused t o t r a n s m i t s i g n a l s . The i n v e n t i o n a l s o r e l a t e s t o a


6/10

US 7 , 0 2 7 , 5 2 4 B23

m e t h o d o f r e c e i v i n g s i g n a l s c o d e d u s i n g t h e e r r o r c o r r e c t i n gc o d e s d e s c r i b e d above and decoded t o r e c o v e r t h e s t a r t i n gs y m b o l s .

The c o d i n g o f QPSK symbols i n a manner t h a t i s t r a n sp a r e n t t o p h a s e r o t a t i o n s c a n b e u s e d f o r t u r b o c o d i n gQAM-l6 ( 1 6 s t a t e q u a d r a t u r e a m p l i tu d e m o d u l a t i o n ) s y mb o l s , c o n s t i t u t i n g a f u r t h e r a s p e c t o f t h e i n v e n t i o n Which canb e u s e d i n d e p e n d e n t l y o f o t h e r a s p e c ts o f t h e i n v e n t i o n .Q A M - l 6 m o d u l a t i o n t r a n s m i t s e a c h o f t h e s i x t e e n 4 - b i tnumbers W i t h a s p e c i ? c p h a s e and a s p e c i ? c a m p l i t u d e o f ac a r r i e r o f g i v e n f r e q u e n c y . T h u s , u s i n g t h e c o n v e n t i o n a lr e p r e s e n t a t i o n i n t h e c o m p l e x p l a n e , f o u r p o i n t s i n e a c hq u a d r a n t a r e d i s t i n g u i s h e d b y t h e i r p o s i t i o n , ie b y t h e i rp h a s e a n d / o r t h e i r a m p l i t u d e , a n d e a c h o f t h e f o u r p o i n t sr e p r e s e n t s a 4 - d i g i t b i n a r y n u m b e r .

A c c o r d i n g t o t h e i n v e n t i o n , t h e f o u r QAM-l s y m b o l s i ne a c h q u a d r an t o f t h e c o m p l e x p l a n e a r e a r r a n g e d s o t h a t t h eb i n a r y numbers have t h e same a s t tWo d i g i t s and s o t h a t t h e? r s t t W o d i g i t s f o r m d i f f e r e n t n u m b e r s : 0 0 , 0 1 , 1 1 a n d 1 0 ,a n d t h o s e numbers a r e a r r a n g e d i n f o u r s u b s e t s o c c u p y i n gt h e W h o l e o f t h e c o m p l e x p l a n e , e a c h s u b s e t i s f o r m e d b y t h es e t o f numbers h a v i n g t h e same ? r s t tWo b i n a r y d i g i t s , andt h e r e f o r e l y i n g i n a d i f f e r e n t one o f t h e f o u r q u a d r a n t s , andt h e c o o r d i n a t e s o f t h e s y m b o l s i n t h e c o m p l e x p l a n e a r echosen s o t h a t a f t e r a r o t a t i o n of 1 / 2 each s u b s e t t a k e s t h ep l a c e o f a n o t h e r s u b s e t .A e t o f Q A M - l 6 s y m b o l s o f t h i s k i n d i s p r o d u c t c o d e db y c o d i n g p a i r s o f i t s o f e a c h QAM-l 6 s y m b o l , e a c h s u c hp a i r f o r m i n g a QPSK s y m b o l , t h e QPSK s y m b o l s a r e c o d e d

i n a manner t h a t i s t r a n s p a r e n t t o p h a s e r o t a t i o n s , and t h ed a t a coded i n t h i s Way s t r a n s m i t t e d W i t h t h e above a r r a n g em e n t i n t h e c o m p l e x p l a n e .

A s an a l t e r n a t i v e t o t h i s , a set o f QAM-l symbols of h i sk i n d c a n be coded b i t by b i t u s i n g a c o n v e n t i o n a l BPSK( b i n a r y p h a s e s h i f t k e y i n g ) c o d e t r a n s p a r e n t t o p h a s e r o t at i o n s .QAM-l6 modulation can be used t o t r a n s m i t d a t a . The

i n v e n t i o n a l s o r e l a t e s t o r e c e i v i n g d a t a m o d u l a t e d i n t h emanner de?ned a b o v e , demodulation c o n s i s t i n g of r e c o v e ri n g t h e s t a r t i n g s y m b o l s f r o m t h e p h a s e s a n d t h e a m p l i t u d e so f t h e r e c e i v e d s i g n a l s .

B R I E F DESCRIPTION OF THE DRAWINGSO t h e r f e a t u r e s a n d a d v a n t a g e s o f t h e i n v e n t i o n W i l l

become a p p a r e n t i n t h e c o u r s e o f t h e f o l l o W i n g d e s c r i p t i o no f e m b o d i m e n t s o f t h e i n v e n t i o n , Which i s g i v e n W i t hr e f e r e n c e t o t h e a c c o m p a n y i n g d r a W i n g s , i n W h i c h :

F I G . 1 i s a diagram of a modulation and demodulationmethod u s i n g a c o d i n g method a c c o r d i n g t o t h e i n v e n t i o n ,

F I G . 2 i s a d i a g r am s h o W i n g QPSK m o d u l a t i o n ,F I G . 3 i s a d i a g r a m e x p l a i n i n g a ? r s t c o d i n g method

a c c o r d i n g t o t h e i n v e n t i o n ,F I G . 4 i s a diagram a n a l o g o u s t o t h a t o f F I G . 3 f o r ad i f f e r e n t embodiment o f t h e m e t h o d ,F I G . 5 i s a d i a g r am s h o W i n g Q A M - l 6 m o d u l a t i o n i n

a c c o r d a n c e W i t h t h e i n v e n t i o n , a n dF I G . 6 i s a diagram o f a QAM-l6 o d u l a t o r a c c o r d i n g t o

t h e i n v e n t i o n .MORE DETAILED DESCRIPTION

T o t r a n s m i t b i n a r y d a t a , QPSK o d u l a t i o n t r a n s m i t s ac a r r i e r o f a r t i c u l a r f r e q u e n c y a n d p a r t i c u l a r a m p l i t u d e a n da s s i g n s t h e p h a s e o f t h e c a r r i e r f o u r d i f f e r e n t v a l u e s r e l a t i v et o a r e f e r e n c e p h a s e . I n th e complex p l a n e shoWn i n F I G . 2 ,tWo s u c c e s s i v e p h a s e s a r e s e p a r a t e d by a n a n g u l a r o f f s e t o f

20

25

30

35

40

45

50

55

60

6 5

43 1 3 / 2 r a d i a n s . The r s t p h a s e i s i n t h e ? r s t q u a d r a n t , t h e s e c o n dp h a s e i s i n t h e s e c o n d q u a d r a n t , t h e t h i r d p h a s e i s in t h e t h i r dq u a d r a n t , a n d t h e f o u r t h p h a s e i s i n t h e f o u r t h q u a d r a n t . F o re x a m p l e , r e l a t i v e t o t h e r e f e r e n c e p h a s e , t h e ? r s t p h a s e i ss h i f t e d b y 1 3 / 4 r a d i a n s , t h e s e c o n d p h a s e b y 3 7 5 / 4 r a d i a n s , t h et h i r d p h a s e b y 5 3 1 3 / 4 r a d i a n s a n d t h e f o u r t h p h a s e b y 7 7 5 / 4r a d i a n s . TWo b i n a r y d i g i t s a r e a s s o c i a t e d W i t h e a c h p h a s e . I na Gray c o r r e s p o n d e n c e o r s u c c e s s i o n o f t h e p h a s e s , and t h u so f t h e b i n a r y n u m b e r s , t h e l a t t e r a r e 0 0 , 0 1 , 1 1 a n d 1 0 , i n t h ep o s i t i v e d i r e c t i o n s t a r t i n g f r o m t h e ? r s t q u a d r a n t . I t c a n b es e e n t h a t , i n t h i s c a s e , o n l y one b i n a r y d i g i t i s modi?ed one a c h p r o g r e s s i o n by o n e s t e p . I n a n a t u r a l r e p r e s e n t a t i o n , f o rWhich t h e numbers a r e shoWn i n b r a c k e t s i n F I G . 2 , t h eb i n a r y n u m b e r s a r e i n t h e f o l l o W i n g p r o g r e s s i o n : 0 0 , 0 1 , 1 0a n d 1 1 . I n o t h e r W o r d s , t h e b i n a r y n u m b e r s c o r r e s p o n d i n g t ot h e p a i r s o f b i n a r y d i g i t s p r o g r e s s n a t u r a l l y , i n i n c r e a s i n go r d e r .

A p a i r ( o r , m o r e g e n e r a l l y , a s e t ) o f b i n a r y d i g i t s i s u s u a l l yr e f e r r e d t o a s a symbol.

F o r d e m o d u l a t i o n , i t i s n e c e s s a r y t o d e t e r m i n e t h e p h a s eo f t h e t r a n s m i t t e d s i g n a l r e l a t i v e t o t h e r e f e r e n c e p h a s e . T h i si s n o t e a s y , i n p a r t i c u l a r b e c a u s e n o i s e c a u s e s r o t a t i o n s .

Modulation and demodulation a r e more e f ? c i e n t i f phased i f f e r e n c e s betWeen tWo c o n s e c u t i v e symbols a r e t r a n s m i tt e d i n s t e a d o f t h e i r p h a s e s a s s u c h . T h i s i s b e c a u s e , i n t h ee v e n t o f r o t a t i o n , t h e p h a s e d i f f e r e n c e betWeen tWo cons e c u t i v e s y m b o l s d o e s n o t c h a n g e . F u r t h e r m o r e , f o r r e a ltime t r a n s m i s s i o n , t h e d a t a i s t r a n s m i t t e d With an e r r o rc o r r e c t i n g code s o t h a t e r r o r s a r e c o r r e c t e d o n l y a t t h er e c e i v e r . The most e f ? c i e n t e r r o r c o r r e c t i n g code s a p r o d u c tc o d e ( t u r b o c o d e ) . H o W e v e r , i t h a s b e e n f o u n d t h a t e x i s t i n gp r o d u c t c o d e s a r e a f f e c t e d b y p h a s e r o t a t i o n s . T h e i n v e n t i o nt h e r e f o r e s e e k s t o p r o v i d e a p r o d u c t c o d e t h a t i s i n s e n s i t i v et o p h a s e r o t a t i o n s .

B e f o r e d e s c r i b i n g p r o d u c t c o d e s a c c o r d i n g t o t h e i n v e nt i o n i n d e t a i l , a QPSK o d u l a t o r and a QPSK e m o d u l a t o rWhich can be used i n t h e c o n t e x t of t h e i n v e n t i o n a r ed e s c r i b e d .The m o d u l a t o r 1 0 ( F I G . 1 ) i n c l u d e s a t W o - d i m e n s i o n a ld i f f e r e n t i a l c o d e r 1 2 a d a p t e d t o s u p p l y c o n s e c u t i v e QPSKs y m b o l s . Thus a ? r s t I b i t o f t h e d i f f e r e n c e betWeen tWoc o n s e c u t i v e s y m b o l s i s o b t a i n e d a t t h e ? r s t o u t p u t 1 2 1 o f t h ec o d e r 1 2 and a s e c o n d Q i t i s o b t a i n e d a t t h e s e c o n d o u t p u t1 2 2 .The s y m b o l s s u p p l i e d by t h e c o d e r 1 2 a r e a p p l i e d t o t h ei n p u t s o f a p r o d u c t c o d e r 1 4 a c c o r d i n g t o t h e i n v e n t i o n ,Whose f u n c t i o n i s d e s c r i b e d l a t e r , i n p a r t i c ul a r W i t h r e f e rence t o FIGS. 3 and 4 . The coder 14 s u p p l i e s a s e t ofs y m b o l s t h a t i n c l u d e , o n t h e o n e h a n d , t h e s y m b o l s a p p l i e dt o i t s i n p u t a n d , o n t h e o t h e r h a n d , s u p p l e m e n t a r y s y m b o l st h a t a r e used f o r e r r o r c o r r e c t i o n a f t e r t r a n s m i s s i o n . Thesymbols a t t h e o u t p u t o f t h e c o d e r 1 4 a r e c o n v e r t e d by aQPSK o d u l a t o r 1 6 i n t o p h a s e s o f c a r r i e r a n d t h e modul a t e d s i g n a l s a r e t r a n s m i t t e d o v e r a c h a n n e l 1 8 , f o r examplea r a d i o channel.

The r e c e i v e r i n c l u d e s a demodulator u n i t 20 Whichi n c l u d e s a QPSK e m o d u l a t o r 2 2 Which r e c e i v e s t h e s i g n a l sf r o m t h e c h a n n e l a n d d e l i v e r s a t i t s o u t p u t s 2 2 1 a n d 2 2 2b i n a r y s y m b o l s t h a t a r e a p p l i e d t o t h e tWo i n p u t s o f ap r o d u c t c o d e d e c o d e r 2 4 t o d e t e r m i n e t h e c o r r e s p o n d i n gs t a r t i n g s y m b o l s a t t h e o u t p u t o f t h e c o d e r 1 2 . The o u t p u ts y m b o l s from t h e d e c o d e r 24 a r e a p p l i e d t o t h e i n p u t o f at W o - d i m e n s i o n a l d i f f e r e n t i a l d e c o d e r 2 6 Which p e r f o r m s t h eo p e r a t i o n t h a t i s t h e i n v e r s e o f h a t e f f e c t e d b y t h e c o d e r 1 2a n d t h e r e f o r e s u p p l i e s t h e s t a r t i n g s y m b o l s a t i t s o u t p u t .

I f t h e demodulator 22 and t h e decoder 24 a r e n o t t o bea f f e c t e d b y p h a s e r o t a t i o n s , i t i s n e c e s s a r y f o r t h e p r o d u c t


7/10

US 7 , 0 2 7 , 5 2 4 B25

c o d e u s e d t o be t r a n s p a r e n t t o r o t a t i o n s o f 3 1 / 2 , a t and 3 7 5 / 2 ;i n o t h e r W o r d s , t h i s k i n d o f r o t a t i o n must t r a n s f o r m e a c hcode Word i n t o a v a l i d code Word, i . e . one from t h e samef a m i l y .A r s t embodiment o f a p r o d u c t c o d e f o r QPSK y m b o l s

t h a t i s t r a n s p a r e n t t o p h a s e r o t a t i o n s W i l l noW be d e s c r i b e dWith r e f e r e n c e to T a b l e I beloW and to FIG. 3 .

TABLEI 1 1 I 1 2 I 1 3 I 1 4Q 2 1 Q 2 2 Q 2 3 Q 2 4I 3 1 I 3 2 I 3 3 I 3 4Q 4 1 Q 4 2 Q 4 3 Q 4 4

F o r a s e t o f b i n a r y d i g i t s o r v a l u e s , c o n v e n t i o n a l p r o d u c tc o d i n g e n t a i l s a r r a n g i n g t h e b i n a r y d i g i t s i n r o W s a n dcolumns and adding to each roW and t o each columnsupplementary b i t s t o be used f o r e r r o r c o r r e ct i o n . The roWand column codes a r e c a l l e d block c o d e s . Because t h e s ecodes a r e Well-known t o t h e person s k i l l e d i n t h e a r t , i t i s n o tn e c e s s a r y t o d e s c r i b e them i n d e t a i l .

T h e a d v a n t a g e o f p r o d u c t c o d i n g s t h a t s t r o n g l y d e g r a d e droWs can be c o r r e c t e d . A oW containing mo r e than tWoe r r o n e o u s b i t s c a n n o t n e c e s s a r i l y be c o r r e c t e d . On h e o t h e rh a n d , i f t h e columns a r e n o t d e g r a d e d , each b i t i n t h e roWc a n t h e r e f o r e be c o r r e c t e d u s i n g t h e e r r o r c o r r e c t i n g c o d e sfrom t h e c o l u m n s . S i m i l a r l y , i f a column s d e g r a d e d b u t t h eroWs a r e n o t , t h e column can be c o r r e c t e d using t h e roWc o d e s .

I n t h e e x a m p l e shoWn i n T a b l e , I r e p r e s e n t s a ? r s t b i t ( f o re x a m p l e t h e m o s t s i g n i ? c a n t b i t ) o f a QPSK s y m b o l a n d Qr e p r e s e n t s t h e s e c o n d b i t o f t h e s y m b o l . I n t h i s s i m p l i ? e de x a m p l e , t W o s y m b o l s ( I n , Q 2 1 ) a n d ( I 1 2 , Q 2 2 ) a r e s h o W n a tt h e i n p u t o f t h e c o d e r 1 4 . T a b l e I i s o b t a i n e d a t t h e o u t p u t o ft h e c o d e r 1 4 . To t h i s end t h e roWs a r e coded c o n v e n t i o n a l l yWith a block code and t h e columns a r e coded i n p a i r s .

Thus roW c o d i n g y i e l d s t h e ? r s t tWo roWs of T a b l e I . Thec o d i n g i s t h e n e f f e c t e d s o t h a t t h e p a i r o f b i t s I n , a n d I l 2s u p p l i e s t h e p a i r o f i t s I 3 1 a n d I 3 2 a n d t h e b i t s Q 2 1 a n d Q 2 2s u p p l y t h e i t s Q 4 1 a n d Q 4 2 . S i m i l a r l y , t h e i t s I 3 3 a n d 3 4 a r et h e r e s u l t o f c o d i n g t h e b i t s I 1 3 a n d I 1 4 a n d t h e b i t s Q 2 3 a n dQ24 a r e c o d e d t o o b t a i n t h e b i t s Q 4 3 and Q 4 4 .

T h i s p r o d u c e s , i n a d d i t i o n t o t h e s t a r t i n g s y m b o l s ( I n ,Q 2 1 ) a n d ( I 1 2 , Q 2 2 ) , s i x o t h e r s y m b o l s , n a m e l y t h e s y m b o l s( I 1 3 : Q 2 3 ) : ( I 1 4 : Q 2 4 ) : ( I 3 1 : Q 4 1 ) : ( I 3 2 : Q 4 2 ) : ( I 3 3 : Q 4 3 ) a n d 1 3 4 :Q 4 4 ) A l l t h e s e s y m b o l s a r e t h e r e f o r e t r a n s m i t t e d b y t h ec h a n n e l 1 8 .

More g e n e r a l l y , a s shoWn in F I G . 3 , i f KL roWs and KCcolumns a r e p r o v i d e d a t t h e o u t s e t , NL-KL roWs and NC-KCcolumns a r e a d d e d . The c o d i n g i s ? r s t e f f e c t e d c o n v e n t i o na l l y by r o W s , i . e . s u p p l e m e n t a r y b i t s a r e added t o e a c h r o W .

Column c o d i n g i s e f f e c t e d i n t h e f o l l o W i n g m a n n e r : t h e? r s t tWo columns a r e c o n s i d e r e d ? r s t , and i n t h o s e columnst h e I b i t s i n t h e o d d - n u m b e r e d r o W s ( I 1 1 , I 1 2 , I 3 1 , I 3 2 , e t c . ) .From t h e s e I b i t s , I v a l u e s a r e d e t e r m i n e d and p l a c e d i n t h eodd-numbered roWs among t h e NL-KL s u p p l e m e n t a r y r o W s .S i m i l a r l y , s u p p l e m e n t a r y p a i r s o f Q i t s a r e d e t e r m i n e df r o m t h e Q a l u e s i n t h e e v e n - n u m b e r e d r o W s ( Q 2 1 , Q 2 2 ,Q 4 1 , Q 4 2 , e t c . ) a n d p l a c e d i n t h e e v e n - n u m b e r ed r o W s amongt h e NL-KL s u p p l e m e n t a r y r o W s .

The same p r o c e d u r e i s t h e n f o l l o W e d W i t h t h e t h i r d andf o u r t h c o l u m n s , t h e ? f t h and s i x t h c o l u m n s , and s o o n ; i ne a c h p a i r o f c o l u m n s , a l l t h e b i t s ( i . e . a l l t h e s y m b o l s o f t h eodd-numbered roWs) a r e c o n s i d e r e d a s a s i n g l e column andt h e e r r o r c o r r e c t i n g b i t s t o be added a r e deduced from them

20

25

30

35

40

45

50

55

60

6 5

6a n d p l a c e d i n t h e odd-numbered r o W s o f t h e s u p p l e m e n t a r yroWs NL-KL o f e a c h d o u b l e c o l u m n .

S i m i l a r l y , a l l t h e Q i t s i n t h e even-numbered roWs o feach p a i r of columns a r e c o n s i d e r e d a s a s i n g l e column, t oWhich a r e added e r r o r c o r r e c t i o n b i t s p l a c e d i n p a i r s i n t h eeven-numbered roWs among t h e N -K supplementary r o W s .

Of o u r s e , t h e I b i t s s u p p l y I b i t s a n d t h e Q i t s s u p p l y Qb i t s . A y m b o l t r a n s m i t t e d b y t h e c h a n n e l c o n s i s t s o f a p a i rof i t s c o n s i s t i n g of an b i t and t h e n e x t Q i t i n t h e samec o l u m n .

C a l c u l a t i o n s h o W s t h a t t h i s t y p e o f p r o d u c t c o d e i st r a n s p a r e n t t o r o t a t i o n s o f t , 3 1 / 2 , 3 7 5 / 2 and J | / 2 . C o n s i d e r? r s t t h e G r a y s u c c e s s i o n 0 0 , 0 1 , l l , 1 0 .

FIG. 2 shoWs t h a t a r o t a t i o n of 1 1 g i v e s r i s e t o t h ef o l l o W i n g t r a n s f o r m a t i o n s o f t h e I a n d Q y m b o l s :

Under t h e s e c o n d i t i o n s , t h e roW and column code v a l u e sr e m a i n t h e same and t h e p r o d u c t c o d e i s t h e r e f o r e t r a n s p a rent t o a r o t a t i o n of t .A o t a t i o n o f 3 1 / 2 y i e l d s :

I I Q

I t can t h e r e f o r e be s e e n t h a t , With a r o t a t i o n of 1 / 2 , t h e IroWs a r e r e p l a c e d by Q oWs and t h e Q oWs a r e r e p l a c e d byi n v e r t e d I r o W s . The roWs a r e decoded c o r r e c t l y . S i m i l a r l y ,i n t h e columns, t h e f a c t t h a t an I roW becomes a Q oW andv i c e - v e r s a means t h a t a f t e r t h e r o t a t i o n o f 3 1 / 2 t h e columnc o d e r e m a i n s t h e s a m e . Thus t h e p r o d u c t c o d e d e s c r i b e dabove i s t r a n s p a r e n t t o a r o t a t i o n of 1 / 2 .A o t a t i o n o f 3 7 5 / 2 c o r r e s p o n d s t o t h e f o l l o W i n g t r a n s f o r

m a t i o n s :

Thus t h e I roWs a r e r e p l a c e d by i n v e r t e d Q oWs and t h eQ roWs a r e r e p l a c e d by I roWs. The roWs a r e decodedc o r r e c t l y a n d , a s i n t h e c a s e o f a r o t a t i o n of 1 / 2 , i t can beseen t h a t a r o t a t i o n of 3 7 5 / 2 means t h a t a column coder e m a i n s t h e s a m e . The p r o d u c t c o d e d e s c r i b e d above i st h e r e f o r e a l s o t r a n s p a r e n t t o a p h a s e r o t a t i o n o f 3 7 5 / 2 .

The p r o d u c t c o d e shoWn i n F I G . 3 i s t h e r e f o r e t r a n s p a r e n tt o p h a s e r o t a t i o n s .I n t h e c a s e o f a n a t u r a l s u c c e s s i o n o f QPSK y m b o l s , a

r o t a t i o n o f t r a d i a n s y i e l d s t o t h e f o l l o W i n g e q u a t i o n s :

A o t a t i o n o f 3 1 / 2 r a d i a n s y i e l d s t h e e q u a t i o n s :( 4 )

Q:Q1:QA o t a t i o n o f 3 7 5 / 2 r a d i a n s y i e l d s t h e e q u a t i o n s :

( 5 )

Because t h e Q i t s a r e coded by t h e same roW o r columnc o d e , a n d b e c a u s e t h e c o d e i s l i n e a r , t h e c o d e i s t r a n s p a r e n tt o r o t a t i o n s of t , 3 1 / 2 and 3 7 5 / 2 .


8/10

US 7 , 0 2 7 , 5 2 4 B27

A e c o n d t y p e o f p r o d u c t c o d e f o r QPSK s y m b o l s W h i c hi s t r a n s p a r e n t t o p h a s e r o t a t i o n s W i l l noW be d e s c r i b e d W i t hr e f e r e n c e t o FIG. 4 .

As W i t h t h e ? r s t e m b o d i m e n t , a s i m p l e e x a m p l e r e p r es e n t e d i n T a b l e I I beloW i s e x p l a i n e d ? r s t . 5

TABLE II 1 1 Q 1 2 I 1 3 Q 1 4

1 0Q 2 1 I 2 2 Q 2 3 I 2 4I 3 1 Q 3 2 I 3 3 Q 3 4Q 4 1 I 4 2 Q 4 3 I 4 4

T h i s e x a m p l e s t a r t s W i t h t W o QPSK s y m b o l s ( I n , Q 1 2 )and ( Q 2 1 , I 2 2 ) Which a r e p l a c e d i n tWo s e p a r a t e r o W s , o n e i nt h e n a t u r a l o r d e r and h e o t h e r i n t h e r e v e r s e o r d e r , a s shoWn;i n o t h e r Words Q 2 1 i s i n t h e same column a s In and 2 2 i s i nt h e same column a s Q 1 2 .

The I b i t s i n t h e ? r s t and second roWs a r e then coded a si f t h e y Were i n t h e same r o W . They t h e r e f o r e s u p p l y t h e b i t sI 1 3 and I 2 4 Which a r e placed on t h e ? r s t and second r o W s , a tt h e 3 r d p o s i t i o n i . e . i n t h e 3 r d c o l u m n ) o n roW ( b i t I 1 3 ) a n di n t h e 4 p o s i t i o n ( 4 t h c o l u m n ) o n r o W 2 ( b i t I 2 4 ) .

S i m i l a r l y , t h e b i t s Q12 and Q 2 1 a r e coded a s i f t h e y Wereon t h e same roW and s u p p l y t h e b i t s Q14 and Q23 Which a r ea l s o p l a c e d on r o W s 1 a n d 2 , r e s p e c t i v e l y i n t h e 4 p o s i t i o n( f o r Q 1 4 ) a n d t h e 3 r d p o s i t i o n ( f o r Q 2 3 ) .

I t can t h u s be s e e n t h a t t h e b i t s I 1 3 and Q14 a r e i n roW 1W i t h t h e same s u c c e s s i o n IQ as t h e b i t s In a n d Q 1 2 a n d ,s i m i l a r l y , t h e b i t s Q23 and I 2 4 a r e on roW 2 With t h e sames u c c e s s i o n Q I a s t h e b i t s Q 2 1 a n d I 2 2 .

The columns a r e coded i n t h e same W a y , i . e . c o n s i d e r i n gt h e b i t s I n a n d I 2 2 f o r m i n g p a r t o f t h e ? r s t a n d s e c o n dc o l u m n s t h a t a r e c o d e d t o g e t h e r . They s u p p l y t h e b i t s I 3 andI 4 2 r e s p e c t i v e l y p l a c e d i n t h e ? r s t a n d s e c o n d c o l u m n s .S i m i l a r l y , t h e b i t s Q 1 2 a n d Q 2 1 o f t h e s e c o n d a n d ? r s tc o l u m n s s u p p l y t h e b i t s Q 3 2 a n d Q 4 1 r e s p e c t i v e l y p l a c e d i nt h e s e c o n d and ? r s t c o l u m n s .

F i n a l l y , t h e b i t s I 3 3 a n d I 4 4 r e s u l t f r o m t h e c o l u m n c o d i n go f t h e i t s I 1 3 a n d 2 4 a n d t h e i t s Q 3 4 a n d Q 4 3 r e s u l t f r o m t h ec o l u m n c o d i n g o f t h e Q i t s l 4 a n d Q 2 3 .

I n a d i f f e r e n t e m b o d i m e n t , t h e b i t s I 3 1 a n d I 4 2 o f t h e 3 r da n d 4 r o w s s u p p l y t h e c o d e b i t s I 3 3 a n d I 4 4 r e s p e c t i v e l yp l a c e d i n t h e 3 r d a n d 4 r o w s a n d t h e b i t s Q 3 2 o f t h e 3 r d roWa n d Q 4 1 o f t h e 4 t h roW s u p p l y t h e c o d e b i t s Q 3 4 a n d Q 4 3r e s p e c t i v e l y p l a c e d on t h e 3 r d a n d 4 r o w s .

20

25

5

More g e n e r a l l y , a s shoWn i n F I G . 4 , t h e s t a r t i n g p o i n t i sa m a t r i x o f QPSK y m b o l s W i t h K L , r o W s a n d KC c o l u m n s .A e r i e s o f s y m b o l s IQ s p l a c e d on t h e odd-numbered roWs1 , 3 , 5 , e t c . a n d a n i n v e r t e d s e r i e s o f s y m b o l s I Q , i . e . a s e r i e si n Which t h e ? r s t b i t becomes t h e s e c o n d , a n d v i c e - v e r s a , i sp l a c e d on t h e even-numbered roWs 2 , 4 , 6 , e t c . T h e r e i st h e r e f o r e a QI s u c c e s s i o n i n each even-numbered r o W . 5 5

NL-KL roWs o f c o d e b i t s and NC-KC columns o f c o d e b i t sa r e added t o t h e above m a t r i x W i t h KL roWs and KC olumnsto form a m a t r i x W i t h NL roWs and NC o l u m n s .

The code b i t s i n t h e supplementary roWs and columns a r ecomputed i n t h e same manner a s described With r e f e r e n c e t oT a b l e I I , i n o t h e r Words c o n s i d e r i n g ? r s t r o W s 1 a n d 2 a n d ,i n t h o s e roWs 1 and 2 , a l l t h e I b i t s Which a r e a s s i g n e dNC-KC code b i t s t h a t a r e a r r a n g e d i n t h e same manner a s i nt h e s t a r t i n g m a t r i x , i . e . f o r t h e ( K C + 1 ) t h p o s i t i o n t h e ? r s t I b i ti s p l a c e d i n t h e ? r s t r o W , f o r t h e ( K c + 2 ) t h p o s i t i o n t h e s e c o n dI b i t i s placed i n t h e second r o W , and s o o n . The samep r o c e d u r e i s a p p l i e d t o t h e Q i t s , i . e . t h e Q i t s o f r o W s 1

6 5

8a n d 2 a r e a s s i g n e d NC-KC c o d e Q i t s , W i t h t h e ? r s t p l a c e di n t h e s e c o n d r o W , t h e s e c o n d i n t h e ? r s t r o W , t h e t h i r d i n t h esecond roW, and so o n .RoWs and 4, roWs 5 and 6 , and s o on a r e t r e a t e d i n t h e

same manner.A a t r i x W i t h NL roWs and NC columns i s t h e n formed

from t h e m a t r i x W i t h KL roWs and NC olumns o b t a i n e d i nt h i s W a y , l i k e W i s e b y c o d i n g t h e c o l u m n s t W o b y t W o , i . e .columns 1 and 2 a r e coded t o g e t h e r , columns 3 and 4 a r ecoded t o g e t h e r , and s o o n . To be more p r e c i s e , i n e a c h p a i ro f c o l u m n s , a l l t h e I b i t s a r e c o n s i d e r e d and a r e a s s i g n e dNL-KL c o d e b i t s t h a t a r e p l a c e d l i k e t h e I b i t s i n t h e samenumbered c o l u m n s . T h u s , i n t h e c a s e o f columns 1 and , t h e? r s t c o d e I b i t i s p l a c e d i n t h e ? r s t column a t t h e ( K L + 1 ) t hp o s i t i o n , t h e s e c o n d c o d e b i t i s p l a c e d i n t h e s e c o n d columna t t h e ( K L + 2 ) t h p o s i t i o n , t h e t h i r d c o d e I b i t i s p l a c e d i n t h e? r s t column t t h e ( K L + 3 ) p o s i t i o n , and s o o n . S i m i l a r l y , i nt h e ? r s t tWo c o l u m n s , a l l t h e Q i t s a r e c o n s i d e r e d , fromW h i c h NL-KL c o d e Q i t s a r e f o r m e d , a n d t h e NL-KL c o d e Qb i t s a r e p l a c e d i n t h e ? r s t and second columns i n t h e samemanner a s t h e s t a r t i n g Q i t s , i . e . t h e ? r s t c o d e Q i t i sp l a c e d i n t h e s e c o n d c o l u m n a t t h e ( K L + 1 ) h p o s i t i o n , t h es e c o n d c o d e Q i t i s p l a c e d i n t h e ? r s t column a t t h e( K L + 2 ) h p o s i t i o n , t h e t h i r d c o d e Q i t i s p l a c e d i n t h e s e c o n dcolumn a t t h e ( K 3 + 3 ) t h p o s i t i o n , and s o o n .

As i n t h e e m b o d i m e n t o f t h e p r o d u c t c o d e ( t u r b o c o d e )d e s c r i b e d W i t h r e f e r e n c e t o F I G . 3 , t h e p r o d u c t c o d e shoWni n F I G . 4 i s t r a n s p a r e n t to r o t a t i o n s o f a t , 3 1 / 2 and 3 7 5 / 2r a d i a n s . T h a t t r a n s p a r e n c y i s deduced from t h e a b o v e e q u at i o n s ( 1 ) , ( 2 ) , ( 3 ) , ( 4 ) , ( 5 ) a n d ( 6 ) .A r o d u c t c o d e f o r QAM-1 6 m o d u l a t i o n t h a t i s a l s ot r a n s p a r e n t t o p h a s e r o t a t i o n s W i l l noW be d e s c r i b e d W i t hr e f e r e n c e t o FIGS. 5 and 6 .

QAM-16 m o d u l a t i o n r e p r e s e n t s t h e s i x t e e n 4 - d i g i t b i n a r yn u m b e r s by a m p l i t u d e a n d p h a s e m o d u l a t i o n o f a c a r r i e r .As shoWn i n F I G . 5 , t h e c o n s t e l l a t i o n o f s i x t e e n b i n a r yn u m b e r s i s r e p r e s e n t e d b y s i x t e e n p o i n t s i n t h e c o m p l e x

p l a n e . Each p o i n t h a s an a b s c i s s a of 1 0 . 5 o r 1 1 . 5 and ano r d i n a t e o f 1 0 . 5 o r 1 1 . 5 . Thus e a c h q u a d r a n t o f t h e complexp l a n e i n c l u d e s f o u r p o i n t s . The i n v e n t i o n c o n s i s t s o f c h o o si n g t h e v a l u e s a s s i g n e d t o e a c h p o i n t i n t h e c o m p l e x p l a n es o t h a t t h e s i x t e e n p o i n t s a r e d i v i d e d i n t o f o u r s u b s e t s eacho f f o u r p o i n t s , e a c h s u b s e t h a v i n g o n e p o i n t i n e a c h q u a dr a n t . A l s o , t h e s u b s e t s a r e such t h a t a r o t a t i o n of 1 3 / 2 r a d i a n sa b o u t t h e o r i g i n c a u s e s one s u b s e t t o t a k e t h e p l a c e ofa n o t h e r s u b s e t .

Thus a ? r s t s u b s e t , Whose p o i n t s a r e r e p r e s e n t e d by at r i a n g l e i n F I G . 5 , i s f o r m e d b y t h e p o i n t s W i t h t h e c o o r d in a t e s ( + 1 . 5 ; + 1 . 5 ) , ( 0 . 5 ; + 1 . 5 ) ; ( 0 . 5 ; 0 . 5 ) a n d ( + 1 . 5 ; 0 . 5 ) . A e c o n d s u b s e t , Whose p o i n t s a r e r e p r e s e n t e d b y as q u a r e i n F I G . 5 , i s f o r m e d by t h e p o i n t s W i t h t h e c o o r d in a t e s ( + 0 . 5 ; + 1 . 5 ) , ( 1 . 5 ; + 1 . 5 ) ; ( 1 . 5 ; 0 . 5 ) a n d ( + 0 . 5 ; 0 . 5 ) . A h i r d s u b s e t , Whose p o i n t s a r e r e p r e s e n t e d b y ac i r c l e i n F I G . 5 , i s f o r m e d by t h e p o i n t s W i t h t h e c o o r d i n a t e s( + 0 . 5 ; + 0 . 5 ) , ( 1 . 5 ; + 0 . 5 ) ; ( 1 . 5 ; 1 . 5 ) a n d ( + 0 . 5 ; 1 . 5 ) .F i n a l l y , t h e f o u r t h s u b s e t , Whose p o i n t s a r e r e p r e s e n t e d b y as t a r i n F I G . 5 , i s f o r m e d by t h e p o i n t s W i t h t h e c o o r d i n a t e s( + 1 . 5 ; + 0 . 5 ) , ( 0 . 5 ; + 0 . 5 ) ; ( 0 . 5 ; 1 . 5 ) a n d ( + 1 . 5 ; 1 . 5 ) .

Thus t h e f o u r p o i n t s of each s u b s e t form a s q u a r e and aconsequence of a r o t a t i o n of 3 1 / 2 r a d i a n s i s t h a t t h e ? r s ts u b s e t t a k e s u p t h e p o s i t i o n o f t h e s e c o n d s u b s e t , t h e s e c o n ds u b s e t t a k e s u p t h e p o s i t i o n o f t h e t h i r d s u b s e t , t h e t h i r ds u b s e t t a k e s u p t h e p o s i t i o n o f t h e f o u r t h s u b s e t , a n d t h ef o u r t h s u b s e t t a k e s up t h e p o s i t i o n o f t h e ? r s t s u b s e t .

A l s o , t h e numbers i n each s u b s e t a r e chosen s o t h a t t h e? r s t tWo b i t s ( t h e more s i g n i ? c a n t b i t s ) a r e t h e same and t h e


9/10

US 7 , 0 2 7 , 5 2 4 B29

l a s t t W o b i t s ( t h e l e s s s i g n i ? c a n t b i t s ) f o r m d i f f e r e n t numb e r s , f o r e x a m p l e n u m b e r s i n a Gray s u c c e s s i o n .Thus t h e ? r s t s u b s e t ( W h o s e p o i n t s a r e marked by a

t r i a n g l e ) h a s t h e same ? r s t tWo d i g i t s 0 0 , a n d t h e s u c c e s s i o no f t h e l a s t tWo d i g i t s , s t a r t i n g f r o m t h e same q u a d r a n t andm o v i n g i n t h e p o s i t i v e d i r e c t i o n , i s 0 0 , 0 1 , l l , 1 0 . F o r t h es e c o n d s u b s e t , Whose p o i n t s a r e marked b y a r e c t a n g l e , t h e? r s t tWo d i g i t s a r e 0 1 ; f o r t h e t h i r d s u b s e t , Whose p o i n t s a r emarked by a c i r c l e , t h e ? r s t tWo d i g i t s a r e 1 1 ; f o r t h e f o u r t hs u b s e t , Whose p o i n t s a r e marked by a s t a r , t h e ? r s t tWo i g i t sare 1 0 .

Note a l s o t h a t t h e l a s t tWo d i g i t s i n e a c h q u a d r a n t a r e t h es a m e . T h u s t h e ? r s t q u a d r a n t i n c l u d e s s y m b o l s b e l o n g i n g t ot h e s e c o n d , t h i r d and f o u r t h s u b s e t s Whose a s t tWo d i g i t s a r e0 0 . I n t h e s e c o n d q u a d r a n t t h e l a s t tWo d i g i t s a r e 0 1 ; i n t h et h i r d q u a d r a n t t h e l a s t tWo d i g i t s a r e 1 1 ; i n t h e f o u r t hq u a d r a n t t h e l a s t tWo d i g i t s a r e 1 0 .A c o n s e q u e n c e o f t h i s a r r a n g e m e n t i n f o u r s u b s e t s

W h e r e b y , a f t e r a r o t a t i o n o f : K r c / 2 r a d i a n s ( W h e r e K s ani n t e g e r ) , o n e s u b s e t o c c u p i e s t h e p o s i t i o n o f a n o t h e r s u b s e t ,i s t h a t QAM-l 6 d a t a W i l l b e a l s o b e t r a n s p a r e n t t o p h a s er o t a t i o n s i f t h e Words t o be t r a n s m i t t e d a r e assigned an e r r o rc o r r e c t i n g c o d e t h a t i s t r a n s p a r e n t t o p h a s e r o t a t i o n s , s u c h a st h e p r o d u c t c o d e d e s c r i b e d a b o v e f o r QPSK m o d u l a t i o n .

Thus t h e d e s i r e d e s u l t , i . e . a t u r b o c o d e t h a t i s t r a n s p a r e n tt o p h a s e r o t a t i o n s , W i l l b e o b t a i n e d i f e a c h 4 - d i g i t b i n a r ynumber s d i v i d e d i n t o t W o 2 - d i g i t b i n a r y numbers a n d e a c ho f t h o s e 2 d i g i t b i n a r y n u m b e r s i s a s s i g n e d a t u r b o c o d et r a n s p a r e n t to p h a s e r o t a t i o n s , a s i f e a c h o f t h e tWo numbersWere t o b e t r a n s m i t t e d u s i n g QPSK o d u l a t i o n .

A s an a l t e r n a t i v e t o t h e a b o v e , a c o n v e n t i o n a l BPSK u r b oc o d e t r a n s p a r e n t t o p h a s e r o t a t i o n s c a n b e u s e d , i n Whiche r r o r c o r r e c t i n g c o d i n g i s p e r f o r m e d i n d i v i d u a l l y f o r e a c hb i t .

T h u s , W i t h t h e c o m b i n a t io n o f a n e r r o r c o r r e c t i n g codea s s i g n e d to e a c h b i t o r t o e a c h p a i r o f b i t s Which i st r a n s p a r e n t t o p h a s e r o t a t i o n s , a n d t h e a r r a n g e m e n td e s c r i b e d a b o v e o f 4 - d i g i t b i n a r y n u m b e r s i n t h e c o m p l e xp l a n e , t h e r e s u l t i n g QAM-l 6 t r a n s m i s s i o n i s t r a n s p a r e n t t op h a s e r o t a t i o n s , e s p e c i a l l y i f a t u r b o c o d e e r r o r c o r r e c t i n gc o d e i s u s e d .

F I G . 6 shoWs a t r a n s m i s s i o n s y s t e m a c c o r d i n g t o t h ei n v e n t i o n .

The t r a n s m i s s i o n s y s t e m i n c l u d e s tWo 2 - d i m e n s i o n a l d i ff e r e n t i a l c o d e r s 50 and 5 2 . Each o f t h e s e d i f f e r e n t i a l c o d e r si s ofthe same t y p e a s t h e coder 12 shoWn i n F I G . 1 . The ? r s ttWo i t s o f e a c h 4 - d i g i t b i n a r y number a r e a p p l i e d t o t h e tWoi n p u t s 5 0 1 a n d 5 0 2 o f t h e d i f f e r e n t i a l c o d e r 5 0 a n d t h e l a s ttWo b i t s o f t h e same 4 - d i g i t number a r e a p p l i e d to t h e tWoi n p u t s 5 2 1 , 5 2 2 o f t h e d i f f e r e n t i a l c o d e r 5 2 . E a c h d i f f e r e n t i a lc o d e r c a l c u l a t e s t h e d i f f e r e n c e betWeen tWo s u c c e s s i v e2 - d i g i t n u m b e r s .

The t W o b i n a r y d i g i t s d e l i v e r e d b y e a c h o f t h e d i f f e r e n t i a lc o d e r s 5 0 , 52 a r e t u r b o coded i n a manner t h a t i s t r a n s p a r e n tt o p h a s e r o t a t i o n s b y r e s p e c t i v e c o d e r s 5 4 a n d 5 6 . Thec o d i n g e f f e c t e d by t h e c o d e r s 5 4 a n d 5 6 i s e i t h e r o f t h eBPSK y p e , m e a n i n g t h a t t h e c o d i n g i s e f f e c t e d i n d i v i d u a l l yon each i t , o r of h e QPSK y p e , a s d e s c r i b e d W i t h r e f e r e n c et o FIG. 3 o r FIG. 4, i n Which t h e tWo b i t s a r e c o n s i d e r e dc o l l e c t i v e l y .

The tWo o u t p u t b i t s of each of t h e c o d e r s 54 and 56 a r et h e n a p p l i e d t o r e s p e c t i v e i n p u t s 5 8 1 , 5 8 2 a n d 5 8 3 , 5 8 4 o f aQAM - l6 m o d u l a t o r 5 8 W h i c h a r r a n g e s t h e 4 - d i g i t b i n a r yn u m b e r s a p p l i e d t o t h e s e i n p u t s i n t h i s Way i n t h e c o m p l e xp l a n e i n t h e manner shoWn i n F I G . 5 .

The m o d u l a t e d s i g n a l s s u p p l i e d by t h e m o d u l a t o r 5 8 a r et r a n s m i t t e d v i a a c h a n n e l 60 and r e c e i v e d by a demodulator

20

25

30

35

40

45

50

55

60

6 5

1 06 2 e f f e c t i n g a n o p e r a t i o n t h a t i s t h e i n v e r s e o f t h a t e f f e c t e db y t h e m o d u l a t o r 5 8 , i . e . d e t e r m i n i n g t h e s y m b o l s ( 4 - d i g i tb i n a r y n u m b e r s) f r o m t h e p h a s e s a n d t h e a m p l i t u d e s o f t h er e c e i v e d s i g n a l s . I n t h i s e x a m p l e , t h e d e m o d u l a t o r 6 2 h a st W o o u t p u t s 6 2 1 , 6 2 2 Which d e l i v e r d i g i t a l s i g n a l s , o n t h e o n eh a n d , t o a ? r s t t u r b o d e c o d e r 6 4 a n d , on t h e o t h e r h a n d , t oa second t u r b o decoder 66 v i a a t i m e - d e l a y u n i t 6 8 . Theo u t p u t s i g n a l s of h e ? r s t decoder 6 4 a r e t r a n s m i t t e d t o a ? r s t2 - d i m e n s i o n a l d i f f e r e n t i a l decoder 70 v i a a second timed e l a y u n i t 7 2 a n d , i n t h i s e x a m p l e , t h e s e c o n d d e c o d e r 6 6t r a n s m i t s i t s o u t p u t s i g n a l s d i r e c t l y t o a s e c o n d 2 - d i m e ns i o n a l d i f f e r e n t i a l d e c o d e r 7 4 .

The t i m e - d e l a y u n i t s 6 8 and 72 and a c o n n e c t i o n 7 6betWeen t h e tWo d e c o d e r s 6 4 and 66 a r e used t o s y n c h r o n i Z et h e o u t p u t s i g n a l s o f t h e d i f f e r e n t i a l d e c o d e r s 7 0 a n d 7 4 .

N o t e t h a t t h e a r r a n g em e n t o f t h e 4 - d i g i t b i n a r y n u m b e r si n QAM - l6 m o d u l a t i o n i n t h e c o m p l e x p l a n e shoWn n F I G .5 g e n e r a l l y e n s u r e s t r a n s p a r e n c y t o p h a s e r o t a t i o n s o f K J ' E / 2( W h e r e K s a n i n t e g e r ) , p r o v i d e d t h a t t h e e r r o r c o r r e c t i n gc o d e s added a r e a l s o t r a n s p a r e n t t o p h a s e r o t a t i o n s . Thesee r r o r c o r r e c t i n g c o d e s can be e i t h e r b l o c k c o d e s , i . e . c o d e so p e r a t i n g roW by r o W , o r t u r b o ( p r o d u c t) c o d e s .

What i s c l a i m e d i s :1 . A e t h o d o f t r a n s m i t t i n g QPSK i g i t a l s i g n a l s i n W h i c h

e a c h 2 - d i g i t b i n a r y n u m b e r , r e f e r r e d to a s a s y m b o l , i sa s s i g n e d a p h a s e o f a c a r r i e r , e a c h o f t h e f o u r 2 - d i g i t b i n a r yn u m b e r s c o r r e s p o n d s t o a q u a d r a n t o f t h e c o m p l e x p l a n e ,a n d s u p p l e m e n t a r y b i n a r y d i g i t s g e n e r a t e d i n a c c o r d a n c eWith an e r r o r c o r r e c t i n g product code a r e added t o a s e t ofb i n a r y d i g i t s t o e n a b l e e r r o r c o r r e c t i o n a t t h e r e c e i v e r , s a i dm e t h o d c o m p r i s i n g t h e s t e p s o f :

p l a c i n g I a n d Q i t s o f a 2 - d i g i t s y m b o l t o b e t r a n s m i t t e di n d i f f e r e n t roWs b u t i n t h e same column, s o t h a t eachroW c o n t a i n s o n l y one t y p e o f b i t , I o r Q ;

e f f e c t i n g t h e e r r o r c o r r e c t i o n c o d i n g roW by roW and t h e nb y p a i r s o f a d j a c e n t c o l u m n s ;d e d u c i n g t h e c o d e I b i t s o f t W o a s s o c i a t e d a d j a c e n tcolumns from t h e I b i t s o f s a i d tWo c o l u m n s ;

d e d u c i n g t h e c o d e Q i t s o f s a i d t W o a s s o c i a t e d a d j a c e n tc o l u m n s f r o m t h e Q i t s o f s a i d c o l u m n s ;

d i s p o s i n g s a i d coded i t s s o t h a t e a c h roW c o n t a i n s o n l yone t y p e o f b i t , I o r Q ; and

t r a n s m i t t i n g t h e p a i r s a d j a c e n t c o d e I a n d Q i t s i n t h esame column a l o n g W i t h t h e 2 d i g i t s y m b o l s t o b et r a n s m i t t e d .

2 . A ethod a c c o r d i n g t o c l a i m 1 , W h e r e i n t h e s y m b o l sform a n a t u r a l s u c c e s s i o n o r a Gray s u c c e s s i o n i n a complexp l a n e .

3 . A ethod a c c o r d i n g t o c l a i m 1 , W h e r e i n t h e s y m b o l su n d e r g o d i f f e r e n t i a l c o d i n g b e f o r e e r r o r c o r r e c t i o n c o d i n g i no r d e r t o t r a n s m i t t h e d i f f e r e n c e betWeen tWo s u c c e s s i v es y m b o l s .

4 . A ethod a c c o r d i n g t o c l a i m 1 a p p l i e d t o t r a n s m i t t i n gQAM-l6 i g i t a l s i g n a l s , W h i c h m e t h o d c o m p r i s e s r e p r e s e n ti n g a 4 - d i g i t b i n a r y number o r s y m b o l b y t h e p h a s e a n d t h ea m p l i t u d e o f a c a r r i e r and e f f e c t i n g e r r o r c o r r e c t i o n c o d i n gon t h e ? r s t t W o b i n a r y d i g i t s a n d t h e l a s t t W o b i n a r y d i g i t s .

5 . A ethod a c c o r d i n g t o c l a i m 4 , W h e r e i n , f o r t r a n s m i ss i o n , t h e s i x t e e n 4 - d i g i t b i n a r y n u m b e r s o r s y m b o l s a r ea r r a n g e d i n a c o m p l e x p l a n e s o t h a t e a c h q u a d r a n t c o n t a i n sf o u r s y m b o l s h a v i n g t W o ? r s t d i g i t s r e p r e s e n t i n g d i f f e r e n tnumbers and t h e same a s t tWo d i g i t s , s a i d s i x t e e n s y m b o l sa r e a r r a n g e d i n f o u r s u b s e t s i n t h e f o u r q u a d r a n t s o f t h ec o m p l e x p l a n e a n d o v e r t h e W h o l e o f t h e c o m p l e x p l a n e ,


10/10

US 7 , 0 2 7 , 5 2 4 B21 1

e a c h s u b s e t i s formed by t h e s e t o f numbers h a v i n g t h e same? r s t t W o b i n a r y d i g i t s , a n d t h e c o o r d i n a t e s o f t h e s y m b o l s i nt h e complex p l a n e a r e chosen s o t h a t a f t e r a r o t a t i o n of: K r c / 2 ( W h e r e K s a n i n t e g e r ) , e a c h s u b s e t t a k e s t h e p l a c eo f a n o t h e r s u b s e t .

6 . Amethod f r e c e i v i n g QPSK i g i t a l s i g n a l s t r a n s m i t t e db y t h e t r a n s m i s s i o n method a c c o r d i n g t o c l a i m 1 , W h i c hmethod i n c l u d e s d e c o d i n g t h a t i s t h e i n v e r s e o f t h e e r r o rc o r r e c t i o n c o d i n g e ? e c t e d a t t h e t r a n s m i t t e r .7 . A e t h o d o f t r a n s m i t t i n g QPSK i g i t a l s i g n a l s i n W h i c he a c h 2 - d i g i t b i n a r y n u m b e r , r e f e r r e d t o a s a s y m b o l , i sa s s i g n e d a p h a s e o f a c a r r i e r , e a c h o f t h e f o u r 2 - d i g i t b i n a r yn u m b e r s c o r r e s p o n d s t o a q u a d r a n t o f t h e c o m p l e x p l a n e ,a n d s u p p l e m e n t a r y b i n a r y d i g i t s a r e added o a s e t o f b i n a r yd i g i t s t o e n a b l e e r r o r c o r r e c t i o n a t t h e r e c e i v e r , Wherein t h ee r r o r c o r r e c t i o n code i s a p r o d u c t c o d e , t h e method comp r i s i n g t h e s t e p s o f :

p l a c i n g t h e I b i t s and Q of a symbol i n t h e same r o W , s ot h a t e a c h o f t h e roWs i s f o r m e d o f p a i r s o f a n d Q i t s ;

d i s p o s i n g t h e roWs and t h e columns s o t h a t , i n e a c hc o l u m n , t h e I a n d Q i t s a l t e r n a t e ;

c o d i n g t h e r o W s a n d t h e c o l u m n s by a d j a c e n t p a i r s s o t h a tt h e code I b i t s a r e d e r i v e d from t h e I b i t s of tWoa s s o c i a t e d a d j a c e n t r o W s ( c o l u m n s ) ;

d e r i v i n g t h e c o d e Q b i t s o f s a i d tWo a d j a c e n t roWs( c o l u m n s ) o n l y from t h e Q i t s o f s a i d tWo roWs( c o l u m n s ) ;d i s p o s i n g t h e code i t s s o t h a t e a c h roW c o n t a i n s p a i r s o fI a n d Q i t s ; a n d

t r a n s m i t t i n g t h e p a i r s o f c o d e I a n d Q i t s i n e a c h roWa l o n g W i t h t h e 2 - d i g i t s y m b o l s t o b e t r a n s m i t t e d .

20

25

30

1 28 . A ethod a c c o r d i n g t o c l a i m 7 , W h e r e i n t h e s y m b o l s

form a n a t u r a l s u c c e s s i o n o r a Gray s u c c e s s i o n i n a complexp l a n e .9 . A ethod a c c o r d i n g t o c l a i m 7 , W h e r e i n t h e s y m b o l s

u n d e r g o d i ? c e r e n t i a l c o d i n g b e f o r e e r r o r c o r r e c t i o n c o d i n g i no r d e r t o t r a n s m i t t h e d i ? e r e n c e betWeen tWo s u c c e s s i v es y m b o l s .1 0 . A ethod a c c o r d i n g t o c l a i m 7 a p p l i e d t o t r a n s m i t t i n gQAM-l6 i g i t a l s i g n a l s , W h i c h m e t h o d c o m p r i s e s r e p r e s e n ti n g a 4 - d i g i t b i n a r y number o r s y m b o l b y t h e p h a s e a n d t h ea m p l i t u d e o f a c a r r i e r and e ? c e c t i n g e r r o r c o r r e c t i o n c o d i n gon t h e ? r s t t W o b i n a r y d i g i t s a n d t h e l a s t t W o b i n a r y d i g i t s .

1 1 . A ethod a c c o r d i n g t o c l a i m 1 0 , W h e r e i n , f o r t r a n sm i s s i o n , t h e s i x t e e n 4 - d i g i t b i n a r y n u m b e r s o r s y m b o l s a r ea r r a n g e d i n a c o m p l e x p l a n e s o t h a t e a c h q u a d r a n t c o n t a i n sf o u r s y m b o l s h a v i n g t W o ? r s t d i g i t s r e p r e s e n t i n g d i ? c e r e n tnumbers and t h e same a s t tWo d i g i t s , s a i d s i x t e e n s y m b o l sa r e a r r a n g e d i n f o u r s u b s e t s i n t h e f o u r q u a d r a n t s o f t h ec o m p l e x p l a n e a n d o v e r t h e W h o l e o f t h e c o m p l e x p l a n e ,e a c h s u b s e t i s formed by t h e s e t o f numbers h a v i n g t h e same? r s t t W o b i n a r y d i g i t s , a n d t h e c o o r d i n a t e s o f t h e s y m b o l s i nt h e complex p l a n e a r e chosen s o t h a t a f t e r a r o t a t i o n of: K r c / 2 ( W h e r e K s a n i n t e g e r ) , e a c h s u b s e t t a k e s t h e p l a c eo f a n o t h e r s u b s e t .

1 2 . A e t h o d o f r e c e i v i n g QPSK i g i t a l s i g n a l s t r a n s m i tt e d b y t h e t r a n s m i s s i o n method a c c o r d i n g t o c l a i m 7 , W h i c hmethod i n c l u d e s d e c o d i n g t h a t i s t h e i n v e r s e o f t h e e r r o rc o r r e c t i o n c o d i n g e ? c e c t e d a t t h e t r a n s m i t t e r .

ber correction in qpsk

Documents