submission may, 2000 doc: ieee802.11-00 / 086 steven gray, nokia slide brief overview of information...
TRANSCRIPT
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
Brief Overview of Information Theory Brief Overview of Information Theory and Channel Coding and Channel Coding
Steven D. Gray
1
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
OutlineOutline
• Information theory
– Gaussian channel
– Rayleigh fading channels
• Two approaches for achieving the same rate
• Convolutional encoding
• Convolutional decoding
• Hardware implementation of a Viterbi
• Conclusions
2
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
Brief Introduction to Information Brief Introduction to Information Theory Theory
);(max)(
YXICxp
Encoder Channel)|( xyp
Decoder
MessageEstimate of Message
W nX nY W
nX Is a codeword from an alphbet of size n (ex. A point in an 8 PSK consellation)
Channel capacity is the highest rate in bits per channel use at which information can be sent with arbitrary low probability of error.
3
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
A Little Information TheoryA Little Information TheoryCapacity for the Gaussian ChannelCapacity for the Gaussian Channel
YXI
PXxp
C ;
E:
max2
X Y
Z
For a Gaussian Channel with Bandwidth, W
W
SNRWC 1log
0N
PSNR :
bits per second
4
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
A Little Information TheoryA Little Information TheoryCapacity for the Flat Rayleigh ChannelCapacity for the Flat Rayleigh Channel
PEeeWC i
1log
1
2
Average Capacity
where
1 !
)()ln()(
k
k
i kk
xxExE
P is the average power and E is Euler's constant
Source: W.C.Y. Lee, "Estimate of Channel Capacity in Rayleigh Fading Environment," IEEE Transactions on Vehicular Technology, Vol. 39, No 3, August 1990.
5
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
A Little Information TheoryA Little Information TheoryCapacity Region Comparison Capacity Region Comparison
5 6 7 8 9 10 11 12 13 14 150
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
bits
/sec
/Hz
SNR or Average Power (dB)
Shannon - Gaussian Channel Shannon - Flat Rayleigh Fading
• For channels of interest (heuristically speaking)- Gaussian capacity is an upper bound- Flat Rayleigh capacity is a lower bound
6
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
A Little Information TheoryA Little Information Theory Gaussian Channel Capacity Gaussian Channel Capacity
Shannon Capacity vs. Existing 2.4 GHz Wireless LAN at 10-6 BER
0 1 2 3 4 5 6 7 8 9 100
0.5
1
1.5
2
2.5
3
3.5
4bi
ts/s
ec/H
z
SNR (dB)
ShannonBarker CCK PBCC
7
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
A Little Information Theory A Little Information Theory Conclusions Conclusions
• Shannon tell us that there is room for exploitation
• Approaches should be pursued to exploit cases when the SNR is good
– With a good code, 20 Mbps is possible in the Gaussian channel when the SNR is 10 dB or less
– Good codes are available with reasonable complexity
8
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
Two Approaches for Achieving Two Approaches for Achieving Same Rate Same Rate
• Approach 1
– Uncoded BPSK modulation + IEEE802.11a without convolutional coding+ Perfect synchronization and channel estimation
+ Rate = 12 Mbps
– Additive White Gaussian Noise (AWGN)
• Approach 2
– Coded QPSK modulation + IEEE802.11a PHY with convolutional coding
+ Rate 1/2, 64 state convolutional code
+ Perfect synchronization and channel estimation
+ Rate = 12 Mbps
– AWGN
9
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
Two Approaches for Achieving Two Approaches for Achieving Same RateSame Rate
-4 -2 0 2 4 6 810
-7
10-6
10-5
10-4
10-3
10-2
10-1
100
SNR
BE
RBit Error Rate, IEEE802.11a 12 Mbits in AWGN, uncoded BPSK and Rate 1/2 QPSK
Uncoded BPSK Rate 1/2 QPSK
10
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
Two Approaches for Achieving Two Approaches for Achieving Same RateSame Rate
-4 -2 0 2 4 6 810
-5
10-4
10-3
10-2
10-1
100
SNR
PE
R
64 byte Packet Error Rate, IEEE802.11a 12 Mbits in AWGN, uncoded BPSK and Rate 1/2 QPSK
Uncoded BPSK Rate 1/2 QPSK
Conclusion: Channel Coding can Improve Spectrum Efficiency
Bandwidth Reduction
11
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
Convolutional Encoding Convolutional Encoding
Data Source
+
+
1,0][ nb30][ psmw p
Storage Element
Generic Rate 1/2 Encoder
00
11
01
10
S0
S1
S2
S3
11 11 11
11
10
01
10
01 0001
00 00 00 00
11
0011 00
10 10
01 01 01
10
11
10
Trellis Diagram • R=1/2• 4 state• Start from all zero state
12
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
Convolutional DecodingConvolutional Decoding
• Optimal, bit error rate, decoding is achieved by maximizing the likelihood function for a given codeword
– Compare the received codeword to all possible codewords and pick output with smallest distance
• Viterbi in 1967 published a dynamic programming algorithm for decoding
• Complexity in decoding is proportional to the number of states and the number of branches into each state
– Example: 64 state code used in PBCC or IEEE802.11a+ 128 metric calculations per transition in the trellis
13
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
Hardware Implementation of ViterbiHardware Implementation of Viterbi
• 64 state code from PBCC and IEEE802.11a
• 32 Add Compare and Select (ACS) units (32 butterflies)
• Trace back length is 32 (should be 4 - 5 times constraint length)
• Input is <3,2,t> and path metrics are <10,9,t>Branch Metric
Computation
Add CompareSelect
Trace BackUnit
Set Initial State
StorePath
Metric
Branch History
Bit StreamSoft Inputs
14
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
Hardware Implementation of ViterbiHardware Implementation of Viterbi
• Register Transfer Logic (RTL) synthesis for Viterbi VHDL is done using Synopsys Design Compiler
• Target for RTL is Xilinx Virtex 1000e Field Programmable Gate Array (FPGA)
• Design complexity
– 55.7K logic gates
– 8Kbytes of Xilinx RAM (4 RAM blocks) for convience
– Actual required RAM is 500 bytes
15
Submission
May, 2000 Doc: IEEE802.11-00/086
Steven Gray, NokiaSlide
ConclusionsConclusions
• Channel coding is a means to improve spectrum efficiency over an uncoded system
• Particularly for achieving rates above 20 Mbps, channel coding will make required SNR's reasonable
• Hardware complexity is absorbed in the digital ASIC
– Impact on IC costs are small
– Engineering design costs are always a factor for a more complex design
16