advances in error control strategies for 5g

Jörg Kliewer

Advances in Error Control Strategies for 5G

The Elisha Yegal Bar-Ness Center For Wireless Communications And Signal Processing Research

5G Requirements

2

[Nokia Networks: Looking ahead to 5G. White paper, April 2014]

Energy Bottleneck

3

Current computational cost of transmission: approx. 6 nJ/bit [Andrews et al. 2014]

Current battery capacity 6.9 Wh (iPhone 6)

Target 10 Gbit/s

Energy Bottleneck

3

Current computational cost of transmission: approx. 6 nJ/bit [Andrews et al. 2014]

Current battery capacity 6.9 Wh (iPhone 6)

Target 10 Gbit/s

Resulting battery life: 5 minutes and 27 seconds!

Coding for *G

4

Quantum leap from 2G to 3G with the adoption of modern iteratively decodable codes (turbo codes, LDPC codes)

3G to 4G basically the same techniques, new: adoption of hybrid ARQ

Coding for *G

4

Quantum leap from 2G to 3G with the adoption of modern iteratively decodable codes (turbo codes, LDPC codes)

3G to 4G basically the same techniques, new: adoption of hybrid ARQ

In order to satisfy the 5G requirements, we need a paradigm change in coding.

Coding Wish List for 5G

5

3G/4G coding is essentially capacity-approaching for point-to-point BI-AWGN


5


Gains in transmission power efficiency to be expected from

‣ Coding for spectrally efficiency communication

‣ Multi-terminal coding and decoding (i.e., for relaying, cooperation, MIMO)


5


Gains in transmission power efficiency to be expected from

‣ Coding for spectrally efficiency communication

‣ Multi-terminal coding and decoding (i.e., for relaying, cooperation, MIMO)

Gains in computational power efficiency equally important

One Code Fits All?

6

Not Really…

7

Not Really…

7

No single scheme which fixes all these issues, but few promising candidates:

Spatially coupled (convolutional) LDPC codes

Non-binary LDPC codes

Polar codes

LDPC Block Codes

8

Uncoded BPSK

Bit

erro

r pro

babi

lity

Shan

non

limit

(dB)

Irregular LDPC-BC

Regular LDPC-BC

Error floor

Waterfall

LDPC Block Codes

8

Uncoded BPSK

Bit

erro

r pro

babi

lity

Shan

non

limit

(dB)

Irregular LDPC-BC

Regular LDPC-BC

Error floor

Waterfall

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

(a) (b)

H =

Tanner graph (3,6) regular LDPC code:

Graph sparsely connected

Spatially Coupled LDPC Codes

9

Invented as convolutional LDPC codes [Jiménez-Feltström & Zigangirov 1999], theory [Kudekar, Richardson, Urbanke 2010]

Asymptotically universally capacity achieving for a wide range of channels and code rates


9



Same performance under belief propagation decoding as for the corresponding block LDPC ensembles under maximum likelihood decoding (threshold saturation)


9



Same performance under belief propagation decoding as for the corresponding block LDPC ensembles under maximum likelihood decoding (threshold saturation)

Decoding complexity and latency reduction by windowed decoding


10

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

H =

H =cc

(cut-and-paste)

(diagonal matrix extension)

(a)

(b)

(c)0 1 L−1L−2

Coupling construction via unwrapping:

Convolutional code structure


10

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

H =

H =cc

(cut-and-paste)


(a)

(b)

(c)0 1 L−1L−2


1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

H =

H =cc

(cut-and-paste)


(a)

(b)

(c)0 1 L−1L−2

Resulting Tanner graph:



10

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

H =

H =cc

(cut-and-paste)


(a)

(b)

(c)0 1 L−1L−2


1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

H =

H =cc

(cut-and-paste)


(a)

(b)

(c)0 1 L−1L−2

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

H =

H =cc

(cut-and-paste)


(a)

(b)

(c)0 1 L−1L−2

Resulting Tanner graph:

Terminated Tanner graph:


Spatially Coupled LDPC Codes: Performance

11

1 1.2 1.4 1.6 1.810

−5

10−4

10−3

10−2

10−1

Eb/N0 (dB)

Bit

errorrate

convolutional gain

(3,6)-regular LDPC-BCn = 4098

(3,6)-regular LDPC-CCνs = 4098

Spatially Coupled LDPC Codes: Performance

12

−1 0 1 2 3 4 50.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Eb/N0 (dB)

Rate

0 0.05 0.1 0.15 0.2 0.25 0.30.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

dmin/n

Term. (3,6)-reg.

Term. (4,8)-reg.

Term. (5,10)-reg.Term. ARJABlock (J, K )-reg.Block ARJA

L=3

L=3

L=3

L=2 L=2

L=4 L=4

L=5

L=5

L=6 L=6

L=7

(3,6)

(4,8)

(5,10) (5,10)(3,6)

(4,8)

Increasingterminationlength L

Increasingterminationlength L

L=4

L=5

L=5

L=5

L=8 L=8

L=7

Shannonlimit

Gilbert-Varshamovbound

[Costello, Dolecek, Fuja, Kliewer, Mitchell, Smarandache, 2014]

Spatially Coupled LDPC Codes: Efficient Decoding

13

. . .

. . .

. . .

. . .

Decodedsymbols

Receivedsymbols. . . . . .

s

Proc. 1Proc. 2Proc. I Proc. I

I(m )Mcs

r

rt0

v

v

− 1

+ 1

Mc

WMc

Mc

WMc

Decodedsymbols

. . .

. . .

. . .

. . .

. . .

. . .

t = 0 t = 1

(a)

(b)

t1

t0

t1

Pipeline decoding:

Spatially Coupled LDPC Codes: Efficient Decoding

13

. . .

. . .

. . .

. . .

Decodedsymbols


s


I(m )Mcs

r

rt0

v

v

− 1

+ 1

Mc

WMc

Mc

WMc

Decodedsymbols

. . .

. . .

. . .

. . .

. . .

. . .

t = 0 t = 1

(a)

(b)

t1

t0

t1

. . .

. . .

. . .

. . .

Decodedsymbols


s


I(m )Mcs

r

rt0

v

v

− 1

+ 1

Mc

WMc

Mc

WMc

Decodedsymbols

. . .

. . .

. . .

. . .

. . .

. . .

t = 0 t = 1

(a)

(b)

t1

t0

t1

Pipeline decoding:

Low-latency low-complexity windowed decoding:

Non-Binary LDPC Codes

14

Code alphabet in

Code alphabet can be equivalent to modulation alphabet

GF(q), q > 2

Better performance at low block lengths than binary codes

Decoding complexity for belief propagation decoding, but with FFT-based decoding [Declercq & Fossorier 2007]


14

Code alphabet in


GF(q), q > 2

O(q2)O(q logq)

Better performance at low block lengths than binary codes

Decoding complexity for belief propagation decoding, but with FFT-based decoding [Declercq & Fossorier 2007]


14

Code alphabet in


GF(q), q > 2

1 00 1 1 0 1 1 0 1 1 10 1 1 0 1 0 1 01 0 0 1 0 1 0 1 1 1

1 1 1 0 1 1 0 00 1 1 0 1 1

0 1 0 01 1

(a) (b)

H =

O(q2)O(q logq)

Non-Binary LDPC Codes: Performance

15

Random codes, N � 2350, R � 0.83

3 3.5 4 4.5 5

10−4

10−5

10−6

10−7

10−8

10−9

10−10

10−11

SNR(dB)

FER

OriginalA−method

GF(4)

GF(8)

GF(16)

4.2 4.4 4.6 4.8 5 5.2

10−3

10−4

10−5

10−6

10−7

10−8

10−9

10−10

10−11

SNR(dB)

FER

OriginalA−method

Binary

GF(4)

GF(16)

GF(8)

QC codes, N � 1200, R � 0.8

[Amiri, Kliewer, Dolecek 2014]

Polar Codes

16

First constructive technique to provably achieve channel capacity with bounded complexity O(n log n) [Arikan 2009]

Polar Codes

16


Closely related to Reed-Muller codes, constructed recursively via Kronecker products

Polar Codes

16


Closely related to Reed-Muller codes, constructed recursively via Kronecker products

Advantages for multi-terminal setups (e.g., broadcast channel [Mondelli et al. 2014])

Take Aways

17

5G requirements: One code fits all?

Take Aways

17


Low complexity en-/decod.

Finite block-length perf.

Spectrally efficient

Suitable for multi-

terminalBinary SC-

LDPC codes


Polar codes

Take Aways

17


Improving finite block length performance of polar codesNon-binary SC-LDPC codes

Open:

Low complexity en-/decod.

Finite block-length perf.

Spectrally efficient

Suitable for multi-

terminalBinary SC-

LDPC codes


Polar codes

Follow Up...

B. Amiri, A. Reisizadeh, J. Kliewer, L. Dolecek: Optimized array-based spatially-coupled LDPC codes: An absorbing set approach, Submitted to ISIT 2015. D. J. Costello, L. Dolecek, T. E. Fuja, J. Kliewer, D. G. M. Mitchell, R. Smarandache: Spatially coupled codes on graphs: Theory and practice, IEEE Communications Magazine, July 2014. E. En Gad, Y. Li, J. Kliewer, M. Langberg, A. Jiang, J. Bruck, Asymmetric error correction and flash-memory rewriting using polar codes, arXiv:1410.3542, Oct. 2014.B. Amiri, J. Kliewer, L. Dolecek: Analysis and enumeration of absorbing sets for non-binary graph-based codes. IEEE Trans. Comm., February 2014. J. Kliewer, D. J. Costello, Jr.: On achieving an asymptotically error-free fixed-point of iterative decoding for perfect a priori information. IEEE Trans. Comm., June 2013. V. Rahti, M. Andersson, R. Thobaben, J. Kliewer, M. Skoglund: Performance analysis and design of two edge type LDPC codes for the BEC wiretap channel, IEEE Trans. Inf. Theory, February 2013.

C. Koller, A. Graell i Amat, J. Kliewer, F. Vatta, K. S. Zigangirov, D. J. Costello, Jr.: Analysis and design of tuned turbo codes. IEEE Trans. Inf. Theory, July 2012.

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advances in error control strategies for 5g

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