Advances in Error Control Strategies for 5G

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Transcription:

Advances in Error Control Strategies for 5G Jörg Kliewer The Elisha Yegal Bar-Ness Center For Wireless Communications And Signal Processing Research

5G Requirements [Nokia Networks: Looking ahead to 5G. White paper, April 2014] 2

Energy Bottleneck 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 3

Energy Bottleneck 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! 3

Coding for *G 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 4

Coding for *G 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. 4

Coding Wish List for 5G 3G/4G coding is essentially capacity-approaching for point-topoint BI-AWGN 5

Coding Wish List for 5G 3G/4G coding is essentially capacity-approaching for point-topoint BI-AWGN 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

Coding Wish List for 5G 3G/4G coding is essentially capacity-approaching for point-topoint BI-AWGN 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 5

One Code Fits All? 6

Not Really 7

Not Really No single scheme which fixes all these issues, but few promising candidates: Spatially coupled (convolutional) LDPC codes Non-binary LDPC codes Polar codes 7

Bit error probability LDPC Block Codes Uncoded BPSK Regular LDPC-BC Shannon limit Waterfall Irregular LDPC-BC Error floor (db) 8

Bit error probability LDPC Block Codes Uncoded BPSK Regular LDPC-BC Waterfall Shannon limit Irregular LDPC-BC Error floor (db) Tanner graph (3,6) regular LDPC code: 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 H = 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 (a) Graph sparsely connected (b) 8

Spatially Coupled LDPC Codes 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

Spatially Coupled LDPC Codes 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 Same performance under belief propagation decoding as for the corresponding block LDPC ensembles under maximum likelihood decoding (threshold saturation) 9

Spatially Coupled LDPC Codes 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 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 9

Spatially Coupled LDPC Codes Coupling construction via unwrapping: H = 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (cut-and-paste) H = cc 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (a) 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (diagonal matrix extension) Convolutional code structure 10

Spatially Coupled LDPC Codes Coupling construction via unwrapping: Resulting Tanner graph: H = 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (cut-and-paste) H = cc 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (a) 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (diagonal matrix extension) Convolutional code structure 10

Spatially Coupled LDPC Codes H = 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (cut-and-paste) Coupling construction via unwrapping: H = 1 0 1 1 1 0 1 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (cut-and-paste) 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 Resulting Tanner graph: H = cc 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (a) 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (diagonal matrix extension) H = cc 1 1 1 0 1 1 0 0 1 0 0 1 1 0 1 1 0 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 0 1 1 0 1 0 0 1 1 (diagonal matrix extension) Terminated Tanner graph: (b) (a) 0 1 L 2 L 1 (c) Convolutional code structure 10

Spatially Coupled LDPC Codes: Performance 10 1 Bit error rate 10 2 10 3 convolutional gain (3,6)-regular LDPC-BC n =4098 10 4 10 5 (3,6)-regular LDPC-CC ν s =4098 1 1.2 1.4 1.6 1.8 E b /N 0 (db) 11

Spatially Coupled LDPC Codes: Performance 0.55 0.5 0.45 0.4 Shannon limit (3,6) (4,8) Term. (3,6)-reg. Term. (4,8)-reg. Term. (5,10)-reg. Term. ARJA Block (J, K)-reg. Block ARJA 0.55 (5,10) (3,6) (5,10) 0.5 0.45 0.4 (4,8) Gilbert-Varshamov bound Rate 0.35 0.3 L=3 0.35 0.3 L=5 0.25 0.2 0.15 0.1 L=2 Increasing termination length L L=3 L=5 L=8 0.25 L=8 L=7 0.2 L=4 L=2 L=5 L=6 L=6 0.15 L=3 Increasing termination L=7 L=4 L=4 0.1 L=5 length L L=5 0.05 1 0 1 2 3 4 5 E b /N 0 (db) 0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 d min /n [Costello, Dolecek, Fuja, Kliewer, Mitchell, Smarandache, 2014] 12

Spatially Coupled LDPC Codes: Efficient Decoding Pipeline decoding: Decoded symbols v Proc. I Proc. I............... v 1 t 0 t 1 I(m s... + 1)Mc (a) Proc. 2 Proc. 1 s r 1 t r t 0 Received symbols 13

Spatially Coupled LDPC Codes: Efficient Decoding Pipeline decoding: Decoded symbols v Proc. I Proc. I............... v 1 t 0 t 1 I(m s... + 1)Mc (a) Proc. 2 Proc. 1 s r 1 t r t 0 Received symbols Low-latency low-complexity windowed decoding: Mc... Mc... WMc...... Decoded symbols WMc t = 0 t = 1 (b)...... 13

Non-Binary LDPC Codes Code alphabet in GF(q), q > 2 Code alphabet can be equivalent to modulation alphabet 14

Non-Binary LDPC Codes Code alphabet in GF(q), q > 2 Code alphabet can be equivalent to modulation alphabet Better performance at low block lengths than binary codes Decoding complexity O(q 2 ) for belief propagation decoding, but O(q log q) with FFT-based decoding [Declercq & Fossorier 2007] 14

Non-Binary LDPC Codes Code alphabet in GF(q), q > 2 Code alphabet can be equivalent to modulation alphabet Better performance at low block lengths than binary codes Decoding complexity O(q 2 ) for belief propagation decoding, but O(q log q) with FFT-based decoding [Declercq & Fossorier 2007] (b) 14

Non-Binary LDPC Codes: Performance Random codes, N 2350, R 0.83 QC codes, N 1200, R 0.8 FER 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 Original A method Binary GF(4) GF(8) GF(16) 4.2 4.4 4.6 4.8 5 5.2 SNR(dB) FER 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 Original A method GF(8) GF(4) GF(16) 3 3.5 4 4.5 5 SNR(dB) [Amiri, Kliewer, Dolecek 2014] 15

Polar Codes First constructive technique to provably achieve channel capacity with bounded complexity O(n log n) [Arikan 2009] 16

Polar Codes First constructive technique to provably achieve channel capacity with bounded complexity O(n log n) [Arikan 2009] Closely related to Reed-Muller codes, constructed recursively via Kronecker products 16

Polar Codes First constructive technique to provably achieve channel capacity with bounded complexity O(n log n) [Arikan 2009] Closely related to Reed-Muller codes, constructed recursively via Kronecker products Advantages for multi-terminal setups (e.g., broadcast channel [Mondelli et al. 2014]) 16

Take Aways 5G requirements: One code fits all? 17

Take Aways 5G requirements: One code fits all? Binary SC- LDPC codes Non-binary LDPC codes Low complexity en-/decod. Finite blocklength perf. Spectrally efficient Suitable for multiterminal Polar codes 17

Take Aways 5G requirements: One code fits all? Binary SC- LDPC codes Non-binary LDPC codes Low complexity en-/decod. Finite blocklength perf. Spectrally efficient Suitable for multiterminal Polar codes Open: Improving finite block length performance of polar codes Non-binary SC-LDPC codes 17

Follow Up... B. Amiri, A. Reisizadeh, J. Kliewer, L. Dolecek: Optimized array-based spatiallycoupled 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 fixedpoint 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. 18

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