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On Decoding Irregular Tanner Codes with Local-Optimality Guarantees [article]

Nissim Halabi, Guy Even
2013 arXiv   pre-print
NWMS decoding is a BP-type algorithm that applies to any irregular binary Tanner code with single parity-check local codes.  ...  We present new certificates that are based on a combinatorial characterization for local-optimality of a codeword in irregular Tanner codes with respect to any MBIOS channel.  ...  Section 7 presents the NWMS iterative decoding algorithm for irregular Tanner codes with single parity-check local-codes, followed by a proof that NWMS finds the locally-optimal codeword.  ... 
arXiv:1107.2677v4 fatcat:cmbnljzw4ff4ppbrlm3c7spkum

Local-Optimality Guarantees for Optimal Decoding Based on Paths [article]

Guy Even, Nissim Halabi
2012 arXiv   pre-print
Also, an iterative message-passing decoding algorithm is guaranteed to find the unique locally-optimal codeword, if one exists.  ...  These local-optimality characterizations are based on combinatorial structures embedded in the Tanner graph of the code.  ...  We note that for even Tanner codes with SPC local codes, the NWMS decoder with uniform weights (i.e., w = 1 h ) is guaranteed to compute the ML-codeword in h iterations provided that a path-based h-locally  ... 
arXiv:1203.1854v2 fatcat:tulfwhpf4rfbdjdchhb362mmba

Regular and irregular progressive edge-growth tanner graphs

Xiao-Yu Hu, E. Eleftheriou, D.M. Arnold
2005 IEEE Transactions on Information Theory  
Regular and irregular LDPC codes using PEG Tanner graphs and allowing symbol nodes to take values over GF( ) ( 2) are investigated.  ...  Lower bounds on the girth of PEG Tanner graphs and on the minimum distance of the resulting low-density parity-check (LDPC) codes are derived in terms of parameters of the graphs.  ...  MacKay for valuable comments and for providing the parity-check matrices of some LDPC codes simulated herein.  ... 
doi:10.1109/tit.2004.839541 fatcat:xngdgthvdracnpxxccls4d7c3e

Low-Density Parity-Check Codes for Nonergodic Block-Fading Channels

Joseph Jean Boutros, Albert Guillen i Fabregas, Ezio Biglieri, Gilles Zemor
2010 IEEE Transactions on Information Theory  
We solve the problem of designing powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel.  ...  Unfortunately, optimal constructions for maximum-likelihood decoding do not perform well under iterative decoding.  ...  Two examples of local graphs whose diversity is not guaranteed are shown in Fig. 8 .  ... 
doi:10.1109/tit.2010.2053890 fatcat:xwccpiko4fbfrgo4g5qa3pwrhy

Renormalization Group Approach To Error-Correcting Codes [article]

Jonathan Yedidia
2001 arXiv   pre-print
This algorithm is based on the "renormalization-group" approach from physics: the idea is to continually replace an error-correcting code with a simpler error-correcting code that has nearly identical  ...  This assessment algorithm can be used as a subroutine in a more general algorithm to search for optimal error-correcting codes of specified blocklength and rate.  ...  When one wants to make real codes of finite blocklength, one is therefore often forced to choose a code which is sub-optimal in the infinite-blocklength limit, with no theoretical guidance.  ... 
arXiv:cond-mat/0106540v1 fatcat:l6iemxlhrncuviisu73jcyldza

Design and Analysis of Low-Density Parity-Check Codes for Block-Fading Channels

Joseph J. Boutros, Albert Guillen i Fabregas, Ezio Biglieri, Gilles Zemor
2007 2007 Information Theory and Applications Workshop  
We solve the problem of designing powerful lowdensity parity-check (LDPC) codes with iterative decoding for the block-fading channel.  ...  This family competes with multiplexed parallel turbo codes suitable for non-ergodic channels and recently reported in the literature.  ...  Therefore, if a sub-optimal decoder achieves full-diversity, the optimal decoder also achieves full-diversity. We consider the min-sum decoder.  ... 
doi:10.1109/ita.2007.4357562 fatcat:gmkzox26frgvfgq3wcqszlpks4

Design Methods for Irregular Repeat–Accumulate Codes

A. Roumy, S. Guemghar, G. Caire, S. Verdu
2004 IEEE Transactions on Information Theory  
Our optimization technique is based on approximating the evolution of the densities (DE) of the messages exchanged by the belief-propagation (BP) message-passing decoder by a one-dimensional dynamical  ...  We optimize the random-like ensemble of irregular repeat-accumulate (IRA) codes for binary-input symmetric channels in the large block-length limit.  ...  Tanner graph of an IRA code. Fig. 1 shows the block diagram of a systematic IRA encoder. A block of information bits is encoded by an (irregular) repetition code of rate .  ... 
doi:10.1109/tit.2004.831778 fatcat:5rxdsqh22zcxzb5pmvp5j6mibu

Spatially coupled sparse codes on graphs: theory and practice

Daniel Costello, Lara Dolecek, Thomas Fuja, Jorg Kliewer, David Mitchell, Roxana Smarandache
2014 IEEE Communications Magazine  
techniques now allow performance within a small fraction of a decibel of capacity with modest encoding and decoding complexity.  ...  and decoded error rate requirements.  ...  On the other hand, irregular codes, pioneered by Luby et al.  ... 
doi:10.1109/mcom.2014.6852099 fatcat:rqxolwc53zbpvpgo7jsuislxpy

Design of Low Complexity Non-binary LDPC Codes with an Approximated Performance-Complexity Tradeoff [article]

Yang Yu, Wen Chen
2020 arXiv   pre-print
manuscript which converges faster than the threshold-optimized non-binary LDPC codes in the low error rate regime.  ...  examine our algorithm by both hard and soft decision decoders.Moreover, simulation shows that the approximated PCT algorithm has accelerated the convergence process by 30% regarding the number of the decoding  ...  forward to design irregular nonbinary LDPC codes with optimized decoding complexity.  ... 
arXiv:2003.00714v1 fatcat:ejvx7ztolrcorj6nrucl3tvpuu

Design of Low Complexity Non-Binary LDPC Codes with an Approximated Performance-Complexity Tradeoff

Yang Yu, Wen Chen
2012 IEEE Communications Letters  
manuscript which converges faster than the threshold-optimized non-binary LDPC codes in the low error rate regime.  ...  We examine our algorithm by both hard and soft decision decoders.  ...  forward to design irregular nonbinary LDPC codes with optimized decoding complexity.  ... 
doi:10.1109/lcomm.2012.021612.112467 fatcat:udm43kb7r5gsvgb4dptktru4dy

Real-time DVB-S2 LDPC decoding on many-core GPU accelerators

Gabriel Falcao, Joao Andrade, Vitor Silva, Leonel Sousa
2011 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
It is well known that LDPC decoding is computationally demanding and one of the hardest signal operations to parallelize.  ...  In this paper we propose parallel algorithms for performing in GPUs the most demanding case of irregular and long length LDPC codes adopted in the Digital Video Broadcasting -Satellite 2 (DVB-S2) standard  ...  LDPC DVB-S2 decoders on Fermi GPUs with CUDA CONCLUSIONS In this paper we proposed and developed efficient parallel algorithms to perform the massive decoding of DVB-S2 LDPC codes on GPUs.  ... 
doi:10.1109/icassp.2011.5946824 dblp:conf/icassp/FernandesASS11 fatcat:dn62v7o2mvhebjlrlcao52qabm

Design of Convergence-Optimized Non-Binary LDPC Codes over Binary Erasure Channel

Yang Yu, Wen Chen, Lili Wei
2012 IEEE Wireless Communications Letters  
derived to design non-binary LDPC codes with convergence-optimized degree distributions.  ...  The resulting one-step decoding tree is cycle-free and achieves lower decoding complexity.  ...  However, the global optimal can not be always guaranteed. Experimental studies show that the local optimal will suffice [8] .  ... 
doi:10.1109/wcl.2012.050112.120297 fatcat:bhyozznvhvf45daf3ls6fre7fi

Design of Convergence-Optimized Non-binary LDPC Codes over Binary Erasure Channel [article]

Yang Yu, Wen Chen, Lili Wei
2020 arXiv   pre-print
derived to design non-binary LDPC codes with convergence-optimized degree distributions.  ...  The resulting one-step decoding tree is cycle-free and achieves lower decoding complexity.  ...  However, the global optimal can not be always guaranteed. Experimental studies show that the local optimal will suffice [8] .  ... 
arXiv:2003.01340v1 fatcat:gdzrtyu2dfgj7fr542e4vjy7uy

Density Evolution for Deterministic Generalized Product Codes on the Binary Erasure Channel at High Rates

Christian Hager, Henry D. Pfister, Alexandre Graell i Amat, Fredrik Brannstrom
2017 IEEE Transactions on Information Theory  
As an application, we discuss the design of irregular GPCs employing a mixture of component codes with different erasure-correcting capabilities.  ...  Our code construction encompasses several classes of GPCs previously proposed in the literature, such as irregular PCs, block-wise braided codes, and staircase codes.  ...  Thus, it comes with similar caveats (e.g., no optimality guarantees for finite code lengths), but also with similar strengths (e.g., an efficient and fast optimization procedure). A.  ... 
doi:10.1109/tit.2017.2689783 fatcat:wge6zd4ewvhvxprgqhg2s7zdla

Density Evolution for Deterministic Generalized Product Codes on the Binary Erasure Channel at High Rates [article]

Christian Häger, Henry D. Pfister, Alexandre Graell i Amat, Fredrik Brännström
2017 arXiv   pre-print
As an application, we discuss the design of irregular GPCs employing a mixture of component codes with different erasure-correcting capabilities.  ...  Our code construction encompasses several classes of GPCs previously proposed in the literature, such as irregular PCs, block-wise braided codes, and staircase codes.  ...  Thus, it comes with similar caveats (e.g., no optimality guarantees for finite code lengths), but also with similar strengths (e.g., an efficient and fast optimization procedure). A.  ... 
arXiv:1512.00433v2 fatcat:x5fpmyznc5g33clb6bxl7chyvy
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