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On the Multiple Threshold Decoding of LDPC codes over GF(q) [article]

Alexey Frolov, Victor Zyablov
2015 arXiv   pre-print
We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested.  ...  At the same time the transition to multiple thresholds does not affect the order of complexity.  ...  We first improve the estimate on ρ. Then we consider multiple threshold decoding of LDPC codes over F q . Multiple threshold majority decoding for binary LDPC codes was first introduced in [4] .  ... 
arXiv:1502.06871v1 fatcat:3mzmkq4b7rhg7pkoqasijgwg3u

Decoding Algorithms for Nonbinary LDPC Codes Over GF$(q)$

David Declercq, Marc Fossorier
2007 IEEE Transactions on Communications  
In this paper, we address the problem of decoding nonbinary LDPC codes over finite fields GF(q), with reasonnable complexity and good performance.  ...  Our simulations on ultra-sparse codes over very high order fields show that non-binary LDPC codes are promising for applications which require low FER for small or moderate codeword lengths.  ...  Decoding threshold of a regular (2, 4) LDPC code over GF(256) vs. correction factors. Threshold value δ = (E b /N 0 ) dB versus the field order for the (d v = 2, d c = 4)-LDPC code.  ... 
doi:10.1109/tcomm.2007.894088 fatcat:mythqnscs5eilauqxfprdt7ilu

Design of Nonbinary LDPC Codes over GF(q) for Multiple-Antenna Transmission

Rong-hui Peng, Rong-rong Chen
2006 MILCOM 2006  
In this paper, we investigate the application of nonbinary low density parity check (LDPC) codes over Galois field GF(q) for multiple-input multiple-output (MIMO) fading channels.  ...  Depending on the size of the Galois field GF(q), we study both iterative systems which employ joint MIMO detection and channel decoding, and non-iterative systems which employ separate MIMO detection and  ...  This is because the ML detector produces the prior probabilities for each GF(q) symbol which can be used directly for nonbinary LDPC decoding over GF(q).  ... 
doi:10.1109/milcom.2006.302526 fatcat:5s7tlrnhe5ddbp4pci2po3ekda

Analysis of Verification-based Decoding on the q-ary Symmetric Channel for Large q [article]

Fan Zhang, Henry D. Pfister
2011 arXiv   pre-print
We discuss and analyze a list-message-passing decoder with verification for low-density parity-check (LDPC) codes on the q-ary symmetric channel (q-SC).  ...  If the maximum list size is unbounded, then we find that any capacity-achieving LDPC code for the binary erasure channel can be used to achieve capacity on the q-SC for large q.  ...  Recall that the idea to use non-binary elements in the parity-check matrix appears in the early works on the LDPC codes over GF (q) [11] . C.  ... 
arXiv:0806.3243v6 fatcat:rr6rvg7cjre6bffkmlcp5etk4y

LDPC Codes over the q-ary Multi-Bit Channel

Rami Cohen, Netanel Raviv, Yuval Cassuto
2019 IEEE Transactions on Information Theory  
An error event occurs when not all the symbol bits are known. To deal with such error events, we use GF(q) low-density parity-check (LDPC) codes and analyze their decoding performance.  ...  This channel models a memory device, where q-ary symbols (q = 2 s ) are stored in the form of current/voltage levels.  ...  The decoding thresholds are given for optimal edge-label distributions. VIII. CONCLUSION This work offers a study of the performance of iterative decoding of GF(q) LDPC codes over the QMBC.  ... 
doi:10.1109/tit.2019.2900894 fatcat:deyhzfmuergmhklr5ogd247uxi

Protograph-based q-ary LDPC codes for higher-order modulation

Andrea Marinoni, Pietro Savazzi, Richard D. Wesel
2010 2010 6th International Symposium on Turbo Codes & Iterative Information Processing  
This paper introduces a protograph-based method for designing q-ary LDPC codes for use with modulations larger than QPSK. Simulations focus on a GF(16), 16-QAM example.  ...  The performance of this baseline GF(16) code was comparable to the best known binary LDPC code for 16-QAM, so that the proposed improvements allow the GF(16) LDPC code to outperform known binary approaches  ...  SYSTEM MODEL This paper uses LDPC codes over GF(q) with q-ary modulation to achieve bandwidth-efficient transmission.  ... 
doi:10.1109/istc.2010.5613806 fatcat:fmnx55uwgnanxdq6newpilf2im

Density Evolution for GF(q) LDPC Codes Via Simplified Message-passing Sets

Brian M. Kurkoski, Kazuhiko Yamaguchi, Kingo Kobayashi
2007 2007 Information Theory and Applications Workshop  
The proposed algorithm is a generalization to GF (q) of Richardson and Urbanke's decoding "Algorithm E" for binary codes.  ...  A message-passing decoder for GF (q) low-density parity-check codes is defined, which uses discrete messages from a subset of all possible binary vectors of length q.  ...  LDPC Codes Over GF (q) A GF (q) LDPC code is the set of code vectors x = (x 1 , . . . , x n ) of length n with elements A = {0, α 0 , α 1 , · · · , α q−2 } with primitive element α from GF (q) such that  ... 
doi:10.1109/ita.2007.4357586 fatcat:w6ofhcdhgfdxtpq3xsa3k6j2je

Design of Spatially Coupled LDPC Codes over GF(q) for Windowed Decoding [article]

Lai Wei, David G. M. Mitchell, Thomas E. Fuja, Daniel J. Costello
2014 arXiv   pre-print
In this paper we consider the generalization of binary spatially coupled low-density parity-check (SC-LDPC) codes to finite fields GF(q), q≥ 2, and develop design rules for q-ary SC-LDPC code ensembles  ...  ensembles constructed over GF(q) using protographs.  ...  PDE to WD in order to calculate the WD threshold of an SC-LDPC code ensemble defined over GF(2 m ).  ... 
arXiv:1411.4373v1 fatcat:3bssuqsd3zcgzkka7nwuqcdun4

Design of regular (2,d/sub c/)-LDPC codes over GF(q) using their binary images

Charly Poulliat, Marc Fossorier, David Declercq
2008 IEEE Transactions on Communications  
In this paper, a method to design regular (2, d c )-LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image.  ...  First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall.  ...  ACKNOWLEDGMENT The authors wish to thank the authors of [8] for providing the comparative results.  ... 
doi:10.1109/tcomm.2008.060527 fatcat:jwgbcjsnzbajnmsuzak4vsja5q

Multiplicatively Repeated Non-Binary LDPC Codes [article]

Kenta Kasai, David Declercq, Charly Poulliat, Kohichi Sakaniwa
2011 arXiv   pre-print
By multiplicatively repeating the (2,3)-regular non-binary LDPC mother code of rate 1/3, we construct rate-compatible codes of lower rates 1/6, 1/9, 1/12,...  ...  Moreover, we propose the decoding algorithm for the proposed codes, which can be decoded with almost the same computational complexity as that of the mother code.  ...  ACKNOWLEDGMENTS The authors are grateful to T. Richardson for providing the data of the multi-edge type LDPC code of rate 1/6 in Fig. 11 .  ... 
arXiv:1004.5367v2 fatcat:b4ejty6c4zblfgr66hcb4hsfby

Non-binary protograph low-density parity-check codes for space communications

Laura Costantini, Balázs Matuz, Gianluigi Liva, Enrico Paolini, Marco Chiani
2012 International Journal of Satellite Communications And Networking  
In the short block length regime, the designed codes gain more than 1 dB with respect to the binary protograph LDPC codes recently proposed for the next generation up-link standard of the Consultative  ...  It is shown that larger coding gains are achieved, outperforming the binary competitors by more than 0.3 dB on the additive white Gaussian noise channel (AWGN).  ...  LDPC codes over non-binary GFs were proposed in [15] . As for binary LDPC codes, decoding is based on belief propagation (BP) that is on message passing along the edges of the Tanner graph.  ... 
doi:10.1002/sat.1004 fatcat:2rg7lqbdrrg53ops2nww5zsqqy

Fountain Coding via Multiplicatively Repeated Non-Binary LDPC Codes

Kenta Kasai, David Declercq, Kohichi Sakaniwa
2012 IEEE Transactions on Communications  
In this paper, we introduce a novel fountain coding scheme with non-binary LDPC codes. The decoding complexity of the proposed fountain code does not depend on the channel.  ...  We study fountain codes transmitted over the binary-input symmetric-output channel.  ...  However, Rathi observed that the threshold for the code ensemble defined over GF(2 m ) and GL(GF(2), m) also have approximately the same threshold within the order of 10 −4 .  ... 
doi:10.1109/tcomm.2012.061112.110177 fatcat:5k33qpf2evh6ppxib7yznv6bdy

Parallel vs. sequential belief propagation decoding of LDPC codes over and Markov sources

N. Yacov, H. Efraim, H. Kfir, I. Kanter, O. Shental
2007 Physica A: Statistical Mechanics and its Applications  
A sequential updating scheme (SUS) for belief propagation (BP) decoding of LDPC codes over Galois fields, GF(q), and correlated Markov sources is proposed, and compared with the standard parallel updating  ...  These results may imply on the 'universality' of the one half convergence speed-up of SUS decoding.  ...  Acknowledgment The research of I.K. is supported in part by the Israel Science Foundation.  ... 
doi:10.1016/j.physa.2006.12.009 fatcat:ffezdpaujbfwtjgk6eev5sagqq

Fountain Codes with Multiplicatively Repeated Non-Binary LDPC Codes [article]

Kenta Kasai, Kohichi Sakaniwa
2010 arXiv   pre-print
In this paper, we introduce a novel fountain coding scheme with non-binary LDPC codes. The decoding complexity of the proposed fountain code does not depend on the channel.  ...  Numerical experiments show that the proposed codes exhibit better performance than conventional fountain codes, especially for small number of information bits.  ...  However, Rathi reported that the threshold for the code ensemble defined over GF(2 m ) and GL(GF(2), m) also have approximately the same threshold within the order of 10 −4 .  ... 
arXiv:1007.0799v2 fatcat:vhowcxqqezgjfmk6opy757hqhi

Low complexity iterative receiver with lossless information transfer for non-binary LDPC coded PDMA system

Hanqing Ding, Qingqing Liu, Zihang Ding, Jin Xu, Zhe Zhang, Weihua Liu, Xueyan Chen
2020 IEEE Access  
Specifically, we considered a 4-ary LDPC over Galois field (GF(4)-LDPC) coded PDMA system with quadrature phase shift keying (QPSK) modulation.  ...  In this work, we first proposed a non-binary low-density parity-check (NB-LDPC) coded pattern division multiple access (PDMA) scheme with the order of the Galois field equal to the size of modulation alphabet  ...  The work of Xueyan Chen was supported by the Science and Technology Research Project of Henan Province (Grant no. 202102210122).  ... 
doi:10.1109/access.2020.3016697 fatcat:nikjzilpmrcq7k2vzp3fagmzku
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