Low-density parity-check codes with rates very close to the capacity of the q -ary symmetric channel for large q

Shokrollahi, Amin; Wang, W.

doi:10.1109/isit.2004.1365310

Cited by 18 publications

(18 citation statements)

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“…We analyze the reasons of FV and classify the FV's into two types. We find that the codes described in [8] and [13] both suffer from type-II FV. In Section IV, we analyze these FV's and propose a scheme that reduces the probability of FV.…”

Section: A Description Of the Decoding Algorithmmentioning

confidence: 79%

“…In Section V, differential evolution is used to optimize code ensembles and simulation results are compared with the theoretical thresholds. The results are also compared with previously published results from [8] and [13]. In Section VI, simulation results are presented.…”

Section: Introductionmentioning

confidence: 92%

“…It is important to note that (1) and (3) were published first in [13,Thm. 2] (by mapping x i = p i and y i = p i + q i ), but were derived independently by us.…”

Section: B De For Unbounded List Size Decoding Algorithmmentioning

confidence: 99%

“…A number of approaches to the q-SC (for large q) based on interleaved Reed-Solomon codes are also possible [5] [12]. In [13], Shokrollahi and Wang discuss two ways of approaching capacity. The first uses a two-stage approach where the first stage uses a Tornado code and verification decoding.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Verification-Based Decoding on the $q$-ary Symmetric Channel for Large $q$

Zhang

Pfister

2011

IEEE Trans. Inform. Theory

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Abstract-A new verification-based message-passing decoder for low-density parity-check (LDPC) codes is introduced and analyzed for the q-ary symmetric channel (q-SC). Rather than passing messages consisting of symbol probabilities, this decoder passes lists of possible symbols and marks some lists as verified. The density evolution (DE) equations for this decoder are derived and used to compute decoding thresholds. If the maximum list size is unbounded, then one finds that any capacity-achieving LDPC code for the binary erasure channel can be used to achieve capacity on the q-SC for large q. The decoding thresholds are also computed via DE for the case where each list is truncated to satisfy a maximum list-size constraint. Simulation results are also presented to confirm the DE results. During the simulations, we observed differences between two verification-based decoding algorithms, introduced by Luby and Mitzenmacher, that were implicitly assumed to be identical. In this paper, the node-based algorithms are evaluated via analysis and simulation.The probability of false verification (FV) is also considered and techniques are discussed to mitigate the FV. Optimization of the degree distribution is also used to improve the threshold for a fixed maximum list size. Finally, the proposed algorithm is compared with a variety of other algorithms using both density evolution thresholds and simulation results.Index Terms-low density parity check codes, message passing decoding, q-ary symmetric channel, verification decoding, list decoding, false verification.

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Section: A Description Of the Decoding Algorithmmentioning

confidence: 79%

Section: Introductionmentioning

confidence: 92%

“…It is important to note that (1) and (3) were published first in [13,Thm. 2] (by mapping x i = p i and y i = p i + q i ), but were derived independently by us.…”

Section: B De For Unbounded List Size Decoding Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of Verification-Based Decoding on the $q$-ary Symmetric Channel for Large $q$

Zhang

Pfister

2011

IEEE Trans. Inform. Theory

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“…They did not exhibit codes that come arbitrarily close to the capacity of the Q-ary symmetric channel, but it is possible to extend their methods to find such codes [11]. In their construction, the error probability of the decoder is at most O(n/Q), which can be much smaller than the error probability obtained using the hashing method.…”

Section: Introductionmentioning

confidence: 99%

Improved Decoding of Interleaved AG Codes

Brown

Minder

Shokrollahi

2005

Lecture Notes in Computer Science

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Abstract. We analyze a generalization of a recent algorithm of Bleichenbacher et al. for decoding interleaved codes on the Q-ary symmetric channel for large Q. We will show that for any m and any the new algorithms can decode up to a fraction of at least βm βm+1 (1−R−2Q −1/2m )− errors, where β = ln(q m −1) ln(q m ) , and that the error probability of the decoder is upper bounded by O(1/q n ), where n is the block-length. The codes we construct do not have a-priori any bound on their length.

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Symbol Message Passing Decoding of Nonbinary Low-Density Parity-Check Codes

Lázaro

Amat

Liva

et al. 2019

2019 IEEE Global Communications Conference (GLOBECOM)

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We present a novel decoding algorithm for q-ary low-density parity-check codes, termed symbol message passing. The proposed algorithm can be seen as a generalization of Gallager B and the binary message passing algorithm by Lechner et al. to q-ary codes. We derive density evolution equations for the q-ary symmetric channel, compute thresholds for a number of regular low-density parity-check code ensembles, and verify those by Monte Carlo simulations of long channel codes. The proposed algorithm shows performance advantages with respect to an algorithm of comparable complexity from the literature.

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Low-density parity-check codes with rates very close to the capacity of the q -ary symmetric channel for large q

Cited by 18 publications

References 1 publication

Analysis of Verification-Based Decoding on the $q$-ary Symmetric Channel for Large $q$

Analysis of Verification-Based Decoding on the $q$-ary Symmetric Channel for Large $q$

Improved Decoding of Interleaved AG Codes

Symbol Message Passing Decoding of Nonbinary Low-Density Parity-Check Codes

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