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

Zhang, Fan; Pfister, Henry D.

doi:10.1109/tit.2011.2165813

Cited by 14 publications

(27 citation statements)

References 24 publications

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“…There is an implicit assumption that the two algorithms perform the same. In fact, they perform differently and the LM2-NB algorithm is superior as observed in [37] [17].…”

Section: )mentioning

confidence: 98%

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Verification Decoding of High-Rate LDPC Codes With Applications in Compressed Sensing

Zhang

Pfister

2012

IEEE Trans. Inform. Theory

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This paper considers the performance of (j, k)-regular low-density parity-check (LDPC) codes with messagepassing (MP) decoding algorithms in the high-rate regime. In particular, we derive the high-rate scaling law for MP decoding of LDPC codes on the binary erasure channel (BEC) and the q-ary symmetric channel (q-SC). For the BEC and a fixed j, the density evolution (DE) threshold of iterative decoding scales like Θ(k −1 ) and the critical stopping ratio scales like Θ(k −j/(j−2) ). For the q-SC and a fixed j, the DE threshold of verification decoding depends on the details of the decoder and scales like Θ(k −1 ) for one decoder.Using the fact that coding over large finite alphabets is very similar to coding over the real numbers, the analysis of verification decoding is also extended to the the compressed sensing (CS) of strictly-sparse signals. A DE based approach is used to analyze the CS systems with randomized-reconstruction guarantees. This leads to the result that strictly-sparse signals can be reconstructed efficiently with high-probability using a constant oversampling ratio (i.e., when the number of measurements scales linearly with the sparsity of the signal). A stopping-set based approach is also used to get stronger (e.g., uniform-in-probability) reconstruction guarantees.

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“…There is an implicit assumption that the two algorithms perform the same. In fact, they perform differently and the LM2-NB algorithm is superior as observed in [37] [17].…”

Section: )mentioning

confidence: 98%

“…For this reason, Sudocodes require a two-phase encoding that prevents the scheme from achieving a constant oversampling rate. A detailed discussion of the LM2-NB algorithm, which is a node-based improvement of the message-based LM2 (LM2-MB), can be found in [17].…”

Section: )mentioning

confidence: 99%

Verification Decoding of High-Rate LDPC Codes With Applications in Compressed Sensing

Zhang

Pfister

2012

IEEE Trans. Inform. Theory

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“…Different simplified message passing algorithms were studied in [7], [8]. Regarding q-ary symmetric channels (q-SCs), a majority-logic-like decoding algorithm was introduced in [9], while verification based decoding algorithms were studied in [10]- [13]. Both algorithms target large field orders.…”

Section: Introductionmentioning

confidence: 99%

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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“…In [12], [13], the authors developed a low-complexity framework for the asymptotic analysis of NB-VB algorithms over sparse random regular sensing graphs. The analysis presented in [12], [13] was significantly faster and more robust against numerical errors compared to the approach of [10].…”

Section: Introductionmentioning

confidence: 99%

Analysis and design of irregular graphs for node-based verification-based recovery algorithms in compressed sensing

Eftekhari

Banihashemi

Lambadaris

2012

2012 IEEE International Symposium on Information Theory Proceedings

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In this paper, we present a probabilistic analysis of iterative node-based verification-based (NB-VB) recovery algorithms over irregular graphs in the context of compressed sensing. Verification-based algorithms are particularly interesting due to their low complexity (linear in the signal dimension n). The analysis predicts the average fraction of unverified signal elements at each iteration where the average is taken over the ensembles of input signals and sensing matrices. The analysis is asymptotic (n → ∞) and is similar in nature to the well-known density evolution technique commonly used to analyze iterative decoding algorithms. Compared to the existing technique for the analysis of NB-VB algorithms, which is based on numerically solving a large system of coupled differential equations, the proposed method is much simpler and more accurate. This allows us to design irregular sensing graphs for such recovery algorithms. The designed irregular graphs outperform the corresponding regular graphs substantially. For example, for the same recovery complexity per iteration, we design irregular graphs that can recover up to about 40% more non-zero signal elements compared to the regular graphs. Simulation results are also provided which demonstrate that the proposed asymptotic analysis matches the performance of recovery algorithms for large but finite values of n.

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

Cited by 14 publications

References 24 publications

Verification Decoding of High-Rate LDPC Codes With Applications in Compressed Sensing

Verification Decoding of High-Rate LDPC Codes With Applications in Compressed Sensing

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

Analysis and design of irregular graphs for node-based verification-based recovery algorithms in compressed sensing

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