Spatial coupling for distributed storage and diversity applications

Jardel, Fanny; Boutros, Joseph J.; Dedeoglu, Volkan; Sarkiss, Mireille; Othman, Ghaya Rekaya-Ben

doi:10.1109/comnet.2015.7566624

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…For each value of M , we performed Monte-Carlo simulations and counted 1000 decoding failures to assess the average block erasure probability P RBC B . These figures show that for b < β max M , the error floor is well estimated by (18) even for small M = 100. It implies that the size-2 stopping sets are the main cause of decoding error.…”

Section: A Random Burst Channel (Rbc)mentioning

confidence: 68%

“…Consider a burst of length b = 2M . We bound the probability of error in (18) by averaging over a random, uniformly distributed starting bit S. Here, S = 1. Hence, we have (ii) by considering only the term for S = 1 in (18) (without the averaging factor 1 M ).…”

Section: Block Erasure Channel (Blec)mentioning

confidence: 99%

“…The decoding failure probability, P RBC B , is averaged over all trials until 1000 decoding failures occur. We also plot the error floor estimation (18) for each M . Moreover, Fig.…”

Section: A Random Burst Channel (Rbc)mentioning

confidence: 99%

“…The tradeoff with these constructions is, however, that they require large syndrome former memories if the burst length becomes large. In addition, closely related structures based on protographs have been proposed in [18], [19], which spatially couple the previously proposed root-check LDPC codes [20] to improve the finite length performance and thresholds. The analysis of the randomly coupled SC-LDPC ensemble of [8], for the case where complete SPs are randomly erased, has been discussed in [21].…”

Section: Introductionmentioning

confidence: 99%

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Finite-Length Analysis of Spatially-Coupled Regular LDPC Ensembles on Burst-Erasure Channels

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Rengaswamy

Schmalen

2018

IEEE Trans. Inform. Theory

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Regular Spatially-Coupled LDPC (SC-LDPC) ensembles have gained significant interest since they were shown to universally achieve the capacity of binary memoryless channels under low-complexity belief-propagation decoding. In this work, we focus primarily on the performance of these ensembles over binary channels affected by bursts of erasures. We first develop an analysis of the finite length performance for a single burst per codeword and no errors otherwise. We first assume that the burst erases a complete spatial position, modeling for instance node failures in distributed storage. We provide new tight lower bounds for the block erasure probability (PB) at finite block length and bounds on the coupling parameter for being asymptotically able to recover the burst. We further show that expurgating the ensemble can improve the block erasure probability by several orders of magnitude. Later we extend our methodology to more general channel models. In a first extension, we consider bursts that can start at a random location in the codeword and span across multiple spatial positions. Besides the finite length analysis, we determine by means of density evolution the maximum correctable burst length. In a second extension, we consider the case where in addition to a single burst, random bit erasures may occur. Finally, we consider a block erasure channel model which erases each spatial position independently with some probability p, potentially introducing multiple bursts simultaneously. All results are verified using Monte-Carlo simulations.

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Section: A Random Burst Channel (Rbc)mentioning

confidence: 68%

Section: Block Erasure Channel (Blec)mentioning

confidence: 99%

“…The decoding failure probability, P RBC B , is averaged over all trials until 1000 decoding failures occur. We also plot the error floor estimation (18) for each M . Moreover, Fig.…”

Section: A Random Burst Channel (Rbc)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite-Length Analysis of Spatially-Coupled Regular LDPC Ensembles on Burst-Erasure Channels

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Rengaswamy

Schmalen

2018

IEEE Trans. Inform. Theory

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“…Recently, it has been shown that protograph-based LDPC codes can increase the diversity order of block fading channels and are thus good candidates for block erasure channels [7], [8]; however, they require large syndrome former memories if the burst length becomes large. Closely related structures based on protographs have been proposed in [9] which spatially couple the special class of root-check LDPC codes [10] to improve the finite length performance and thresholds.…”

Section: Introductionmentioning

confidence: 99%

Spatially Coupled LDPC codes affected by a single random burst of erasures

Aref

Rengaswamy

Schmalen

2016

2016 9th International Symposium on Turbo Codes and Iterative Information Processing (ISTC)

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Abstract-Spatially-Coupled LDPC (SC-LDPC) ensembles achieve the capacity of binary memoryless channels (BMS), asymptotically, under belief-propagation (BP) decoding. In this paper, we study the BP decoding of these code ensembles over a BMS channel and in the presence of a single random burst of erasures. We show that in the limit of code length, codewords can be recovered successfully if the length of the burst is smaller than some maximum recoverable burst length. We observe that the maximum recoverable burst length is practically the same if the transmission takes place over binary erasure channel or over binary additive white Gaussian channel with the same capacity. Analyzing the stopping sets, we also estimate the decoding failure probability (the error floor) when the code length is finite.

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