Protograph design for spatially-coupled codes to attain an arbitrary diversity order

Hassan, Najeeb ul; Andriyanova, Iryna; Lentmaier, Michael; Fettweis, Gerhard

doi:10.1109/itwf.2015.7360752

Cited by 4 publications

(2 citation statements)

References 12 publications

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“…Recently, in [16], [17], it has been shown that some welldesigned protograph-based LDPC codes can increase the diversity order of block fading channels and are thus also good candidates for block erasure channels. The tradeoff with these constructions is, however, that they require large syndrome former memories if the burst length becomes large.…”

Section: Introductionmentioning

confidence: 99%

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

Aref

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: Introductionmentioning

confidence: 99%

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

Aref

Rengaswamy

Schmalen

2018

IEEE Trans. Inform. Theory

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“…in an increased required window length and thus also in an increased complexity. 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

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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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SC-LDPC codes over the block-fading channel: Robustness to a synchronisation offset

Andriyanova¹,

Hassan²,

Lentmaier³

et al. 2015

2015 IEEE International Black Sea Conference on Communications and Networking (BlackSeaCom)

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Spatially-Coupled LDPC (SC-LDPC) codes have been recently shown to be very efficient for transmissions over nonergodic channels, in particular over block-fading channels [1]. In fact, it is possible to design a SC-LDPC code with any given code diversity [2]. In this work, we investigate the performance of SC-LDPC codes over block-fading channels, assuming a mismatch (or offset) between the first bit of a transmission packet and a first bit of a codeword. Such a mismatch is called the synchronisation offset, and it has a negative impact on the code diversity. We propose a data-allocation scheme for SC-LDPC codes that allows to obtain a robustness to the synchronisation offset. Combined together with the code design from [2], it allows to design efficient SC-LDPC codes, whose performance degrades only slowly under imperfect transmission conditions.

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Protograph design for spatially-coupled codes to attain an arbitrary diversity order

Cited by 4 publications

References 12 publications

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

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

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

SC-LDPC codes over the block-fading channel: Robustness to a synchronisation offset

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