Spatially-coupled nearly-regular LDPC code ensembles for rate-flexible code design

Abstract

Spatially coupled regular LDPC code ensembles have outstanding performance with belief propagation decoding and can perform close to the Shannon limit. In this paper we investigate the suitability of coupled regular LDPC code ensembles with respect to rate-flexibility. Regular ensembles with good performance and low complexity exist for a variety of specific code rates. On the other hand it can be observed that outside this set of favorable rational rates the complexity and performance penalty become unreasonably high. We therefore propose ensembles with slight irregularity that allow us to smoothly cover the complete range of rational rates. Our simple construction allows a performance with negligible gap to the Shannon limit while maintaining complexity as low as for the best regular code ensembles. At the same time the construction guarantees that asymptotically the minimum distance grows linearly with the length of the coupled blocks.

Spatially Coupled LDPC Codes Constructed by Parallelly Connecting Multiple Chains

“…Kudekar et al named this phenomenon threshold saturation and proved it rigorously for the binary erasure channels (BEC) in [2] and the binary-input memoryless symmetric-output (BMS) channels in [3]. After that, several new SC-LDPC codes were constructed to further improve the performance by introducing irregularity [4]- [6].…”

“…It was shown that the new ensemble outperforms parallel, independent spatially coupled codes and offers an increased resilience against burst errors. In [6], two types of nearly-regular SC-LDPC ensembles were investigated. Both ensembles were built upon the mixture of two favorable regular codes.…”

“…Compared with the codes in [4]- [6], the proposed codes have the following properties. Firstly, PC-MSC-LDPC codes are constructed by exchanging the edges between different chains, in contrast with those constructed by changing the degree of the variable nodes [4], [5].…”

“…Secondly, compared with the ensemble in [5] which adjusts the rate via puncturing the variable nodes, the rates of the proposed PC-MSC-LDPC ensemble can be varied by changing the rate of each chain. Thirdly, the construction method in [6] is realized by coupling previously designed irregular component codes, while the PC-MSC-LDPC ensemble is constructed by directly connecting multiple regular chains, which allows each chain to have a different coupling width and coupling length. Finally, the proposed ensemble with finite coupling length has excellent thresholds over the whole rate range, while the boundary mixing ensemble in [6] performs worse in the medium rate range even with infinite coupling length.…”

“…Thirdly, the construction method in [6] is realized by coupling previously designed irregular component codes, while the PC-MSC-LDPC ensemble is constructed by directly connecting multiple regular chains, which allows each chain to have a different coupling width and coupling length. Finally, the proposed ensemble with finite coupling length has excellent thresholds over the whole rate range, while the boundary mixing ensemble in [6] performs worse in the medium rate range even with infinite coupling length. When compared with the direct neighbor mixing ensemble in [6] which has high implementation complexity, the proposed ensemble is constructed by directly connecting multiple different regular chains.…”