Rate-compatible spatially-coupled LDPC code ensembles with nearly-regular degree distributions

Abstract

Spatially-coupled regular LDPC code ensembles have outstanding performance with belief propagation decoding and can perform arbitrarily close to the Shannon limit without requiring irregular graph structures. In this paper, we are concerned with the performance and complexity of spatially-coupled ensembles with a rate-compatibility constraint. Spatially-coupled regular ensembles that support rate-compatibility through extension have been proposed before and show very good performance if the node degrees and the coupling width are chosen appropriately. But due to the strict constraint of maintaining a regular degree, there exist certain unfavorable rates that exhibit bad performance and high decoding complexity. We introduce an altered LDPC ensemble construction that changes the evolution of degrees over subsequent incremental redundancy steps in such a way, that the degrees can be kept low to achieve outstanding performance close to Shannon limit for all rates. These ensembles always outperform their regular counterparts at small coupling width.

Rate‐compatible spatially coupled LDPC code ensembles by partial repetition extension

“…All member codes in this code family are proved to be capacity‐achieving over the binary erasure channel (BEC), but they are required to satisfy the regularity constraints on the node degrees, which will result in high complexity for low rate member code due to its large degree. Concerning this issue, RC‐SCLDPC code ensembles constructed by introducing slight irregularity were proposed in [11], which can decrease complexity while keeping capacity‐approaching thresholds for all rates. Different from coupling the conventional RC‐LDPC codes, a class of protograph‐based RC‐SCLDPC codes constructed by coupling the raptor‐like LDPC codes are proposed in [12], which achieved an almost uniform gap to Shannon limit over the BEC as well as the additive white Gaussian noise (AWGN) channel.…”

Construction and Decoding of Rate‐Compatible Globally Coupled LDPC Codes

“…Unlike the SC-LDPC codes which have some conventional design methods for RC-LDPC codes, such as puncturing variable nodes from the codes with low rate and extending variable nodes to the codes with high rate, the classical GC-LDPC codes are mostly restricted to invariant code rate [11,20,[22][23][24][25]. And the existing construction methods of GC-LDPC codes are not flexible enough for RC code design.…”