English

Spatially Coupled Generalized LDPC Codes: Asymptotic Analysis and Finite Length Scaling

Information Theory 2021-04-19 v2 math.IT

Abstract

Generalized low-density parity-check (GLDPC) codes are a class of LDPC codes in which the standard single parity check (SPC) constraints are replaced by constraints defined by a linear block code. These stronger constraints typically result in improved error floor performance, due to better minimum distance and trapping set properties, at a cost of some increased decoding complexity. In this paper, we study spatially coupled generalized low-density parity-check (SC-GLDPC) codes and present a comprehensive analysis of these codes, including: (1) an iterative decoding threshold analysis of SC-GLDPC code ensembles demonstrating capacity approaching thresholds via the threshold saturation effect; (2) an asymptotic analysis of the minimum distance and free distance properties of SC-GLDPC code ensembles, demonstrating that the ensembles are asymptotically good; and (3) an analysis of the finite-length scaling behavior of both GLDPC block codes and SC-GLDPC codes based on a peeling decoder (PD) operating on a binary erasure channel (BEC). Results are compared to GLDPC block codes, and the advantages and disadvantages of SC-GLDPC codes are discussed.

Keywords

Cite

@article{arxiv.1910.14110,
  title  = {Spatially Coupled Generalized LDPC Codes: Asymptotic Analysis and Finite Length Scaling},
  author = {David G. M. Mitchell and Pablo M. Olmos and Michael Lentmaier and Daniel J. Costello},
  journal= {arXiv preprint arXiv:1910.14110},
  year   = {2021}
}

Comments

Revised version submitted to the IEEE Transactions on Information Theory