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

David G.M. Mitchell, Pablo M. Olmos, Michael Lentmaier, Daniel J. Costello

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)3708 - 3723
Number of pages16
JournalIEEE Transactions on Information Theory
Volume67
Issue number6
Early online date2021
DOIs
Publication statusPublished - 2021 Jun 1

Subject classification (UKÄ)

  • Other Electrical Engineering, Electronic Engineering, Information Engineering

Keywords

  • Block codes
  • Complexity theory
  • Convolutional codes
  • Electronic mail
  • finite length scaling
  • Generalized LDPC codes
  • Iterative decoding
  • iterative decoding thresholds
  • Maximum likelihood decoding
  • Message passing
  • minimum distance
  • spatially coupled codes

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