Spatially coupled generalized LDPC codes: asymptotic analysis and finite length scaling Articles uri icon

publication date

  • June 2021

start page

  • 3708

end page

  • 3723

issue

  • 6

volume

  • 67

International Standard Serial Number (ISSN)

  • 0018-9448

Electronic International Standard Serial Number (EISSN)

  • 1557-9654

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

  • generalized ldpc codes; spatially coupled codes; iterative decoding thresholds; minimum distance; finite length scaling