Spatially Coupled Generalized LDPC Codes: Asymptotic Analysis and Finite Length Scaling
arXiv:1910.14110 · doi:10.1109/TIT.2021.3071743
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.
arXiv commentRevised version submitted to the IEEE Transactions on Information Theory
References in corpus (9)
- Threshold Saturation via Spatial Coupling: Why Convolutional LDPC Ensembles Perform so well over the BEC
- Staircase Codes: FEC for 100 Gb/s OTN
- Spatially Coupled LDPC Codes Constructed from Protographs
- Windowed Decoding of Protograph-based LDPC Convolutional Codes over Erasure Channels
- A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes
- On the Minimum Distance of Generalized Spatially Coupled LDPC Codes
- Design of LDPC Code Ensembles with Fast Convergence Properties
- A Probabilistic Peeling Decoder to Efficiently Analyze Generalized LDPC Codes Over the BEC
- A Refined Scaling Law for Spatially Coupled LDPC Codes Over the Binary Erasure Channel