On the Convergence Speed of Spatially Coupled LDPC Ensembles Under Window Decoding

TL;DR

This paper investigates the wave-like propagation of information in spatially coupled LDPC codes under window decoding, providing bounds on propagation speed to optimize decoding iterations.

Contribution

It introduces a theoretical analysis of information propagation speed in window decoding for spatially coupled LDPC codes, aiding in efficient decoder design.

Findings

Information propagates at a constant speed under window decoding.

An upper bound for propagation speed on the binary erasure channel is established.

Guidelines for the number of decoding iterations are derived.

Abstract

It is known that windowed decoding (WD) can effectively balance the performance and complexity of spatially coupled low-density parity-check (LDPC) codes. In this study, we show that information can propagate in a wave-like manner at a constant speed under WD. Additionally, we provide an upper bound for the information propagation speed on the binary erasure channel, which can assist in designing the number of iterations required within each window.