A simple proof of threshold saturation for coupled scalar recursions


Conference Paper

Low-density parity-check (LDPC) convolutional codes (or spatially-coupled codes) have been shown to approach capacity on the binary erasure channel (BEC) and binary-input memoryless symmetric channels. The mechanism behind this spectacular performance is the threshold saturation phenomenon, which is characterized by the belief-propagation threshold of the spatially-coupled ensemble increasing to an intrinsic noise threshold defined by the uncoupled system. In this paper, we present a simple proof of threshold saturation that applies to a broad class of coupled scalar recursions. The conditions of the theorem are verified for the density-evolution (DE) equations of irregular LDPC codes on the BEC, a class of generalized LDPC codes, and the joint iterative decoding of LDPC codes on intersymbol-interference channels with erasure noise. Our approach is based on potential functions and was motivated mainly by the ideas of Takeuchi et al. The resulting proof is surprisingly simple when compared to previous methods. © 2012 IEEE.

Full Text

Duke Authors

Cited Authors

  • Yedla, A; Jian, YY; Nguyen, PS; Pfister, HD

Published Date

  • December 14, 2012

Published In

Start / End Page

  • 51 - 55

Electronic International Standard Serial Number (EISSN)

  • 2165-4719

International Standard Serial Number (ISSN)

  • 2165-4700

International Standard Book Number 13 (ISBN-13)

  • 9781457721151

Digital Object Identifier (DOI)

  • 10.1109/ISTC.2012.6325197

Citation Source

  • Scopus