A simple proof of threshold saturation for coupled vector recursions

Published

Conference Paper

Convolutional low-density parity-check (LDPC) codes (or spatially-coupled codes) have now been shown to achieve capacity on binary-input memoryless symmetric channels. The principle behind this surprising result is the threshold-saturation phenomenon, which is defined by the belief-propagation threshold of the spatially-coupled ensemble saturating to a fundamental threshold defined by the uncoupled system. Previously, the authors demonstrated that potential functions can be used to provide a simple proof of threshold saturation for coupled scalar recursions. In this paper, we present a simple proof of threshold saturation that applies to a wide class of coupled vector recursions. The conditions of the theorem are verified for the density-evolution equations of: (i) joint decoding of irregular LDPC codes for a Slepian-Wolf problem with erasures, (ii) joint decoding of irregular LDPC codes on an erasure multiple-access channel, and (iii) admissible protograph codes on the BEC. This proves threshold saturation for these systems. © 2012 IEEE.

Full Text

Duke Authors

Cited Authors

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

Published Date

  • December 1, 2012

Published In

  • 2012 Ieee Information Theory Workshop, Itw 2012

Start / End Page

  • 25 - 29

International Standard Book Number 13 (ISBN-13)

  • 9781467302234

Digital Object Identifier (DOI)

  • 10.1109/ITW.2012.6404671

Citation Source

  • Scopus