A proof of threshold saturation for spatially-coupled LDPC codes on BMS channels


Conference Paper

Low-density parity-check (LDPC) convolutional codes have been shown to exhibit excellent performance under low-complexity belief-propagation decoding [1], [2]. This phenomenon is now termed threshold saturation via spatial coupling. The underlying principle behind this appears to be very general and spatially-coupled (SC) codes have been successfully applied in numerous areas. Recently, SC regular LDPC codes have been proven to achieve capacity universally, over the class of binary memoryless symmetric (BMS) channels, under belief-propagation decoding [3], [4]. In [5], [6], potential functions are used to prove that the BP threshold of SC irregular LDPC ensembles saturates, for the binary erasure channel, to the conjectured MAP threshold (known as the Maxwell threshold) of the underlying irregular ensembles. In this paper, that proof technique is generalized to BMS channels, thereby extending some results of [4] to irregular LDPC ensembles. We also believe that this approach can be expanded to cover a wide class of graphical models whose message-passing rules are associated with a Bethe free energy. © 2012 IEEE.

Full Text

Duke Authors

Cited Authors

  • Kumar, S; Young, AJ; Maoris, N; Pfister, HD

Published Date

  • December 1, 2012

Published In

  • 2012 50th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2012

Start / End Page

  • 176 - 184

International Standard Book Number 13 (ISBN-13)

  • 9781467345385

Digital Object Identifier (DOI)

  • 10.1109/Allerton.2012.6483215

Citation Source

  • Scopus