Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 60, Issue 12, Pages 7389-7415Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2014.2360692
Keywords
Convolutional LDPC codes; density evolution; entropy functional; potential functions; spatial coupling; threshold saturation
Funding
- National Science Foundation [0747470, 1320924]
- Swiss National Foundation [200020-140388]
- Swiss National Science Foundation (SNF) [200020_140388] Funding Source: Swiss National Science Foundation (SNF)
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1320924, 0747470] Funding Source: National Science Foundation
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Spatially-coupled low-density parity-check (LDPC) codes, which were first introduced as LDPC convolutional codes, have been shown to exhibit excellent performance under low-complexity belief-propagation decoding. This phenomenon is now termed threshold saturation via spatial coupling. Spatially-coupled codes have been successfully applied in numerous areas. In particular, it was proven that spatially-coupled regular LDPC codes universally achieve capacity over the class of binary memoryless symmetric (BMS) channels under belief-propagation decoding. Recently, potential functions have been used to simplify threshold saturation proofs for scalar and vector recursions. In this paper, potential functions are used to prove threshold saturation for irregular LDPC and low-density generator-matrix codes on BMS channels, extending the simplified proof technique to BMS channels. The corresponding potential functions are closely related to the average Bethe free entropy of the ensembles in the large-system limit. These functions also appear in statistical physics when the replica method is used to analyze optimal decoding.
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