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BSC Thresholds for Code Ensembles Based on “Typical Pairs” Decoding

Aji, Srinivas and Jin, Hui and Khandekar, Aamod and MacKay, David J. C. and McEliece, Robert J. (2001) BSC Thresholds for Code Ensembles Based on “Typical Pairs” Decoding. In: Codes, Systems, and Graphical Models. IMA Volumes in Mathematics and its Applications. No.123. Springer , New York, NY, pp. 195-210. ISBN 978-0-387-95173-7.

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In this paper, we develop a method for closely estimating noise threshold values for ensembles of binary linear codes on the binary symmetric channel. Our method, based on the “typical pairs” decoding algorithm pioneered by Shannon, completely decouples the channel from the code ensemble. In this, it resembles the classical union bound, but unlike the union bound, our method is powerful enough to prove Shannon’s theorem for the ensemble of random linear codes. We apply our method to find numerical thresholds for the ensembles of low-density parity-check codes, and “repeat-accumulate” codes.

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Additional Information:© 2001 Springer-Verlag New York, Inc. The work of Aji, Jin, Khandekar, and McEliece on this paper was supported by NSF grant no. CCR-9804793, and grants from Sony, Qualcomm, and Caltech's Lee Center for Advanced Networking. David Mackay’s work is supported by the Gatsby Charitable Foundation.
Funding AgencyGrant Number
Sony CorporationUNSPECIFIED
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
Gatsby Charitable FoundationUNSPECIFIED
Subject Keywords:Linear Code; LDPC Code; Typical Pair; Weight Enumerator; Iterative Decode
Series Name:IMA Volumes in Mathematics and its Applications
Issue or Number:123
Record Number:CaltechAUTHORS:20200204-145114201
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101118
Deposited By: Tony Diaz
Deposited On:04 Feb 2020 22:59
Last Modified:16 Nov 2021 17:59

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