Bit-optimal decoding of codes whose Tanner graphs are trees

Authors:
E. Soljanin;E. Offer
Affiliations:
Bell Laboratories, Lucent Technologies, 700 Mountain Avenue room 2C-177, Murray Hill, NJ;Institute of Comm. Eng., Munich University of Technology, 80290 Munich, Germany
Venue:
Discrete Applied Mathematics - Special issue: International workshop on coding and cryptography (WCC 2001)
Year:
2003

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Abstract

We introduce a group algebra formulation for bit-optimal decoding of binary block codes. We use this new framework to give a simple algebraic proof that Pearl's and Gallager's belief propagation decoding algorithms are bit-optimal when the Tanner graph of the code is a tree. We believe that these derivations of known results give new insights into the issues of decoding on graphs from the algebraic coding theorist's point of view.