Bit-optimal decoding of codes whose Tanner graphs are trees

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. (C) 2003 Elsevier Science B.V. All rights reserved.