Cycle length distributions in graphical models for iterative decoding

Abstract

This paper analyses the distribution of cycle lengths in turbo decoding graphs. It is known that the widely-used iterative decoding algorithm for turbo codes is in fact a special case of a quite general local message-passing algorithm for efficiently computing posterior probabilities in acyclic directed graphical (ADG) models (also known as "belief networks"). However, this local message-passing algorithm in theory only works for graphs with no cycles. Why it works in practice (i.e., performs near-optimally in terms of bit decisions) on ADGs for turbo codes is not well understood since turbo decoding graphs can have many cycles.