Stochastic Iterative Decoders

Abstract

This paper presents a stochastic algorithm for iterative error control decoding. We show that the stochastic decoding algorithm is an approximation of the sum-product algorithm. When the code's factor graph is a tree, as with trellises, the algorithm approaches maximum a-posteriori decoding. We also demonstrate a stochastic approximations to the alternative update rule known as successive relaxation. Stochastic decoders have very simple digital implementations which have almost no RAM requirements. We present example stochastic decoders for a trellis-based Hamming code, and for a Block Turbo code constructed from Hamming codes.