Stochastic Iterative Decoders

TL;DR

This paper introduces a simple, low-memory stochastic decoding algorithm that approximates the sum-product algorithm and approaches MAP decoding on tree-structured codes, demonstrated on Hamming and Turbo codes.

Contribution

It proposes a novel stochastic iterative decoding method that simplifies implementation and approximates optimal decoding, extending to various code structures.

Findings

Decoding performance closely approaches MAP decoding on tree codes.

Stochastic decoders require minimal RAM and are easy to implement.

Effective for Hamming and Turbo codes.

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.