Turbo Decoding on the Binary Erasure Channel: Finite-Length Analysis and Turbo Stopping Sets

TL;DR

This paper analyzes turbo decoding over the binary erasure channel, introducing turbo stopping sets, exact failure conditions, and improved decoding algorithms with better error performance, supported by theoretical analysis and simulations.

Contribution

It adapts the concept of stopping sets to turbo decoding on the BEC, providing exact failure conditions and proposing improved algorithms with enhanced error performance.

Findings

Turbo stopping sets characterize decoding failure.

Improved turbo decoding algorithm shows better error performance.

An enumeration algorithm for small turbo stopping sets is developed.

Abstract

This paper is devoted to the finite-length analysis of turbo decoding over the binary erasure channel (BEC). The performance of iterative belief-propagation (BP) decoding of low-density parity-check (LDPC) codes over the BEC can be characterized in terms of stopping sets. We describe turbo decoding on the BEC which is simpler than turbo decoding on other channels. We then adapt the concept of stopping sets to turbo decoding and state an exact condition for decoding failure. Apply turbo decoding until the transmitted codeword has been recovered, or the decoder fails to progress further. Then the set of erased positions that will remain when the decoder stops is equal to the unique maximum-size turbo stopping set which is also a subset of the set of erased positions. Furthermore, we present some improvements of the basic turbo decoding algorithm on the BEC. The proposed improved turbo decoding algorithm has substantially better error performance as illustrated by the given simulation results. Finally, we give an expression for the turbo stopping set size enumerating function under the uniform interleaver assumption, and an efficient enumeration algorithm of small-size turbo stopping sets for a particular interleaver. The solution is based on the algorithm proposed by Garello et al. in 2001 to compute an exhaustive list of all low-weight codewords in a turbo code.