Finite-length analysis of turbo decoding on the binary erasure channel

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. In the first part 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 until 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. In the second part 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