Turbo stopping sets: the uniform interleaver and efficient enumeration

The performance of turbo decoding on the binary erasure channel (BEC) can be characterized in terms of turbo stopping sets. 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. The concept of turbo stopping sets is an adaptation of stopping sets from the theory of iterative belief-propagation (BP) decoding of low-density parity-check (LDPC) codes. The main results in this work are 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