  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.
