Computer Science – Information Theory
Scientific paper
2011-03-08
Computer Science
Information Theory
Submitted to the 2011 IEEE International Symposium on Information Theory
Scientific paper
In this work, we consider pseudocodewords of (relaxed) linear programming (LP) decoding of 3-dimensional turbo codes (3D-TCs), recently introduced by Berrou et al.. Here, we consider binary 3D-TCs while the original work of Berrou et al. considered double-binary codes. We present a relaxed LP decoder for 3D-TCs, which is an adaptation of the relaxed LP decoder for conventional turbo codes proposed by Feldman in his thesis. The vertices of this relaxed polytope are the pseudocodewords. We show that the support set of any pseudocodeword is a stopping set of iterative decoding of 3D-TCs using maximum a posteriori constituent decoders on the binary erasure channel. Furthermore, we present a numerical study of small block length 3D-TCs, which shows that typically the minimum pseudoweight (on the additive white Gaussian noise (AWGN) channel) is smaller than both the minimum distance and the stopping distance. In particular, we performed an exhaustive search over all interleaver pairs in the 3D-TC based on quadratic permutation polynomials over integer rings with a quadratic inverse. The search shows that the best minimum AWGN pseudoweight is significantly smaller than the best minimum distance.
Amat Alexandre Graell i.
Helmling Michael
Rosnes Eirik
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