Pseudocodewords of linear programming decoding of 3-dimensional turbo codes
Paper in proceedings, 2011

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 (with input block length K = 128) based on quadratic permutation polynomials over integer rings with a quadratic inverse. The search shows that the best minimum AWGN pseudoweight is strictly smaller than the best minimum/stopping distance.

Author

Eirik Rosnes

University of Bergen

Michael Helmling

Fraunhofer-Institut fur Techno- und Wirtschaftsmathematk

Alexandre Graell i Amat

Chalmers, Signals and Systems, Communication and Antenna Systems, Communication Systems

IEEE International Symposium on Information Theory - Proceedings

21578095 (ISSN)

1643-1647 6033823

Subject Categories

Computer and Information Science

DOI

10.1109/ISIT.2011.6033823

More information

Latest update

5/17/2019