Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes

• In this paper, we consider pseudocodewords of (relaxed) linear programming (LP) decoding of 3-dimensional turbo codes (3D-TCs). We present a relaxed LP decoder for 3D-TCs, adapting the relaxed LP decoder for conventional turbo codes proposed by Feldman in his thesis. We show that the 3D-TC polytope is proper and $C$-symmetric and make a connection to finite graph covers of the 3D-TC factor graph. This connection is used to 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 compute ensemble-average pseudoweight enumerators of 3D-TCs and perform a finite-length minimum pseudoweight analysis for small cover degrees. Moreover, an explicit description of the fundamental cone of the 3D-TC polytope is given. Finally, we present an extensive numerical study of small-to-medium block length 3D-TCs, which shows that 1) typically (i.e., in most cases), when the minimum distance $d_{min}$ and/or the stopping distance $h_{min}$ is high, the minimum pseudoweight (on the additive white Gaussian noise channel) is strictly smaller than both $d_{min}$ and $h_{min}$ and that 2) the minimum pseudoweight grows with the block length, at least for small-to-medium block lengths.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Kommunikationssystem (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Communication Systems (hsv//eng)

Publikations- och innehållstyp

art (ämneskategori)

ref (ämneskategori)