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Minimum Pseudoweight Analysis of 3-Dimensional Turbo Codes

Eirik Rosnes ; Michael Helmling ; Alexandre Graell i Amat (Institutionen för signaler och system, Kommunikationssystem)
IEEE Transactions on Communications (0090-6778). Vol. 62 (2014), 7, p. 2170-2182.
[Artikel, refereegranskad vetenskaplig]

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.



Denna post skapades 2014-07-21. Senast ändrad 2016-06-30.
CPL Pubid: 200622

 

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Institutioner (Chalmers)

Institutionen för signaler och system, Kommunikationssystem

Ämnesområden

Kommunikationssystem

Chalmers infrastruktur