Pseudocodewords of linear programming decoding of 3-dimensional turbo codes
Pseudocodewords of linear programming decoding of 3-dimensional turbo codes
复制标题
3维turbo码线性规划译码的伪码字
DOI：
10.1109/isit.2011.6033823
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
A. G. Amat
中科院分区：
文献类型：
--
作者：
E. Rosnes;Michael Helmling;A. G. Amat
在这项工作中，我们考虑伪码字（松弛）线性规划（LP）解码的3维Turbo码（3D-TC），最近推出的Berrou等人。在这里，我们考虑二进制3D-TC，而Berrou等人的原始工作考虑双二进制码。本文提出了一种适用于3D-TC的松弛LP译码器，它是对Feldman在其论文中提出的适用于传统Turbo码的松弛LP译码器的改进。这个松弛多面体的顶点是伪码字。我们表明，任何伪码字的支持集是一个停止集的迭代解码的3D-TC使用最大后验成分解码器的二进制擦除信道。此外，我们对小块长度3D-TC进行了数值研究，结果表明，通常最小伪八（在加性白色高斯噪声（AWGN）通道上）小于最小距离和停止距离。特别地，我们基于具有二次逆的整数环上的二次置换多项式对3D-TC（输入块长度K = 128）中的所有交织器对执行穷举搜索。搜索表明，最佳最小AWGN伪八严格小于最佳最小/停止距离。
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.