The parameterized Gallager’s first bounds based on conditional triplet-wise error probability

Jia Liu

Mathematics and Computers in Simulation (MATCOM), 2019, vol. 163, issue C, 32-46

Abstract: In this paper, the conditional triplet-wise error probability is proposed to improve Gallager’s first bounds based on the general framework of parameterized Gallager’s first bounding technique (GFBT) of binary linear block codes over additive white Gaussian noise (AWGN) channels, which can alleviate the repeated accumulations caused by the use of the pair-wise error probability. Within the recently proposed bounding framework based on nested Gallager regions, three well-known upper bounds, namely, the sphere bound (SB) of Herzberg and Poltyrev, the tangential bound (TB) of Berlekamp, and the tangential-sphere bound (TSB) of Poltyrev, are visited. Within the proposed bounding framework based on conditional triplet-wise error probability, the three well-known bounds can be improved by exploring more detailed geometrical structure of the code when upper bounding the error probabilities. Numerical results show that the proposed bounding framework is useful since the proposed bounds can even improve the TSB, which is considered as one of the tightest upper bounds.

Keywords: Additive white Gaussian noise (AWGN) channel; Gallager’s first bounding technique (GFBT); Maximum-likelihood (ML) decoding; Parameterized GFBT; Triplet-wise error probability (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:163:y:2019:i:c:p:32-46

DOI: 10.1016/j.matcom.2019.02.005

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