Improved Sphere Bound on the MLD Performance of Binary Linear Block Codes via Voronoi Region

Jia LIU  Meilin HE  Jun CHENG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E100-A   No.12   pp.2572-2577
Publication Date: 2017/12/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory and Techniques
additive white Gaussian noise (AWGN) channel,  binary linear block code,  Gallager's first bounding technique (GFBT),  maximum-likelihood decoding (MLD),  sphere bound,  Voronoi region,  

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In this paper, the Voronoi region of the transmitted codeword is employed to improve the sphere bound on the maximum-likelihood decoding (MLD) performance of binary linear block codes over additive white Gaussian noise (AWGN) channels. We obtain the improved sphere bounds both on the frame-error probability and the bit-error probability. With the framework of the sphere bound proposed by Kasami et al., we derive the conditional decoding error probability on the spheres by defining a subset of the Voronoi region of the transmitted codeword, since the Voronoi regions of a binary linear block code govern the decoding error probability analysis over AWGN channels. The proposed bound improves the sphere bound by Kasami et al. and the sphere bound by Herzberg and Poltyrev. The computational complexity of the proposed bound is similar to that of the sphere bound by Kasami et al.