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Improved Sphere Bound on the MLD Performance of Binary Linear Block Codes via Voronoi Region
Jia LIU Meilin HE Jun CHENG
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E100A
No.12
pp.25722577 Publication Date: 2017/12/01
Online ISSN: 17451337
DOI: 10.1587/transfun.E100.A.2572
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications) Category: Coding Theory and Techniques Keyword: additive white Gaussian noise (AWGN) channel, binary linear block code, Gallager's first bounding technique (GFBT), maximumlikelihood decoding (MLD), sphere bound, Voronoi region,
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Summary:
In this paper, the Voronoi region of the transmitted codeword is employed to improve the sphere bound on the maximumlikelihood decoding (MLD) performance of binary linear block codes over additive white Gaussian noise (AWGN) channels. We obtain the improved sphere bounds both on the frameerror probability and the biterror 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.

