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

Abstract

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.