二进制线性分组码球形界的深入研究（英文）

在二进制线性分组码的最大似然译码错误概率的性能分析上，紧致可分析的上界技术起到了兼具理论与实用价值的作用．采用余弦定理及三个码字组成一个非钝角三角形的理论，详细地证明了Ｋａｓａｍｉ等人提出的球形界（很少被引用）等价于Ｈｅｒｚｂｅｒｇ和Ｐｏｌｔｙｒｅｖ提出的球形界，并分析对比了两者的计算复杂度．结果表明：Ｋａｓａｍｉ等人提出的球形界属于Ｇａｌｌａｇｅｒ第一上界技术，并且相比于Ｈｅｒｚｂｅｒｇ和Ｐｏｌｔｙｒｅｖ提出的球形界，具有较低的计算复杂度，可以更高效地应用在高信噪比和高维码（Ｔｕｒｂｏ码和低密度奇偶校验码）的性能分析中.

Further result on the sphere bound of binary linear block codes

Tight analytical upper bounds served as a useful theoretical and engineering tool for evaluating the performance of maximum-likelihood decoded (MLD) binary linear block codes, the law of cosines and the fact that any three codewords forming a non-obtuse triangle were employed.The sphere bound proposed by Kasami et al, which was rarely cited in the literatures, was derived in a detailed way to be equivalent to the sphere bound proposed by Herzberg and Poltyrev.The computation complexity of the two bounds was also analysed.The results showed that the sphere bound proposed by Kasami et al was based on Gallager’s first bounding technique (GFBT) and had a lower computation complexity, which could be more efficiently used in high signal-to-noise ratio (SNR) and on the performance analysis for the codes, such as Turbo code and low density parity check code (LDPC) code.