Abstract：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.
2018, Vol. 31 
