Sphere bound revisited: A new simulation approach to performance evaluation of binary linear codes over AWGN channels

In this paper, the sphere bound (SB) is revisited within a general bounding framework based on nested Gallager regions. We show that the SB proposed by Herzberg et al. is equivalent to the SB proposed by Kasami et al.. Interestingly, this general framework provides a new way to evaluate the performance of binary linear codes over additive white Gaussian noise (AWGN) channels. This simulation approach relies on only the geometry structure of the code itself. Therefore, simulation results can be used to evaluate not only the performance over AWGN channels but also that over other symmetrical real channels. Numerical results obtained with the new performance evaluation approach are presented.