Improved tangential sphere bound on the bit-error probability of concatenated codes

The tangential sphere bound of Poltyrev is a tight upper bound on the word error probability P-W of linear codes with maximum likelihood decoding and is based on the code's distance spectrum. An extension of the TSB to a boun d on bit-error probability P-b is given by Sason/Shitz. In this paper, we i mprove the tangential sphere bound on P-b and apply the new method to some examples. Our comparison to other bounds as well as to simulation results s hows an improved tightness, particularly for signal-to-noise ratios below t he value corresponding to the computational cutoff rate R-o.