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

The tangential sphere bound (TSB) of Poltyrev (1994) 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 bound on the bit-error probability P_b is given by Sason/Shitz (see IEEE Trans. Inform. Theory, vol.46, p.24-47, 2000). We improve 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 shows an improved tightness, particularly for signal-to-noise ratios below the value corresponding to the computational cutoff rate R_o