On the Error Exponents of Improved Tangential Sphere Bounds

The performance of maximum-likelihood (ML) decoded binary linear block codes over the additive white Gaussian noise (AWGN) channel is addressed via the tangential sphere bound (TSB) and two of its recent improved versions. The correspondence is focused on the derivation of the error exponents of these bounds. Although it was shown that some recent improvements of the TSB tighten this bound for finite-length codes, it is demonstrated in this correspondence that their error exponents coincide. For an arbitrary ensemble of binary linear block codes, the common value of these error exponents is explicitly expressed in terms of the asymptotic growth rate of the average distance spectrum