On the Error Exponents of Some Improved Tangential-Sphere Bounds

Details On the Error Exponents of Some Improved Tangential-Sphere Bounds On the Error Exponents of Some Improved Tangential-Sphere Bounds

2006-07-02

arxiv.org/abs/cs/0607004v2

Computer Science

Information Theory

Submitted to the IEEE Trans. on Information Theory (as a correspondence), March 2006. Revised (August 2006)

Scientific paper

The performance of maximum-likelihood (ML) decoded binary linear block codes over the AWGN channel is addressed via the tangential-sphere bound (TSB) and two of its recent improved versions. The paper is focused on the derivation of the error exponents of these bounds. Although it was exemplified that some recent improvements of the TSB tighten this bound for finite-length codes, it is demonstrated in this paper 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.

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