A Sphere-Packing Exponent Approximation

The sphere-packing bound represents a suitable tool for assessing the limiting performance of a digital communication system. In fact, most of the modern transmission techniques, adopting capacity approaching codes, such as turbo codes, or Low Density Parity Check (LDPC) codes, may offer a performance that is within 1 dB from the bound, both for Additive White Gaussian Noise (AWGN) and for the fading channel. Unfortunately, the sphere-packing exponent may be difficult to compute, and this may prevent its adoption as a performance estimator. This paper presents and discusses the accuracy of an approximate expression of the bound, that may be used for evaluating the achievable performance of a communication system, without resorting to cumbersome simulations.