On Computing Shannon’s Sphere Packing Bound and Applications

Abstract

A new method to numerically evalu- ate Shannon’s lower bound is presented in this pa- per. This new method is based on the Incomplete Beta function and permits the exact evaluation of the Sphere Packing Bound for a large range of code sizes, rates and probability of error. Comparisons with cur- rent standards (DVB–RCS, DVB–S2 and 3GPP) are also presented and discussed. It is shown that cur- rent standard coding schemes are about 0.6dB from the Shannon Limit corrected for Binary Signalling.