This paper derives an improved sphere-packing (ISP) bound targeting codes ofshort to moderate block lengths. We first review the 1967 sphere-packing (SP67)bound for discrete memoryless channels, and a recent improvement by Valemboisand Fossorier. These concepts are used for the derivation of a new lower boundon the decoding error probability (referred to as the ISP bound) which isuniformly tighter than the SP67 bound and its recent improved version. Under amild condition, the ISP bound is applicable to general memoryless channels, andsome of its applications are exemplified. Its tightness is studied by comparingit with bounds on the ML decoding error probability. It is exemplified that theISP bound suggests an interesting alternative to the 1959 sphere-packing (SP59)bound of Shannon for the Gaussian channel, especially for digital modulationsof high spectral efficiency.
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