Performance of Sphere Decoding of Block Codes

A sphere decoder searches for the closest lattice point within a certain search radius. The search radius provides a tradeoff between performance and complexity. We focus on analyzing the performance of sphere decoding of linear block codes. We analyze the performance of soft-decision sphere decoding on AWGN channels and a variety of modulation schemes. A hard-decision sphere decoder is a bounded distance decoder with the corresponding decoding radius. We analyze the performance of hard-decision sphere decoding on binary and q-ary symmetric channels. An upper bound on the. performance of maximum-likelihood decoding of linear codes defined over F-q (e.g. Reed-Solomon codes) and transmitted over q-ary symmetric channels is derived and used in the analysis. We then discuss sphere decoding of general block codes or lattices with arbitrary modulation schemes. The tradeoff between the performance and complexity of a sphere decoder is then discussed.