On the Performance of Sphere Decoding of Block Codes

The performance of sphere decoding of block codes over a variety of channels is investigated. We derive a tight bound on the performance of maximum likelihood decoding of linear codes on q-ary symmetric channels. We use this result to bound the performance of q-ary hard decision sphere decoders. We also derive a tight bound on the performance of soft decision sphere decoders on the AWGN channel for BPSK and M-PSK modulated block codes. The performance of soft decision sphere decoding of arbitrary finite lattices or block codes is also analyzed