It is shown that soft maximum-likelihood decoding for block-coded modu
lation (BCM) can be performed using the code tree. It is easy to gener
ate the code tree for any type of block code, linear as well as nonlin
ear. A reduce tree is obtained from the code tree. The trellis for a b
lock code can be obtained from the reduced tree. Using this structure
to perform computations in parallel, a scheme is proposed for the impl
ementation of the soft decoder. Back tracking, necessary in a soft dec
oder using the Viterbi algorithm on a trellis, is eliminated.