Optimum decision methods are employed to discriminate between in-sync and out-of-sync operations in Viterbi decoders when the received data sequence is given in analog form (soft decisions). The exact solution to this discrimination problem, however, appears too complex in many practical cases. A suboptimum algorithm is then proposed that can be implemented as a hardware device, external to the decoder. This algorithm is recognized as a modified version of an earlier technique known as the "reencoding method". Analysis and simulations indicate that the modification produces remarkably good results not only in comparison with the reencoding method but also with previous techniques discussed in literature.>

We study the construction and decoding of binary multilevel coset codes. This construction, originally introduced by Blokh and Zyablov in 1974 and by Zinov'ev in 1976, shows remarkable analogies with most recent schemes of coded modulations. Basic elements of the construction are an inner code, head of a partition chain having suitable distance properties, and a set of outer codes, generally nonbinary. For each partition level there is an outer code whose alphabet has the same order of the partition: in this way it is possible to associate every partition subset to a code symbol. It is well known that these codes can be efficiently decoded by the so called "multistage decoding." We show that good codes (in terms of performance/complexity) can be constructed using Reed-Muller (RM) codes as inner codes. To this aim RM codes are revisited in the framework of the above construction and decoding techniques. In particular we describe a family of decoders for RM codes which include Forney's (1988) and Hemmati's (1989) decoders as special cases. Finally, we present some examples of efficient binary codes based on RM codes, and assess their performance via computer simulation.>