Binary multilevel coset codes based on Reed-Muller codes

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.<
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