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This report presents the most recent results of an investigation into the complexity of decoding error-correcting codes and the development of efficient and practical decoding techniques. The most important result has been the discovery of a new general mathematical framework in which digital decoding and analog demodulation become special cases of a more general class of decoding-demodulation functions. Although we have only just begun to explore the many possibilities opened up by this discovery, results of practical importance have already been produced, including an optimum soft-decision symbol-by-symbol decoding algorithm for linear codes whose complexity varies inversely with code rate. (Author)