The optimum mean-square estimate for decoding binary block codes
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By the use of abstract Fourier analysis on groups, the optimum mean-square-error decoding rule is developed for a fixed block code. The optimum one-to-one coding role to be used with this optimum decoder is derived, and a procedure for simultaneous optimization over both encoding and decoding rules is given. It is shown that there is a linear encoding rule which is optimum. A system which implements the optimum decoding rule is outlined. The major difference between this work and others involving coding for mean-square error is that the decoding rule developed here is a mapping from binary n -tuples directly into the real numbers with the optimization being over all possible mappings into the real numbers. As such the system developed here replaces both the error-correction and digital-to-analog conversion components used in most numerical data transmission systems.
[1] Thomas R. Crimmins,et al. Minimization of mean-square error for data transmitted via group codes , 1969, IEEE Trans. Inf. Theory.
[2] G. C. Clark,et al. PCM Transmission with Minimum Mean-Square Error , 1966 .
[3] Thomas R. Crimmins,et al. Mean-square-error optimum coset leaders for group codes , 1970, IEEE Trans. Inf. Theory.
[4] L. H. Loomis. An Introduction to Abstract Harmonic Analysis , 1953 .