| 摘要 |
The Conway-Sloane decoding method presents a general premise that for any given highly complex block code, an attempt should be made to find a subcode of that given block code that is less complex to decode. The given complex block code may then be maximum likelihood decoded with reduced complexity by cycling over the subcode and its cosets. Extending this general premise to Reed-Muller codes, and in particular to a second order Reed-Muller (or Kerdock) code, reduced maximum likelihood decoding complexity is obtained by cycling over a found subcode (and its cosets) of the second order Reed-Muller (or Kerdock) code. A first order Reed-Muller code comprises just such a suitable subcode which, like the parity check for the Golay codes analyzed by Conway and Sloane, has a known less complex maximum likelihood decoding solution utilizing a fast Hadamard Transform.
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