| Abstract: | We introduce the concept of weighted-output decoding, which enables us to perform many successive decodings without information loss. The design of a coding system for the additive white Gaussian channel can thus be viewed as a means for combining many simple codes. We illustrate this concept by the example of parity-check codes which are combined according to Elias' iterated product. Examination of the performance thus obtained leads us to criticize the conventional minimal distance criterion and to propose as a criterion a proximity measure of the weight distribution of the code with respect to the binomial one. According to this point of view, the iterated product of parity-check codes appears as a means of decimation of the set of n-tuples. |
