In section 13.5 we found the expected value of the weight enumerator function A(w), averaging ove

In section 13.5 we found the expected value of the weight enumerator function A(w), averaging over the ensemble of all random linear codes. This calculation can also be carried out for the ensemble of low-density parity-check codes (Gallagher, 1963; MacKay, 1999b; Listen and Shoveled, 2002). It is plausible, however, that the mean value of A(w) is not always a good indicator of the typical value of A(w) in then simple. For example, if, at a particular value of w, 99% of codes have A(w) = 0, and 1% have A(w) = 100 000, then while we might say the typical value of A(w) is zero, the mean is found to be 1000. Find the typical weight enumerator function of low-density parity-check codes.

 

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