AWGN coding theorems from ensemble weight enumerators
D. Divsalar, Samuel J. Dolinar, H. Jin, Robert J. McEliece · 2002
We develop AWGN coding theorems for ensembles of codes for which we can calculate, or at least closely estimate, the ensemble weight enumerator. As a rule, for such an ensemble we can find a threshold c such that if E/sub b//N/sub 0/>c, then the ensemble maximum-likelihood error probability approaches zero. This threshold is always better, and usually much better, than can be obtained from the union bound. The role of low-weight code words is the key.