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Channel Codes by Shu Lin, William Ryan

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8Ensemble Enumerators for Turbo and LDPC Codes

Weight enumerators or weight-enumerating functions are polynomials that represent in a compact way the input and/or output weight characteristics of the encoder for a code. The utility of weight enumerators is that they allow us to easily estimate, via the union bound, the performance of a maximum-likelihood (ML) decoder for the code. Given that turbo and LDPC codes employ suboptimal iterative decoders this may appear meaningless, but it is actually quite sensible for at least two reasons. One reason is that knowledge of ML-decoder performance bounds allows us to weed out weak codes. That is, if a code performs poorly for the ML decoder, we can expect it to perform poorly for an iterative decoder. ...

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