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On the interpretation of the APP algorithm as an LLR filter

A channel decoder employing the a posteriori probability (APP) algorithm can be formulated so that its inputs and its outputs are log-likelihood-ratios (LLR): channel LLRs of the code bits are accepted, and a posteriori LLRs of the info bits and/or the code bits are delivered. Since decoding improves the reliability, the APP algorithm can be interpreted as a non-linear filter for LLRs. The "LLR amplification" depends on the distance properties of the channel code; for high signal-to-noise ratios it is dominated by the minimum distance.