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Probability Density Function of Reliability Metrics in BICM with Arbitrary Modulation: Closed-form through Algorithmic Approach

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3 Author(s)
Szczecinski, L. ; Inst. Nat. de la Rech. Sci., Quebec Univ., Montreal, QC ; Bettancourt, R. ; Feick, R.

In the popular bit-interleaved coded modulation (BICM) the output of the channel encoder and the input of the modulator are separated by a bit-level interleaver. From the decoder's point of view, the modulator, the transmission channel, and the demodulator (calculating bits' reliability metrics) become a memoryless BICM channel with binary inputs and real outputs. In unfaded channels, the BICM channel's outputs (reliability metrics) are known to be Gaussian for binary- or quaternary phase shift keying but their probability density function (PDF) is not known for higher-order modulation. We fill this gap by presenting an algorithmic method to calculate closed-form expressions for the PDF of reliability metrics in BICM with arbitrary modulation and bits-to-symbol mapping when the so-called max-log approximation is applied. Such probabilistic description of BICM channel is useful to analyze, from an information- theoretic point of view, any BICM constellation/mapping design.

Published in:

Communications, IEEE Transactions on  (Volume:56 ,  Issue: 5 )