Mapping optimization for the map turbo-detector with channel estimation

In this paper, we consider a bit interleaved coded modulation (BIC M) scheme over a frequency selective channel. At the receiver, a turbo-detector composed of a maximum a posteriori (MAP) equalizer, and a MAP decoder is used. The channel is supposed to be unknown at the receiver and estimated using pilot symbols. The aim of the paper is to optimize the mapping between the coded bits and the transmitted modulated symbols in this context. To do this, we derive an upper bound of the bit error probability (BEP) at the output of the equalizer fed with a priori information from the decoder and with the channel estimation. We then give an analytical approximate expression of this BEP when the a priori information provided by the decoder is reliable (most errors at the output of the equalizer are isolated). We propose to find the mapping minimizing this expression. Since an exhaustive search is very complicated when the modulation order is high, we propose to approach the solution using the Binary Switching Algorithm (BSA).