In this paper, we consider linear precoders for Bit-Interleaved Coded Modulation with iterative decoding (BICM-ID) on AWGN channels. In a BICM-ID set-up, the encoder and symbol mapper are separated by an interleaver in order to achieve better performance and to allow a simplified (yet sub-optimal) decoding strategy. However, careful design of the symbol mapper is imperative in order to achieve a satisfactory performance. An alternative solution to the design of the (multi-dimensional) mapper is rendered by inserting a precoder before the symbol mapper. A precoder allows for more flexibility and its design is often less involved than the design of a symbol mapper. Based upon a pairwise error probability (PEP) argument, we derive fairly simple design criteria from which we can easily obtain optimal precoders. Simulation results back our analytical findings.
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