Polar Coding for Bit-Interleaved Coded Modulation

Abstract

A polar coding scheme is proposed for reliable communication over channels with bit-interleaved coded modulation (BICM). In an ideal information-theoretic model, BICM schemes are modeled as a set of multiple binary-input channels that experience different reliabilities. This model is referred to as multichannel. The conventional scheme for encoding information over multi-channels is to encode separately across the individual constituent channels, which requires multiple encoders and decoders. As opposed to the conventional scheme, we take advantage of the recursive structure of polar codes to construct a unified compound polar code. The proposed scheme has a single encoder and decoder and can be used over multi-channels, in particular over channels with BICM. We prove that the scheme achieves the multi-channel capacity with the same error decay rate as in Arıkan's polar codes. Furthermore, due to more levels of channel polarization, we obtain a better finite block length performance compared with the separated polarization scheme. This is confirmed through various simulations over the binary erasure channel and with transmissions over additive white Gaussian noise (AWGN) and fast fading channels with BICM and different modulation orders.