Bit-Interleaved Coded Modulation

• Authors: Albert Guillén i Fàbregas;Alfonso Martinez;Giuseppe Caire
• Venue: Foundations and Trends in Communications and Information Theory
• Year: 2008

The principle of coding in the signal space follows directlyfrom Shannon's analysis of waveform Gaussian channels subject to aninput constraint. The early design of communication systems focusedseparately on modulation, namely signal design anddetection, and error correcting codes, which deal witherrors introduced at the demodulator of the underlying waveformchannel. The correct perspective of signal-space coding, althoughnever out of sight of information theorists, was brought back intothe focus of coding theorists and system designers by Imai's andUngerböck's pioneering works on coded modulation. Morerecently, powerful families of binary codes with a good tradeoffbetween performance and decoding complexity have been(re-)discovered. Bit-Interleaved Coded Modulation (BICM) is apragmatic approach combining the best out of both worlds: it takesadvantage of the signal-space coding perspective, whilst allowingfor the use of powerful families of binary codes with virtually anymodulation format. BICM avoids the need for the complicated andsomewhat less flexible design typical of coded modulation. As amatter of fact, most of today's systems that achieve high spectralefficiency such as DSL, Wireless LANs, WiMax and evolutionsthereof, as well as systems based on low spectral efficiencyorthogonal modulation, feature BICM, making BICM thede-facto general coding technique for waveform channels.The theoretical characterization of BICM is at the basis ofefficient coding design techniques and also of improved BICMdecoders, e.g., those based on the belief propagation iterativealgorithm and approximations thereof. In this text, we review thetheoretical foundations of BICM under the unified framework oferror exponents for mismatched decoding. This framework allows anaccurate analysis without any particular assumptions on the lengthof the interleaver or independence between the multiple bits in asymbol. We further consider the sensitivity of the BICM capacitywith respect to the signal-to-noise ratio (SNR), and obtain awideband regime (or low-SNR regime) characterization. We reviewefficient tools for the error probability analysis of BICM that gobeyond the standard approach of considering infinite interleavingand take into consideration the dependency of the coded bitobservations introduced by the modulation. We also present boundsthat improve upon the union bound in the region beyond the cutoffrate, and are essential to characterize the performance of modernrandomlike codes used in concatenation with BICM. Finally, we turnour attention to BICM with iterative decoding, we review extrinsicinformation transfer charts, the area theorem and code design viacurve fitting. We conclude with an overview of some applications ofBICM beyond the classical coherent Gaussian channel.