Bit-Interleaved Coded Modulation

Abstract

The principle of coding in the signal space follows directly from Shannon's analysis of waveform Gaussian channels subject to an input constraint. The early design of communication systems focused separately on modulation, namely signal design and detection, and error correcting codes, which deal with errors introduced at the demodulator of the underlying waveform channel. The correct perspective of signalspace coding, although never out of sight of information theorists, was brought back into the focus of coding theorists and system designers by Imai's and Ungerböck's pioneering work on coded modulation. More recently, powerful families of binary codes with a good tradeoff between performance and decoding complexity have been (re-) discovered. Bit-Interleaved Coded Modulation (BICM) is a pragmatic approach combining the best out of both worlds: it takes advantage of the signal-space coding perspective, whilst allowing for the use of powerful families of binary codes with virtually any modulation format.BICM avoids the need for the complicated and somewhat less flexible design typical of coded modulation. As a matter of fact, most of today's systems that achieve high spectral efficiency such as DSL, Wireless LANs, WiMax and evolutions thereof, as well as systems based on low spectral efficiency orthogonal modulation, feature BICM, making BICM the de-facto general coding technique for waveform channels. The theoretical characterization of BICM is at the basis of efficient coding design techniques and also of improved BICM decoders, e.g., those based on the belief propagation iterative algorithm and approximations thereof. In this monograph, we review the theoretical foundations of BICM under the unified framework of error exponents for mismatched decoding. This framework allows an accurate analysis without any particular assumptions on the length of the interleaver or independence between the multiple bits in a symbol. We further consider the sensitivity of the BICM capacity with respect to the signal-to-noise ratio (SNR), and obtain a wideband regime (or low-SNR regime) characterization. We review efficient tools for the error probability analysis of BICM that go beyond the standard approach of considering infinite interleaving and take into consideration the dependency of the coded bit observations introduced by the modulation. We also present bounds that improve upon the union bound in the region beyond the cutoff rate, and are essential to characterize the performance of modern randomlike codes used in concatenation with BICM. Finally, we turn our attention to BICM with iterative decoding, we review extrinsic information transfer charts, the area theorem and code design via curve fitting. We conclude with an overview of some applications of BICM beyond the classical coherent Gaussian channel.6 Applications 122 6.

Capacity-Achieving Sparse Superposition Codes via Approximate Message Passing Decoding

“…Finally, we mention that bit-interleaved coded modulation [24] is a technique widely used for communication over AWGN channels. Some alternative approaches to designing high-rate codes for the AWGN channel are low-density lattice codes [25] and the recently proposed polar lattices [26].…”

Underwater Optical Wireless Communications in Swarm Robotics: A Tutorial

“…In order to improve the spectral efficiency, it is advisable to combine channel coding with the modulation scheme. In bitinterleaved coded modulation (BICM), the channel encoder is separated from the modulator by a bit-wise interleaver [95]. Consequently, a serial concatenated coding scheme arises.…”

Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

“…Coded modulation (CM), which combines multi-level modulation with forward error correction (FEC), is indispensable for digital communication strategies targeting high transmission rates. To realize CM, different techniques have been proposed in the literature, such as multilevel coding (MLC) [ 1 , 2 ], trellis CM [ 3 ], and bit-interleaved CM (BICM) [ 4 , 5 , 6 , 7 , 8 ]. Among the many proposed CM architectures, the de-facto standard is to combine a high-order modulation format with a binary FEC code using a binary labeling strategy, frequently in the absence of an interleaver, and to use bit-metric decoding (BMD) at the receiver [ 7 ], which corresponds to the BICM paradigm.…”