Zehavi (1992) showed that the performance of coded modulation over a Rayleigh fading channel can be improved by bit-wise interleaving the encoder output and by using an appropriate soft-decision metric as an input to a Viterbi decoder. The goal of this paper is to present in a comprehensive fashion the theory underlying bit-interleaved coded modulation, to provide tools for evaluating its performance, and to give guidelines for its design.

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Bit-Interleaved Coded Modulation

Maximum-likelihood (ML) decoding algorithms for Gaussian multiple-input multiple-output (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using number-theoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the Viterbo-Boutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the Schnorr-Euchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a near-ML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.

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On maximum-likelihood detection and the search for the closest lattice point

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 signal-space 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 Ungerbock's pioneering works 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 text, 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.

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The availability of location information has become a key factor in today's communications systems allowing location based services. In outdoor scenarios, the mobile terminal position is obtained with high accuracy thanks to the global positioning system (GPS) or to the standalone cellular systems. However, the main problem of GPS and cellular systems resides in the indoor environment and in scenarios with deep shadowing effects where the satellite or cellular signals are broken. In this paper, we survey different technologies and methodologies for indoor and outdoor localization with an emphasis on indoor methodologies and concepts. Additionally, we discuss in this review different localization-based applications, where the location information is critical to estimate. Finally, a comprehensive discussion of the challenges in terms of accuracy, cost, complexity, security, scalability, etc. is given. The aim of this survey is to provide a comprehensive overview of existing efforts as well as auspicious and anticipated dimensions for future work in indoor localization techniques and applications.

Recent Advances in Indoor Localization: A Survey on Theoretical Approaches and Applications

The emerging massive/large-scale multiple-input multiple-output (LS-MIMO) systems that rely on very large antenna arrays have become a hot topic of wireless communications. Compared to multi-antenna aided systems being built at the time of this writing, such as the long-term evolution (LTE) based fourth generation (4G) mobile communication system which allows for up to eight antenna elements at the base station (BS), the LS-MIMO system entails an unprecedented number of antennas, say 100 or more, at the BS. The huge leap in the number of BS antennas opens the door to a new research field in communication theory, propagation and electronics, where random matrix theory begins to play a dominant role. Interestingly, LS-MIMOs also constitute a perfect example of one of the key philosophical principles of the Hegelian Dialectics, namely, that “quantitative change leads to qualitative change.” In this treatise, we provide a recital on the historic heritages and novel challenges facing LS-MIMOs from a detection perspective. First, we highlight the fundamentals of MIMO detection, including the nature of co-channel interference (CCI), the generality of the MIMO detection problem, the received signal models of both linear memoryless MIMO channels and dispersive MIMO channels exhibiting memory, as well as the complex-valued versus real-valued MIMO system models. Then, an extensive review of the representative MIMO detection methods conceived during the past 50 years (1965–2015) is presented, and relevant insights as well as lessons are inferred for the sake of designing complexity-scalable MIMO detection algorithms that are potentially applicable to LS-MIMO systems. Furthermore, we divide the LS-MIMO systems into two types, and elaborate on the distinct detection strategies suitable for each of them. The type-I LS-MIMO corresponds to the case where the number of active users is much smaller than the number of BS antennas, which is currently the mainstream definition of LS-MIMO. The type-II LS-MIMO corresponds to the case where the number of active users is comparable to the number of BS antennas. Finally, we discuss the applicability of existing MIMO detection algorithms in LS-MIMO systems, and review some of the recent advances in LS-MIMO detection.

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Fifty Years of MIMO Detection: The Road to Large-Scale MIMOs

Soft output detection for signals transmitted on linear channels is investigated. A particular emphasis is made for signal detection on multiple antenna channels. The a posteriori information at the detector output is evaluated from a shifted spherical list of point candidates. The spherical list is centered on the maximum likelihood point, which has the great advantage of stabilizing the list size. Thus, the sphere radius is selected in order to control the list size and to cope with the boundaries of the finite multiple antenna constellation. Our new soft output sphere decoder is then applied to the computation of constrained channel capacity and to the iterative detection of a coded transmission. For example, we achieved a signal-to-noise ratio at 1.25 dB from capacity limit on a 4/spl times/4 MIMO channel with 16-QAM modulation and a 4-state rate 1/2 parallel turbo code.

Soft-input soft-output lattice sphere decoder for linear channels

The space-time bit-interleaved coded modulation (ST-BICM) is an efficient technique to obtain high diversity and coding gain on a block-fading multiple-input multiple-output (MIMO) channel. Its maximum-likelihood (ML) performance is computed under ideal interleaving conditions, which enables a global optimization taking into account channel coding. Thanks to a diversity upper bound derived from the Singleton bound, an appropriate choice of the time dimension of the space-time coding is possible, which maximizes diversity while minimizing complexity. Based on the analysis, an optimized interleaver and a set of linear precoders, called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed precoders have good performance with respect to the state of the art and exist for any number of transmit antennas and any time dimension. With turbo codes, they exhibit a frame error rate which does not increase with frame length.

Space–Time Coding Techniques With Bit-Interleaved Coded Modulations for MIMO Block-Fading Channels

Multidimensional binary mappings for bit-interleaved coded modulations (BICMs) on ergodic multiple-antenna channels with iterative decoding are presented. After derivation of a closed-form expression for the pairwise error probability under ideal maximum-likelihood (ML) decoding, the design criterion for mapping optimization is established from the ML performance of the ideally interleaved channel. It coincides with the figure of merit derived from the genie condition when the iterative receiver converges to perfect a priori information. Multidimensional mapping constructions that exhibit high signal-to-noise ratio (SNR) gains without increasing the complexity of the a posteriori probability (APP) detection are proposed. They allow for a reduced decoding complexity as they achieve near turbo code performance with a single convolutional code.

Multidimensional mappings for iteratively decoded BICM on multiple-antenna channels

A method for decoding at least one signal, including: receiving the at least one signal, the at least one signal being transmitted by at least one transmitting antenna and received by at least one receiving antenna; defining a sphere having a predetermined radius and being centered on a particular symbol chosen among predetermined symbols forming a lattice constellation of symbols which may be received by the receiving antenna; and producing estimated symbols representative of at least one transmitted symbol carried by the at least one signal and identified among the predetermined symbols included in the sphere and likelihood values associated to the estimated symbols.

Sphere decoding of symbols transmitted in a telecommunication system

The present invention concerns a system for transmitting information data from a transmitter to a receiver over nested block channel, the transmitter (TRD) comprising an encoder (ENC) following an error correcting code structure, the receiver (RCV) comprising a decoder (DEC) defined according to the error correcting code structure, the nested block channel (NBCH) comprising a scaled BPSK binary modulator (BM), the amplitude of which may vary from one bit transmission to the other. Such system is characterized in that the coding rate (Rc) of the encoder (ENC) or the parameters (D,L) of the nested block channel (NBCH) are selected dependently one from each other to achieve a target diversity order of the system and to maximize the coding gain.

Nicolas Gresset

Papers

Soft-input soft-output lattice sphere decoder for linear channels

Space–Time Coding Techniques With Bit-Interleaved Coded Modulations for MIMO Block-Fading Channels

Multidimensional mappings for iteratively decoded BICM on multiple-antenna channels

Sphere decoding of symbols transmitted in a telecommunication system

System for transmitting information data from a transmitter to a receiver over a nested block channel