Bit-interleaved Coded Modulation Systems Research Articles

Signal Shaping for BICM at Low SNR

The generalized mutual information (GMI) of bit-interleaved coded modulation (BICM) systems, sometimes called the BICM capacity, is investigated at low signal-to-noise ratio (SNR). The combinations of input alphabet, input distribution, and binary labeling that achieve the Shannon limit <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${- 1.59}\;{\rm dB}$</tex></formula> are completely characterized. The main conclusion is that a BICM system with probabilistic shaping achieves the Shannon limit at low SNR if and only if it can be represented as a zero-mean linear projection of a hypercube. Hence, probabilistic shaping offers no extra degrees of freedom to optimize the low-SNR BICM-GMI, in addition to what is provided by geometrical shaping. The analytical conclusions are confirmed by numerical results, which also show that for a fixed input alphabet, probabilistic shaping can improve the BICM-GMI in the low and medium SNR range.

Multi-Edge-Type Low-Density Parity-Check Codes for Bandwidth-Efficient Modulation

A method of designing low-density parity-check codes for bandwidth-efficient high-order modulation is proposed. A multi-edge-type LDPC code ensemble is used to improve the correspondence between modulation bit-channel capacity and bit-level protection in a bit-interleaved coded modulation system. A key innovation is the development of a multi-dimensional extrinsic information transfer (EXIT) vector field technique for the analysis and design of multi-edge-type codes. A condition, sufficient for the decoder to converge, is derived on the multi-dimensional EXIT vector field, and this condition is used as a constraint in code optimization. Code designs indicate that the proposed method produces codes matching the performance of codes designed using best available methods in ensemble threshold, and is capable of achieving identical finite-length error rates with shorter block-lengths. In addition to simplified design complexity, the resulting codes allow for low-complexity implementation and rate-adaptivity, and hence are well-suited for adaptive modulation systems.

Achievable secrecy rate of bit-interleaved coded modulation schemes

We study the impact of various modulation mapping strategies and signal constellation shapes on the secrecy rates achievable with bit-interleaved coded modulation (BICM) schemes. Transmission over an ergodic Rayleigh fading channel is assumed throughout this work. Various constellations and mapping techniques are considered in this work to maximize the capacity difference between the main channel and the eavesdropper channel, rather than to optimize the capacity of both channels. We show that in terms of achievable secrecy rate, Gray and Quasi-Gray mappings only perform well at low SNR but outperformed by other mapping techniques when SNR increases. The proper design of signal mapping can significantly enhance the achievable secrecy rate in BICM schemes. It is indicated that the key parameter to the secrecy rate of a BICM system is the distance spectrum of Euclidean distances for mappings.

Power Allocation for Cooperative Bit-Interleaved Coded Modulation Systems with Decode-Remap-and-Forward Relaying

Cooperative bit-interleaved coded modulation (BICM) is a key technology for the next-generation wireless communication systems. This paper investigates power allocation for the cooperative BICM systems with decode-remap-and-forward (DRF) relaying. Unlike the conventional decode-and-forward relays, the DRF relays may choose different constellation mappings from that of source so as to obtain a remapping gain. In spite of its importance, the power allocation in such a system has not yet been explored in the literature. Two new power allocation methods are proposed, aiming to minimize bit error rate at the destination. The first uses a cost function based on the minimum weighted squared-Euclidean distance (called PA-MWSED) and is optimized with the sub-gradient method. The second is based on a generalized MWSED (called PA-GMWSED) and is optimized with the Simplex method after the optimization is re-cast as a linear programming problem. Generally speaking, PA-MWSED has a better performance than PA-GMWSED but requires a higher complexity. Numerical results show that both of the proposed methods outperform the equal gain power allocation with large margins.

Bit-Interleaved Coded Modulation Systems with Iterative Decoding and Partial Reusing QAM Signal Points

A new method of reusing a subset of an M-QAM signal constellation is presented for Bit-Interleaved Coded Modulation systems with Iterative Decoding (BICM-ID). In addition to the remapping of high-energy signals to low-energy signals in order to save the average signal energy as a shaping technique known so far, a new scheme of remapping low-energy signals to high-energy signals is proposed in order to gain the equivalent distance when decoding bits, often called the Squared Euclidean Weights (SEW). Numerical analysis and simulation results show that the partial reuse of the signals in the BICM-ID system with 16-QAM can improve the system performance in terms of lowering the bit error rate in the error floor region.

On Construction of Bit-Interleaved Coded Modulation Systems with Iterative Decoding

A new construction of Bit-Interleaved Coded Modulation systems with Iterative Decoding (BICM-ID) is proposed to achieve the best performance over white additive Gaussian noise (AWGN) channels, assuming that the ideal feedback (IF) holds for iterative decoding. For a class of so-called regular IF mappings, new upper bounds for error probabilities are presented for both cases of BICM-ID systems using overall and in-line interleaving. Search results for component Recursive Systematic Convolutional (RSC) codes with and without puncturing are reported for 4-PSK and 8-PSK signal sets.

Channel estimation in bit-interleaved coded modulation with iterative decoding

This study improves the fading channel estimation in bit-interleaved coded modulation systems with iterative decoding (BICM-ID) and signal space diversity (SSD) by embedding a training sequence. Existing training schemes work well at high signal-to-noise ratio (SNR) or slowly time-varying channels whereas the applications of BICM-ID are beneficial at low SNR and fast time-varying fading channels. Motivated by the power/bandwidth efficiency of the SSD technique and the fact that superimposed training outperforms pilot symbol-assisted modulation (PSAM) training over relatively fast time-varying channels, a new superimposed training sequence is explored. The proposed training sequence inserts pilot bits into the coded bits prior constellation mapping and signal rotation. This becomes a superimposed training sequence in the rotated symbols and helps the estimator to track fast variation of the channel gains. A soft iterative channel estimator is developed to work with the superimposed training sequence. The performance of the proposed scheme, namely SSD-pilot, is shown to be superior to PSAM scheme. To gauge the performance improvement achieved with the proposed channel estimation, an analytical bound on the asymptotic bit error probability for BICM-ID using SSD over correlated fading channels is provided. The Cramer-Rao bound on the mean-square error of the channel estimator is also derived to evaluate the performance of the iterative channel estimator.

Irregular Convolutional Codes in Multiantenna Bit-Interleaved Coded Modulation Under Iterative Detection and Decoding

This paper develops a family of irregular convolutional codes for bit-interleaved coded modulation (BICM) systems under iterative detection and decoding. Irregular convolutional codes are constructed through irregular puncturing over multiple mother codes of different memory. Strategies based on fixed- and variable-size trellises are proposed to connect different memory mother codes. The use of irregular puncturing and code memory yields improved coding efficiency with the aid of extrinsic information transfer charts. Under ergodic and quasi-static fading conditions, multiantenna BICM systems using the proposed codes outperform comparable turbo-coded systems and multilevel coding strategies.

Optimum Power Allocation and Bit Loading for BICM Systems

This paper introduces a joint bit loading and power allocation algorithm for systems combining bit-interleaved coded modulation (BICM) with multicarrier transmission. The proposed algorithm maximizes the mutual information, so it can be regarded as a generalization of mercury/waterfilling policy that incorporates bit loading. The followed approach relies on irregular modulation and power to cast the problem in the framework of convex optimization. This allows to derive the optimum solution without resorting to greedy algorithms, embedding the bit loading in the definition of an equivalent constellation such that the complexity increase with respect to mercury/waterfilling is negligible. While irregular modulation plays a key role in algorithm definition, it is proved that only a few subcarriers employ it and it is shown that a practical low complexity algorithm can be obtained with minimal losses that does not use irregular modulation.

An analytical approach for performance evaluation of BICM transmission over Nakagami-m fading channels

Bit-interleaved coded modulation (BICM) has established itself as a quasi-standard for bandwidth- and power-efficient wireless communication. In this paper, we present an analytical approach to evaluate the performance of BICM transmission over frequency-flat fading additive white Gaussian noise channels. The statistic of the fading envelope is modeled as Nakagami-m distributed, which spans a wide range of practical multipath fading scenarios through adjustment of the m-parameter. For this setup, we derive approximations for the bit-error rate (BER) and cutoff rate of BICM. Different from previously proposed methods, our analysis is valid for general quadrature amplitude modulation and phase shift keying signal constellations and arbitrary bit-to-symbol mapping rules, and it results in simple closed-form expressions. The key idea is to use well-chosen subsets of signal points to approximate the probability density function of reliability metrics used for decoding. This approximation is accurate for signal-to-noise ratio regions of interest for BICM systems with moderate coding complexity such as, e.g., convolutional coded BICM systems. Based on this approximation we also derive an asymptotic BER expression, which reveals the diversity order and coding gain of BICM. The usefulness of the proposed analytical approach is validated through numerical and simulation results for a number of BICM transmission examples.

Improving the Performance of Chaos-Based Modulations Via Serial Concatenation

This paper proposes a serially concatenated system with an outer convolutional channel encoder and an inner chaos-based coded modulator. With the help of the principles of symbolic dynamics, the chaotic modulation can be described in terms of a trellis. Owing to this, we show that the resulting system can be designed and analyzed following developments made for serially concatenated channel codes (SCCCs) or bit-interleaved coded-modulation systems. We show how the iterative decoding algorithm used in this concatenated framework can be analyzed through the well-known extrinsic information transfer chart device and how the bit error rate can be bounded using the transfer function of the convolutional channel encoder. Comparison with a related SCCC system in both additive white Gaussian noise and frequency-nonselective fading channels shows that this kind of chaos-based systems keeps the potential advantages of coded-modulation-based systems. We are thus confident that the principles shown here can lead to the design of competitive chaotic discrete communication systems.

A New LLR Approximation for BICM Systems with HARQ

In this letter, a new approximation of log-likelihood ratio (LLR) for soft input channel decoding is proposed. Conventional simplified LLR using log-sum approximation can degrade the performance of bit interleaved coded modulation (BICM) systems employing hybrid automatic repeat request (HARQ) at low SNR. The proposed LLR performs as well as the exact LLR, and at the same time, requires only a small number of elementary operations.

Performance of BICM-SC and BICM-OFDM systems with diversity reception in non-gaussian noise and interference

In this paper, we present a general mathematical framework for performance analysis of single-carrier (SC) and orthogonal frequency division multiplexing (OFDM) systems employing popular bit-interleaved coded modulation (BICM) and multiple receive antennas. The proposed analysis is applicable to BICM systems impaired by general types of fading (including Rayleigh, Ricean, Nakagami-m, Nakagami-q, and Weibull fading) and general types of noise and interference with finite moments such as additive white Gaussian noise (AWGN), additive correlated Gaussian noise, Gaussian mixture noise, co-channel interference, narrowband interference, and ultra-wideband interference. We present an approximate upper bound for the bit error rate (BER) and an accurate closed-form approximation for the asymptotic BER at high signal-to-noise ratios for Viterbi decoding with the standard Euclidean distance branch metric. For the standard rate-1/2 convolutional code the proposed approximate upper bound and the asymptotic approximation become tight at BERs of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> and 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-12</sup> , respectively. However, if the code is punctured to higher rates (e.g. 2/3 or 3/4), the asymptotic approximation also becomes tight at a BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> . Exploiting the asymptotic BER approximation we show that the diversity gain of BICM systems only depends on the free distance of the code, the type of fading, and the number of receive antennas but not on the type of noise. In contrast their coding gain strongly depends on the noise moments. Our asymptotic analysis shows that as long as the standard Euclidean distance branch metric is used for Viterbi decoding, BICM systems optimized for AWGN are also optimum for any other type of noise and interference with finite moments.

Convergence Behavior Analysis and Detection Switching for the Iterative Receiver of MIMO-BICM Systems

The iterative receivers with a list sphere detector (LSD) and a parallel interference canceller (PIC) for multiple-input-multiple-output (MIMO) bit-interleaved coded modulation systems are considered. The convergence behaviors of these iterative detection and decoding schemes are analyzed via variance transfer (VT) functions. For ergodic channels, we show that the waterfall region of an iterative receiver can be predicted using a variance exchange graph. For slow fading channels, we show that the frame error rate of the iterative receiver is essentially limited by the early interception rate of the iterative receiver. Moreover, we show that the VT function of an LSD with a small list size is superior to that of a PIC at a high-variance region, whereas it is worse than that of a PIC at a low-variance region. Then, we propose a detection switching (DSW) approach for the iterative receiver and present a DSW criterion based on cross entropy. By applying the DSW, we show that the near-capacity performance can be achieved with a significantly reduced complexity.

An iterative reliability-based decoding for LDPC coded modulation system

In this paper, A Belief Propagation concatenated Orderd-Statistic Decoder (BP-OSD) based on accumulated Log-Likelihood Ratio (LLR) is proposed for medium and short lengths Low Density Parity-Check (LDPC) codes coded Bit-Interleaved Coded Modulation (BICM) systems. The accumulated soft output values delivered by every BP iteration are used as reliability values of Soft-Input Soft-Output OSD (SISO-OSD) decoder and the soft output of SISO-OSD is used as a priori probabilities of the demodulator for the next iteration. Simulation results show that this improved algorithm achieves noticeable performance gain with only modest increase in computation complexity.

Derivative of BICM mutual information

The derivative of the mutual information corresponding to bit-interleaved coded modulation systems is determined. The derivative follows as a linear combination of minimum-mean-squared error functions of a coded modulation set. The result finds applications in the analysis of communications systems in the wideband regime and in the design of power allocation over parallel channels.

Reduced-Complexity Receiver Structures for Space–Time Bit-Interleaved Coded Modulation Systems

Transmission efficiency in radio channels can be considerably improved by using multiple transmit and receive antennas and employing a family of schemes called space-time (ST) coding. Both extended range and/or improved bandwidth efficiency can be achieved, compared with a radio link with a single transmit and receive antenna. Bit-interleaved coded modulation schemes give diversity gains on fading channels with higher order modulation constellations combined with conventional binary convolutional codes also for the case of a single transmit and receive antenna radio link. In this paper, we study a family of flexible bandwidth-efficient ST coding schemes which combine these two ideas in a narrowband flat-fading channel and single-carrier modems. We address receiver complexity for the case of a large number of transmit antennas and higher order modulation constellations. Especially, we focus on practical configurations, where the number of transmit antennas is greater than that of receive antennas. Simplified receivers using tentative decisions are proposed and evaluated by means of simulations. Tradeoffs between complexity reduction and performance loss are presented. We emphasize systems that are of particular interest in applications where the number of transmit antennas exceeds the number of receive antennas. A system with four transmit antennas with an eight-fold complexity reduction and a performance loss of about 1 dB is demonstrated

A Tight BER Upper Bound for Bit-Interleaved Coded Modulation with Square QAM and Gray Labeling

Bit-interleaved coded modulation (BICM) is a bandwidth-efficient coded system with diversity order higher than that of Ungerboeck's trellis-coded modulation on fading channels. In this paper, we investigate the BER (bit error rate) performance of BICM in the additive white Gaussian and Rayleigh fading channels. A new upper bound is given for the square QAM constellation with gray labeling, which constitutes a large portion of practical applications of BICM systems. The new upper bound is tighter than the well-known BICM union bound proposed in G. Caire et al. (1998)

Reduced-Complexity Receiver Structures for Space&amp;#8211;Time Bit-Interleaved Coded Modulation Systems

Reduced-Complexity Receiver Structures for Space&amp;#8211;Time Bit-Interleaved Coded Modulation Systems

Error Probability of Bit-Interleaved Coded Modulation in Wireless Environments

The bit-interleaved coded modulation (BICM) method is efficient in mitigating multipath fading by providing time diversity. In this paper, union bounds on the bit and packet error probabilities of the BICM are derived. In the derivation, the authors assume the uniform interleaving of coded bits prior to mapping them onto the signal constellation. This results in a random distribution of the error bits in a codeword over the transmitted symbols. This distribution is evaluated, and the corresponding pairwise error probability is derived. Union bounds are functions of the distance spectrum of the channel code and the signal constellation used in the BICM system. The authors consider BICM systems operating over additive white Gaussian noise (AWGN), Rayleigh, Rician, and Nakagami fading channels. Results show that the new bounds are tight to simulation curves for different channel models. The proposed bounds are general for any coding scheme with a known distance spectrum.