Low-complexity LDPC-coded iterative MIMO receiver based on belief propagation algorithm for detection

In this paper, we analyze an orthogonal frequency division multiplexing (OFDM) system employing combined space- time-frequency (STF) codes and an iterative receiver with extrinsic information transfer (EXIT) charts and bit-error rate plots. As STF codes, we examine orthogonal space-time block codes (OSTBCs), cyclic delay diversity, and discontinuous Doppler diversity. We present a combined STF code for eight transmit antennas with rate one. Another contribution of this work is the EXIT chart analysis demonstrating that EXIT charts are not always a suitable tool to analyze the performance of iterative receivers for STF coded OFDM systems. Further, error floors due to the mapping can be removed even for correlated channels by differential encoding and code doping the bits before the modulator.

This paper proposes an extrinsic information transfer (EXIT) chart analysis and an asymptotic bit error rate (BER) prediction method to speed up the design of high rate RCM-LDGM hybrid codes over AWGN and fast Rayleigh channels. These codes are based on a parallel concatenation of a rate compatible modulation (RCM) code with a low-density generator matrix (LDGM) code. The decoder uses the iterative sum-product algorithm to exchange information between the variable nodes (VNs) and the two types of constituent check nodes: RCM-CN and LDGM-CN. The novelty of the proposed EXIT chart procedure lies on the fact that it mixes together the analog RCM check nodes with the digital LDGM check nodes, something not possible in previous multi-edge EXIT charts proposed in the literature.

The joint Viterbi detector/decoder (JVDD) has been proposed as an alternative to the powerful and ubiquitous low-density parity check (LDPC) coding schemes, that are used in the majority of channel coding applications today. At shorter block lengths, the JVDD is able to outperform the state-of-the-art LDPC decoder that can be found in many of today’s systems, from deep-space communications to the digital video broadcasting standard, to the advanced television standard committee 3.0. Researchers have developed the tools to analyze the performance of the LDPC decoder, which is known as the sum-product algorithm or message passing algorithm. These tools include density evolution (DE) and extrinsic information transfer (EXIT) charts. To date, no similar such analysis exists for the JVDD. In the current paper we perform a similar preliminary analysis on the JVDD algorithm akin to what DE and EXIT charts are for the LDPC decoder. The current new analysis of the JVDD allows prediction of its probability of error based on the probability distribution functions of the metrics used within the algorithm. Our analysis plays a similar role to the abovementioned tools developed for the LDPC decoder: it allows us to predict the performance of the JVDD under various conditions (such as varying SNR’s, thresholds, and block lengths), it improves our understanding of the JVDD algorithm and the match against Monte-Carlo simulations verifies our assumptions on the main error-causing mechanisms within the JVDD.

In this paper, the rate achievable in Multiple-Input-Multiple-Output (MIMO) systems with iterative receivers based on linear front-end (FE) processing is investigated. First, the communication with Gaussian input signal is assumed and the Extrinsic Information Transfer (EXIT) chart is applied to evaluate the achievable sum rate. Then, the method for deriving the EXIT chart for a more practical case has been introduced. As a specific model, which fits the real turbo receivers better, communication with large size uniform constellations is discussed where the information being exchanged between the receiver's iterative block are Log-Likelihood-Ratios (LLRs) of the transmitted bits. It is shown that, in this situation, the iterative process does not improve the performance from achievable sum rate point of view in both high and low SNR regimes. However, the iterative process is shown to help in the medium SNR range, which is the range of interest.

EXtrinsic Information Transfer (EXIT) chart is a graphical tool for analysis of low density parity check (LDPC) and other codes with iterative decoding. In this paper, we propose the design of LDPC codes for coded modulation schemes by application of linear programming with conditions derived from EXIT charts. Points on the EXIT curve for bit and check node operations are first computed either using analysis or by simulation. The entire EXIT curve is then obtained by linear interpolation. Finally, the EXIT curves are optimized to obtain the maximum possible rate for the code under a given threshold condition. To demonstrate the design procedure, we consider the cases of M-PAM and 8-PSK over the additive white Gaussian noise (AWGN) channel. The optimization method presented is versatile, and can be extended to other constellations and situations easily.

In this letter, the concept of multiple serially-concatenated codes is invoked in the context of stochastic resonance (SR), where the achievable performance is improved by increasing noise power. More specifically, the receiver's iterative decoding process is characterized with the aid of extrinsic information transfer (EXIT) charts, such that the SR effect induced by a non-linear component is taken into account. Our simulation results demonstrate that although the SR demodulator's log-likelihood ratio (LLR) outputs are not Gaussian distributed, the corresponding EXIT trajectory matches the prediction from the associated inner- and outer-codes' EXIT curves, while reaching the perfect convergence point in terms of mutual information. Therefore, an infinitesimally low bit-error ratio (BER) is attained by appropriately designing the channel code's parameters based on EXIT charts.

In previous works, density evolution schemes have been used to design an irregular low-density parity-check (LDPC) code for the multi-input multi-output (MIMO) systems. However the code design based on the density evolution can be used only for simple code structure like LDPC codes and repeat-accumulate (RA) codes. Recently simple and accurate irregular LDPC code design method based on the extrinsic information transfer (EXIT) chart was introduced for an AWGN channel. This code design scheme is much flexible, therefore it can be used for any kind of code structure like turbo codes. In this paper we design an irregular LDPC code for a MIMO system using the EXIT chart based scheme. The EXIT charts are used to obtain the optimal edge degree distribution of the irregular LDPC code combined with the MMSE-SIC MIMO detector. This scheme can be generalized for designing the optimal iterative MIMO detector combined with any kind of channel codes including turbo codes.

Free space optical (FSO) communication has received attention because of its high bandwidth, less expensive deployment and error prone links. But the FSO signals attenuate significantly due to the atmospheric and varying channel conditions. A hybrid optical/RF (radio frequency) communication system is an alternative communication system to cope with FSO signal attenuations. In such hybrid FSO/RF communication system, power and rate adaptation due to the varying channel conditions is another challenge. We have already proposed a novel puncturing optimization algorithm to solve the adaptation issue. A single pair of encoder and decoder has been suggested in order to avoid additional component cost, computational complexity and synchronisation issues. The extrinsic information transfer (EXIT) chart is well-known technique to measure the convergence of a code. In this research work, we analyse the behaviour of the EXIT chart for the hybrid optical/RF communication system.

The computational complexity and hence energy consumption of a low-density parity-check (LDPC) decoder employing fixed point (FP) computation is commensurate with the operand width (OW) of the FP representation employed. Therefore low OWs are desirable, but, if the OW is too low, then an inevitable performance degradation will be introduced. For that reason it is desirable to determine the minimum OW that does not impose a significant performance degradation. Previous efforts have advocated different OWs based on results obtained using time-consuming bit-error ratio (BER) simulations. However, these BER simulations are extremely time consuming, owing to the requirement of considering a range of channel signal-to-noise ratios (SNRs). Therefore, in this paper, we propose the employment of extrinsic information transfer (EXIT) charts to overcome this drawback. Furthermore, EXIT-chart analysis has the additional benefit of offering insights into the specific causes of the performance degradations encountered. Finally, a FP scheme having an overall OW of 6 bits is proposed for the implementation of the min-sum algorithm (MSA).

In this paper we derive a novel extrinsic information transfer (EXIT) function for a channel estimator that uses both pilot symbols and soft decoding information. We consider a CDMA system with forward error correction that employs iterative multiuser detection based on soft interference cancellation and single user decoding. The J function is useful in convergence analysis as it provides a mapping between mutual information and variance. J functions are derived for both the flat-fading Rayleigh channel and channel estimate, allowing the a priori inputs to the channel estimator, interference canceller and decoder to be modeled. Algorithms for obtaining the EXIT functions for the three receiver blocks are proposed. We then combine the EXIT functions to create an EXIT chart that can be used to predict the behaviour of the overall receiver. Simulations are run for a 3GPP-like receiver in a mobile environment with a vehicle speed of 100 km/h. It is found that under these conditions, the detector trajectory closely matches our proposed EXIT chart.

In MIMO communication system the conventional Turbo-BLAST receiver using Gray mapping converges slow. For this reason, an improved Turbo-BLAST scheme with Anti-Gray mapping is proposed in this paper. Research has shown that the iterative receiver using new scheme outperforms the convention alone and obtains a faster convergence rate. Also, an improved receiver based on soft interference cancellation and MMSE filtering is proposed: The posterior information not extrinsic information is fed back from outer decoder to inner detector. A better performance is attained without increasing the computational complexity. Simulation results and Extrinsic Information Transfer (EXIT) chart analysis all demonstrate this.

For a multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system, time-varying multipath fading of channel destroys the orthogonality among subcarriers and leads to serious intercarrier interference (ICI). The system performance degrades more severely as normalized Doppler frequency increases. In order to mitigate the effect of time-varying fading, a low-complexity iterative receiver with joint ICI cancellation and pilot-assisted channel estimation is proposed. The initial channel state information (CSI) is estimated by performing time-domain interpolation and least-square (LS) method on the received pilot symbols. The soft outputs are obtained from the decoders after low-complexity linear minimum mean-square error (LC-LMMSE) detection. In the following stages, the soft outputs are feedback to update the CSI estimation. Furthermore, a ¿linear statistics combining¿ (LSC) technique is used to improve the performance of the proposed equalizer by combining the outputs of LC-LMMSE and parallel interference canceler (PIC) with weighting coefficients estimated by maximizing the signal to interference-plus-noise ratio (SINR) at the output of LSC. The complexity of system is significantly reduced by restricting the interference to neighboring subcarriers and employing the LC-LMMSE by limiting the frequency-domain CSI into diagonal region. The simulation results show that the proposed iterative receiver with estimated CSI approaches the ICI-free bound even at very high mobility scenarios.

Low Power Wide Area (LPWA) networks aim at connecting low cost devices with high constraints on the link budget. Focusing on the physical layer, the combination of Frequency Shift Keying (FSK) modulation and coding in the same process has been shown efficient when associated to a turbo receiver. This paper considers the optimization of Turbo-FSK parameters for the LPWA context using the EXtrinsic Information Transfer (EXIT) Chart analysis. After adapting the metric to the FSK waveforms, EXIT chart performance results are extended and compared to short packet lengths using extensive Bit Error Rate (BER) computations.

The convergence rate of iterative decoding of Gallager codes on the additive white Gaussian noise (AWGN) channel using the sum-product algorithm (SPA) under the flooding schedule (FS) is compared with that under the turbo-decoding schedule (TDS). Analyses using extrinsic information transfer (EXIT) charts show that TDS exhibits a much faster convergence behavior than FS.

A new decoding scheme for product accumulate (PA) code over a space optical Poisson/pulse-position modulation (PPM) channel is investigated. In this scheme, the PPM and the accumulator of the PA code are taken as a single inner code, decoded with an iterative demodulating-decoding technique based on Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm, rather than belief propagation (BP) algorithm in the original scheme. Simulation results show that this scheme provides much better bit error rate (BER) performance. At a BER of 10−5, the new scheme has a gain of 1.8 dB more than the original one. In addition, extrinsic information transfer (EXIT) charts are employed to analyze and compare the performance. The results indicate that the new scheme has not only better BER performance, but also lower error floor.