Analysis of Near-Capacity Iterative Decoding Schemes for Wireless Communication Using EXIT Charts

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.

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 digital communications, 90 or 180 degree phase ambiguity between the receiver and transmitter carrier is a serious problem for the coherent demodulation. To remove their phase ambiguity, differential quadrature phase shift keying (DQPSK) was proposed with the cost of a remarkable 2.4 dB performance degradation. Based on the iterative decoding (ID) scheme, an efficient joint convolutional code (CC)-coded DQPSK method is proposed to close the gap between quadrature phase shift keying (QPSK) and DQPSK. Using the extrinsic information transfer (EXIT) chart technique, we unveil that the low-complexity convolutional codes outperform the high-complexity Turbo codes for the ID scheme. Simulation results turn out that the proposed scheme can overcome the error-floor effect, and achieve almost 3.54 dB and 0.9 dB signal-to-noise ratio (SNR) gain compared with the non-iterative CC at 10−5 Bit Error Rate (BER)and iterative Turbo schemes at 10−7 BER, respectively.

With the substantial growth in number of wireless devices, future communication demands overarching research to design high‐throughput and efficient systems. We propose an intelligent Convergent Source Mapping (CSM) approach incorporating Differential Space‐Time Spreading (DSTS) technique with Sphere Packing (SP) modulation. The crux of CSM process is assured convergence by attaining an infinitesimal Bit‐Error Rate (BER). Data Partitioning (DP) H.264 video codec is deployed to gauge the performance of our intelligent and efficient system. For the purpose of efficient and higher data rates, we have incorporated compression efficient source encoding along with error resiliency and transmission robustness features. The proposed system follows the concept of iterations between the Soft‐Bit Source‐Decoder (SBSD) and Recursive Systematic Convolutional (RSC) decoder. Simulations of the DSTS‐SP‐assisted CSM system are presented for the correlated narrowband Rayleigh channel, using different CSM rates but constant overall bit‐rate budget. The SP‐assisted DSTS systems are mainly useful in decoding algorithms that operate without requiring Channel State Information (CSI). The effects of incorporating redundancy via different CSM schemes on the attainable performance and convergence of the proposed system are investigated using EXtrinsic Information Transfer (EXIT) charts. The effectiveness of the proposed system is demonstrated through IT++ based proof‐of‐concept simulations. The Peak Signal‐to‐Noise Ratio (PSNR) analysis shows that using Rate‐2/6 CSM with minimum Hamming distance (dH,min) of 4 offers about 5 dB gain, compared to an identical overall system code rate but with Rate‐2/3 CSM and dH,min of 2. Furthermore, for a consistent value of dH,min and overall rate, the Rate‐2/3 CSM scheme beats the Rate‐5/6 CSM by about 2 dB at the PSNR degradation point of 2 dB. Moreover, the proposed system with Rate‐2/3 CSM scheme furnishes an Eb/N0 gain of 20 dB when compared with the uniform‐rate benchmarker. Clearly, we can say that higher dH,min and lower CSM values are favourable for our proposed setup.

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.

Bit-interleaved coded modulation with iterative decoding (BICM-ID) is investigated for bandwidth efficient transmissions, where the error performance can be improved by employing a suitable symbol mapping. This paper first introduces a low-complexity regular mapping optimization for BICM-ID and 8PSK, for the purpose of finding the optimal mapping. Furthermore, the irregular mapping optimization is proposed for a closer approach to the channel capacity. The extrinsic information transfer (EXIT) chart analysis is aided for the proposed optimization algorithms to provide design guidelines of mappings. The bit error rate (BER) results demonstrate that the BICM-ID system with the proposed optimal irregular mapping outperforms the other mappings used for comparison, and yields about 0.5dB away from the channel capacity over the additive white Gaussian noise (AWGN) channel.

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.

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.

Visible light communication (VLC) uses run-length limited (RLL) code to avoid flickering and support different dimming ranges. In this paper, we design an error control coding scheme for VLC using polar code as a forward error correction (FEC) code in serial concatenation with an RLL code. We propose to use soft iterative decoding between RLL code and polar code. Extrinsic information transfer (EXIT) chart is also used to illustrate the proposed serial concatenated scheme's iterative decoding behavior. We will show improvement in bit error rate (BER) performance as compared to the hard decoding based polar code proposed in the literature for VLC.

We propose a novel class of short block codes (SBCs) designed for guaranteed convergence to an infinitesimally low bit error ratio (BER), which relies on the joint optimisation of soft-bit assisted iterative source and channel decoding. An iterative detection aided combination of SBC assisted soft-bit source decoding (SBSD) and a rate-1 precoder was used to evaluate the attainable performance of the proposed scheme for transmission of data-partitioned (DP) H.264 source coded video over correlated narrowband Rayleigh fading channels. Additionally, we demonstrated the effects of different SBCs having diverse minimum Hamming distances [d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H,min</sub> ] but identical coding rates on both the overall BER performance as well as on the objective video quality expressed in terms of the Peak Signal-to-Noise Ratio (PSNR). The convergence behaviour of the iterative decoding scheme using SBCs as a function of d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H,min</sub> is analysed by utilising extrinsic information transfer (EXIT) charts. Explicitly, our experimental results show that the proposed error protection scheme using SBCs associated with d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H,min</sub> = 6 outperforms the identical-code-rate SBCs having d <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H,min</sub> = 3 by about 3 dB at the PSNR degradation point of 1 dB. Additionally, an E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> /N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> gain of 27 dB is attained using iterative soft-bit source and channel decoding with the aid of rate-1/3 SBCs relative to the identical-rate benchmarker.

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.

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 contribution we jointly optimize the number of activated MIMO layers and the number of bits per symbol under the constraint of a given fixed data throughput and integrity. In analogy to bit-interleaved coded irregular modulation, we introduce a Broadband MIMO-BICM scheme, where different signal constellations and mappings were used within a single codeword. Extrinsic information transfer (EXIT) charts are used for analyzing and optimizing the convergence behaviour of the iterative demapping and decoding. Our results show that in order to achieve the best bit-error rate, not necessarily all MIMO layers have to be activated.

Modulation-Mode Assignment for SVD-assisted Downlink Multiuser MIMO Transmission Schemes with Iterative DetectionSince the capacity of multiple-input multiple-output (MIMO) systems increases linearly with the minimum number of antennas at both, the transmitter as well as the receiver side, MIMO systems have attracted a lot of attention for both frequency and non-frequency selective channels and reached a state of maturity. By contrast, MIMO-aided multiple-user systems require substantial further research. In comparison to zero-forcing (ZF) multiuser transmission techniques, where all users are treated jointly, the investigated singular value decomposition (SVD) assisted DL multiuser MIMO solution takes the individual user's channel characteristics into account. In analogy to bit-interleaved coded irregular modulation, we introduce a MIMO-BICM scheme, where different user-specific signal constellations and mapping arrangement were used within a single codeword. Extrinsic information transfer (EXIT) charts are used for analyzing and optimizing the convergence behaviour of the iterative demapping and decoding. Our results show that in order to achieve the best bit-error rate, not necessarily all user-specific MIMO layers have to be activated.