Extrinsic Information Transfer Curves Research Articles

Design and Analysis of Joint Source-Channel Code System with Fixed-Length Code

As the demands of multimedia and data services increase, efficient communication systems are being investigated to meet the high data rate requirements. Joint source-channel coding (JSCC) schemes were proposed for improving overall system performance. However, existing JSCC systems may suffer a symbol error rate (SER) performance loss when residual source redundancy is not fully exploited. This paper presents a novel, low-complexity JSCC system, which consists of a fixed-length source block code and an irregular convolutional channel code. A simple approach is proposed to design source codes that minimize the SER of source detection and guarantee the convergence of iterative source-channel decoding (ISCD). To improve the waterfall performance of ISCD, the channel code is optimized by using the extrinsic information transfer (EXIT) chart and the concept of irregular code. The channel code is constituted by recursive non-systematic convolutional (RNSC) subcodes. The weights of subcodes are optimized to make the EXIT curves of the channel decoder and the source decoder well-matched, and therefore, a near-capacity performance is achieved. Simulation results show that the proposed system achieves more than 1 dB gains and 0.3 dB gains compared to the separate source-channel code system and the other optimal JSCC systems, respectively. Additionally, the performance of the proposed system is within 1 dB deviation from the Shannon limit capacity.

Unity-Rate Coding Improves the Iterative Detection Convergence of Autoencoder-Aided Communication Systems

A forward error correction (FEC) and unity-rate coded (URC) autoencoder (AE)-assisted communication system is proposed for the first time, which relies on soft iterative decoding for attaining a vanishingly low error probability. The AE-demapper is specifically designed for directly calculating the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">extrinsic</i> logarithmic likelihood ratios (LLRs), which can be directly entered into the URC decoder for soft iterative decoding. This avoids the potential degradation due to the conversion of symbol probabilities to bit LLRs. A comprehensive capacity analysis of the AE is performed, which demonstrates the capacity advantage of the AE-aided constellation design over its conventional quadrature amplitude modulation (QAM)/ phase shift keying (PSK) counterpart. Furthermore, we carry out its EXtrinsic Information Transfer (EXIT) chart analysis, which indicates that as a benefit of our URC, the EXIT curve always reaches the [1,1] point of perfect convergence, leading to a vanishingly low error probability. More explicitly, our bit error ratio (BER) and block error ratio (BLER) results demonstrate that the proposed FEC-URC-AE system achieves significant iterative gains both in additive white Gaussian noise (AWGN) and Rayleigh channels, outperforming both its model-based FEC-AE and its conventional coded QAM/QPSK counterparts.

Polar Code and Symbol Mapping Design for Multi-Level Cell Spin-Torque Transfer Magnetic Random Access Memory

Multi-level-cell (MLC) spin-torque transfer magnetic random access memory (STT-MRAM) suffers from reliability issues due to the highly asymmetric error rates of its hard and soft domains. In this communication, we have proposed to include a symbol mapper prior to writing bits to the MRAM and have jointly optimized the mapping and polar codes with iterative, soft-cancellation (SCAN) decoder. Specifically, we perform code search and symbol mapping based on the extrinsic information transfer curves of <i>a posteriori</i> probability demapper and the SCAN decoder. We identify a number of variations of Gray code-based mappings, each promising best waterfall, convergence, and/or error-floor performances. In particular, our simulation results demonstrate that one of our proposed mapping achieves a bit-error-rate which is nearly three orders of magnitude lower than that of the conventional binary mapping and outperforms other Gray-code variants at a resistance spread up to 18&#x0025; and hard bit write errors up to multiples of 10^&#x2212;3.

Investigating Suitable Multiple Access Techniques for Harbor Wireless Communication Systems

The multiple access communications for harbor environment are suffering from both low quality transmission due many metallic obstacles and overloaded networks due to the huge number of users/devices of logistic monitoring. This paper proposes a coded random access (CRA) scheme with a degree distribution suitable for harbor environment to serve many devices and provide communications with high reliability. The degree distribution is optimized using extrinsic information transfer (EXIT) charts by keeping that two EXIT curves do not intersect at low mutual information points. Since we are working on the network level, of which the benefit of broadband communications is kept for the fairness with the narrowband transmission, we convert the gain of broadband transmissions into an equivalent gain to the narrowband transmissions based on the Shannon channel capacity and coding theory. We then compare CRA to carrier sense multiple access with collision avoidance (CSMA/CA), because CSMA/CA has better performance compared to other techniques, such as ALOHA and Slotted ALOHA. We evaluate the performance of the proposed CRA and CSMA/CA using a series of computer simulation in additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels in terms of throughput and packet-loss rate (PLR). The results confirmed that CRA with the proposed degree distribution is more suitable than CSMA/CA as a multiple access technique for harbor wireless communications, indicated that the proposed CRA has higher throughput and lower PLR. The results of this study are expected to contribute to the development of future harbor communication systems.

Simple Iterative Channel Coding and Modulation for Harbor Wireless Communications

Monitoring systems at the harbor require a simple communication technique to save battery energy, strong in error correction, and suitable to the harbor channel model, of which the channel is predicted to have more number of path. This paper proposes (i) a harbor channel model and (ii) a simple iterative repetition coding for harbor wireless communication of monitoring systems. The harbor channel model is derived using a series of computer simulations based on real-field harbor environmental parameters, while the proposed iterative channel coding is based on the repetition codes assisted by a doped accumulator (ACC) with a doping technique. Channel coding and doping rates are designed using an Extrinsic Information Transfer (EXIT) chart and are evaluated using a series of computer simulations in terms of Bit Error Rate (BER) and Frame Error Rate (FER) performances with an outage performance as the theoretical baseline for comparison. Since the EXIT curve of the repetition codes has steep curve, we use a non-Gray Quadrature Phase Shift Keying (QPSK) to achieve a better matching between the decoder and the demapper of harbor channels. We found that the proposed simple repetition codes and non-Gray demapper provide excellent performances for harbor communications with a cliff of BER curve. The results of this paper are expected to contribute to the development of a reliable wireless communications for the harbor monitoring applications.

Design and Convergence Analysis of an IIC-based BICM-ID Receiver for FBMC-QAM Systems

Next generation cellular networks are expected to connect billions of devices through its massive machine-type communication (mMTC) use case. To achieve this, waveforms with improved spectral confinement and high spectral efficiency compared to cyclic-prefix orthogonal division multiplexing (CP-OFDM) are required. In this paper, filter-bank muilticarrier with quadrature amplitude modulation (FBMC-QAM) is studied as an alternative to CP-OFDM for such applications. However, FBMC-QAM presents the challenge of high intrinsic interference due to the loss of complex orthogonality in time-frequency domain. Bit-interleaved coded modulation with iterative decoding (BICM-ID) has been shown to exhibit capacity-approaching decoding performance. Therefore, in this paper, an iterative interference cancellation (IIC) based BICM-ID receiver is designed to cancel the intrinsic interference in FBMC-QAM systems. The proposed receiver consist of an inner decoder, which combines iterative demodulation and interference cancellation, and an outer decoder which is a low density parity check (LDPC) channel decoder. To evaluate the convergence behaviour of the proposed receiver, extrinsic information transfer (EXIT) chart analysis is employed, where EXIT curves for the components of the iterative decoder are derived. Numerical results show that the intrinsic interference in FBMC-QAM systems can be removed by adopting the proposed IIC-based BICM-ID receiver. With a receiver that is able to successfully cancel intrinsic interference, FBMC-QAM becomes an interesting alternative waveform for asynchronous mMTC applications due to its superior frequency localization compared to CP-OFDM. Furthermore, it has been shown that FBMC-QAM with the IIC-based receiver can achieve similar bit-error-rate (BER) performance as a CP-OFDM benchmark under different fading channels. Finally, the complexity of the proposed receiver for FBMC-QAM is analysed and compared to the complexity of the CP-OFDM benchmark.

Symbol Mapping Design for Bit-Interleaved Polar-Coded Modulation With Iterative Decoding

In this letter, we design a bit-interleaved polar-coded modulation system with iterative decoding subject to constraints on complexity, error floor, and waterfall region performance. We show that the hill-like trajectory of polar code extrinsic information transfer curves allows us to predict the gap of the bottleneck region that a polar code achieves at a given received signal-to-noise ratio for a given labeling rule. Using the gap, we propose a 3-D linear objective function to optimize for error floor, waterfall region performance, and complexity. The objective function requires Monte Carlo simulations for only three points on the extrinsic information transfer curve of the demapper for a given labeling rule. Our simulations show that the proposed method designs labeling rule and polar code duos that trade off error-floor and waterfall region performance with complexity and latency.

Asymptotic Analysis and Spatial Coupling of Counter Braids

A counter braid (CB) is a novel counter architecture introduced by Lu et al. in 2007 for per-flow measurements on high-speed links which can be decoded with low complexity using message passing (MP). CBs achieve an asymptotic compression rate (under optimal decoding) that matches the entropy lower bound of the flow size distribution. In this paper, we apply the concept of spatial coupling to CBs to improve the performance of the original CBs and analyze the performance of the resulting spatially-coupled CBs (SC-CBs). We introduce an equivalent bipartite graph representation of CBs with identical iteration-by-iteration finite-length and asymptotic performance. Based on this equivalent representation, we then analyze the asymptotic performance of single-layer CBs and SC-CBs under the MP decoding algorithm proposed by Lu et al. . In particular, we derive the potential threshold of the uncoupled system and show that it is equal to the area threshold. We also derive the Maxwell decoder for CBs and prove that the potential threshold is an upper bound on the Maxwell decoding threshold, which, in turn, is a lower bound on the maximum a posteriori (MAP) decoding threshold. We then show that the area under the extended MP extrinsic information transfer curve (defined for the equivalent graph), computed for the expected residual CB graph when a peeling decoder equivalent to the MP decoder stops, is equal to zero precisely at the area threshold. This, combined with the analysis of the Maxwell decoder and simulation results, leads us to the conjecture that the potential threshold is, in fact, equal to the Maxwell decoding threshold and hence a lower bound on the MAP decoding threshold. Interestingly, SC-CBs do not show the well-known phenomenon of threshold saturation of the MP decoding threshold to the potential threshold characteristic of spatially-coupled low-density parity-check codes and other coupled systems. However, SC-CBs yield better MP decoding thresholds than their uncoupled counterparts. Finally, we also consider SC-CBs as a compressed sensing scheme and show that low undersampling factors can be achieved.

EXIT Chart-Based IRA Code Design for TDMR Turbo-Equalization System

We present an extrinsic information transfer (EXIT) chart-based design technique for irregular repeat-accumulate (IRA) codes used in 2-D magnetic recording (TDMR) turbo-equalization systems. The channel model includes Voronoi magnetic grains, 2-D intersymbol interference (2D-ISI) and additive white Gaussian noise (AWGN). The receiver uses a 2D-ISI BCJR equalizer and an IRA decoder. For one outer equalizer-decoder iteration, we propose theory and simulation-based methods for computing EXIT curves. The simulation method calculates experimental EXIT curves for the check node decoder (CND) and the combination of the variable node decoder (VND) and an equalizer. The theoretical approach recursively calculates CND and VND Gaussian mixture model parameters in order to calculate EXIT curves. We then fit the VND and CND EXIT curves to find optimized variable node degree distributions. Simulation results show that the TDMR-optimized IRA codes achieve up to a 6.2% density increase in user bits/grain (U/G) compared with IRA codes designed for AWGN channels. The theory-based code designs achieve the same or better U/G as the simulation-based designs, but require 98% less design computation time. We also derive optimized IRA codes for iterative turbo-equalization; these codes can achieve simultaneous U/G gains and SNR savings compared with AWGN-optimized codes.

EXIT Chart Aided LDPC Code Design for Symmetric Alpha-Stable Impulsive Noise

In this letter, an iterative analysis method based on an extrinsic information transfer (EXIT) chart and quantized density evolution is developed for low-density parity-check (LDPC) codes over channels with symmetric alpha-stable ( $\text{S}\alpha \text{S}$ ) impulsive noise. Based on the proposed scheme, a method to optimize ensembles of LDPC codes under different levels of impulsiveness is presented and it is shown that the information rates of our optimized code ensembles can achieve 95.4% and 94.7% of the channel capacity for $\alpha =1.8$ and $\alpha =1$ , respectively. Furthermore, experimental results, including EXIT curves, thresholds, and bit-error rate performance of optimized code ensembles, are obtained to verify the effectiveness of our analysis.

Performance optimisation for bit‐interleaved coded modulation with iterative demapping with max‐log‐ maximum a posterior detection

Max-log-maximum a posterior (MAP) detection is preferred in practical systems rather than log-MAP because of its lower complexity, but also suffers from a considerable performance loss. In this study, the authors focus on the performance optimisation for (doped) bit-interleaved coded modulation with iterative demapping schemes where max-log-MAP detection is employed. First, they study the effects of max-log-MAP detection to the extrinsic information transfer curves of the (doped) demapper and decoder, and reselect the constellation labelling. Second, they find that the small difference between max-log-MAP and log-MAP detection in each iteration would be accumulated during the whole iterative procedure referred to as error accumulation, which causes a large performance loss, and consequently they propose some methods to control the error accumulation. Owing to the labelling reselection and error-accumulation control, the proposed scheme exhibits several tenths to 1 dB gains, compared with the conventional schemes, while maintaining low complexity.

EXIT-Chart-Based LDPC Code Design for 2D ISI Channels

In this paper, optimization of low-density parity-check (LDPC) codes to approach the symmetric information rate (SIR) of two-dimensional (2-D) intersymbol interference (ISI) channels is proposed for high-density magnetic recording, such as bit-patterned magnetic recording (BPMR) and 2-D magnetic recording (TDMR). The code design makes use of the modified Extrinsic Information Transfer (EXIT) chart, where the optimal variable node degree is searched by selecting the best check node degree to fit the check node decoder (CND) EXIT curve to the EXIT curve of the variable node decoder (VND) curve combined with 2-D detector. Simulation results show that LDPC codes with code length 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> bits optimized for a 2-D ISI channel corresponding to 4 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> recording density can achieve bit error rate 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> at signal-to-noise ratio 0.33 dB away from the SIR. To our knowledge, this is the first capacity-approaching LDPC code successfully optimized for a 2-D ISI channel.

EXIT Chart Based Design of Irregular LDPC Codes for Large-MIMO Systems

In this letter, we characterize the extrinsic information transfer (EXIT) behavior of a factor graph based message passing algorithm for detection in large multiple-input multiple-output (MIMO) systems with tens to hundreds of antennas. The EXIT curves of a joint detection-decoding receiver are obtained for low density parity check (LDPC) codes of given degree distributions. From the obtained EXIT curves, an optimization of the LDPC code degree profiles is carried out to design irregular LDPC codes matched to the large-MIMO channel and joint message passing receiver. With low complexity joint detection-decoding, these codes are shown to perform better than off-the-shelf irregular codes in the literature by about 1 to 1.5 dB at a coded BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> in 16 × 16, 64 × 64 and 256 × 256 MIMO systems.

Stochastic-Resonance Based Iterative Detection for Serially-Concatenated Turbo Codes

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.

EXIT-constrained BICM-ID design using extended mapping

This article proposes a novel design framework, EXIT-constrained binary switching algorithm (EBSA), for achieving near Shannon limit performance with single parity check and irregular repetition coded bit interleaved coded modulation and iterative detection with extended mapping (SI-BICM-ID-EM). EBSA is composed of node degree allocation optimization using linear programming (LP) and labeling optimization based on adaptive binary switching algorithm jointly. This technique achieves exact matching between the Demapper (Dem) and decoder's extrinsic information transfer (EXIT) curves while the convergence tunnel opens until the desired mutual information (MI) point. Moreover, this article proposes a combined use of SI-BICM-ID-EM with Doped-ACCumulator (D-ACC) and modulation doping (MD) to further improve the performance. In fact, the use of D-ACC and SI-BICM-ID (noted as DSI-BICM-ID-EM) enables the right-most point of the EXIT curve of the combined demapper and D-ACC decoder (Ddacc), denoted as DemDdacc, to reach a point very close to the (1.0, 1.0) MI point. Furthermore, MD provides us with additional degree-of-freedom in "bending" the shape of the demapper EXIT curve by choosing the mixing ratio of modulation formats, and hence the left most point of the demapper EXIT curve can flexibly be lifted up/pushed down with MD aided DSI-BICM-ID-EM (referred to as MDSI-BICM-ID-EM). Results of the simulations show that near-Shannon limit performance can be achieved with the proposed technique; with a parameter set obtained by EBSA for MDSI-BICM-ID-EM, the threshold signal-to-noise power ratio (SNR) is only roughly 0.5 dB away from the Shannon limit, for which the required computational complexity per iteration is at the same order as a Turbo code with only memory-2 convolutional constituent codes.

Very Simple BICM-ID Using Repetition Code and Extended Mapping with Doped Accumulator

This paper proposes very simple bit-interleaved coded modulation with iterative detection (BICM-ID) as a spectrally efficient signal transmission scheme, where irregular repetition code and extended mapping with rate-1 doped accumulator (ACC) are combined to achieve a clear turbo-cliff. Doped ACC is used for close matching of the demapper and decoder’s extrinsic information transfer curves. Although the proposed BICM-ID system is very simple, it can achieve excellent performances and completely eliminate bit-error-rate floor. An exemplifying result for extended non-Gray mapped 4-quadrature amplitude modulation symbol shows that with 0.916 bits/channel use, turbo-cliff happens at 1.27 dB away from the Shannon limit.

EXIT analysis of M-algorithm based MIMO detectors and LDPC code design optimization

This paper investigates joint design and optimization of both low density parity check (LDPC) codes and M-algorithm based detectors including iterative tree search (ITS) and soft-output M-algorithm (SOMA) in multiple-input multiple-output (MIMO) systems via the tool of extrinsic information transfer (EXIT) charts. First, we present EXIT analysis for ITS and SOMA. We indicate that the extrinsic information transfer curves of ITS obtained by Monte Carlo simulations based on output log-likelihood rations are not true EXIT curves, and the explanation for such a phenomenon is given, while for SOMA, the true EXIT curves can be computed, enabling the code design. Then, we propose a new design rule and method for LDPC code degree profile optimization in MIMO systems. The algorithm can make the EXIT curves of the inner decoder and outer decoder match each other properly, and can easily attain the desired code with the target rate. Also, it can transform the optimization problem into a linear one, which is computationally simple. The significance of the proposed optimization approach is validated by the simulation results that the optimized codes perform much better than standard non-optimized ones when used together with SOMA detector.

EXIT-Chart-Aided Three-Stage Concatenated Ultrawideband Time-Hopping Spread-Spectrum Impulse Radio Design

A serially concatenated and iteratively decoded irregular variable-length coding (IrVLC) scheme is amalgamated with a unity-rate precoded time-hopping (TH) pulse-position-modulation (PPM)-aided ultrawideband (UWB) spread-spectrum (SS) impulse radio design. The proposed design is capable of operating at low SNRs in Nakagami-m fading channels contaminated by partial band noise jamming (PBNJ) as a benefit of lossless IrVLC joint source and channel coding. Although this scheme may readily be used for lossless video or audio compression, for example, we only used it here for lossless near-capacity data transmission. A number of component variable-length-coding (VLC) codebooks having different coding rates are utilized by the IrVLC scheme for encoding specific fractions of the input source symbol stream. EXtrinsic Information Transfer (EXIT) charts are used to appropriately select these fractions to shape the inverted EXIT curve of the IrVLC and, hence, to match that of the inner decoder, which allows us to achieve an infinitesimally low bit error ratio (BER) at near-capacity SNR values.

Optimal Puncturing Ratios and Energy Allocation for Multiple Parallel Concatenated Codes

We propose a systematic design framework for optimal, low-complexity punctured multiple parallel concatenated codes (MPCCs), based on minimizing the convergence threshold using extrinsic information transfer (EXIT) charts. As the convergence threshold is related to the area between the two EXIT curves, the corresponding optimization problem is equivalent to a curve-fitting problem. The EXIT curves are determined by the respective EXIT functions of the constituents, which can be conveniently shaped through the use of random puncturing and unequal energy allocations across parallel coding streams. The design task is therefore to find the optimal combination of constituents, puncturing ratios, and energy allocation for matching the EXIT curves. A search over all rate-one convolutional codes of memory length four or less is performed, identifying 98 classes of codes with unique EXIT functions out of a total of 310 codes. Low-complexity MPCCs with up to four constituents are found, where the convergence thresholds are observed to be within 0.1 dB or less of the fundamental minimum signal-to-noise ratio (SNR) corresponding to the binary phase-shift keying (BPSK) capacity for code rates 1/3 les R les 7/8. Further allowing for unequal energy allocation, the convergence thresholds for lower code rates are similarly improved.

On the Performance and Complexity of Irregular Variable Length Codes for Near-Capacity Joint Source and Channel Coding

In this paper we propose a novel irregular variable length coding (IrVLC) scheme for near-capacity joint source and channel coding. We employ a number of component variable length coding (VLC) codebooks having different coding rates for encoding particular fractions of the input source symbol stream. These fractions may be chosen with the aid of extrinsic information transfer (EXIT) charts in order to shape the inverted EXIT curve of the IrVLC codec for ensuring that it does not cross the EXIT curve of a serially concatenated channel codec. In this way, an open EXIT chart tunnel may be created even at low Eb/N0 values that are close to the capacity bound of the channel. We propose iteratively decoded serially concatenated IrVLC designs amalgamated with Trellis coded modulation (TCM). These schemes are shown to be capable of operating within 0.6 dB of the uncorrelated narrowband Rayleigh fading channel's capacity bound using an average interleaver length of 217,500 bits and an effective bandwidth efficiency of 1.56 bit/s/Hz, assuming ideal Nyquist filtering. By contrast, the equivalent-rate regular VLC-based bench-marker schemes were found to be capable of operating at a higher distance of 1.1 dB from the capacity bound, which is nearly twice that of the proposed IrVLC-TCM scheme. Additionally, an irregular convolutional coiling (IrCC) based bench-marker was found to be capable of operating at 0.8 dB from the capacity bound, owing to its slightly eroded performance when operating with the considered interleaver length.