Soft-input Soft-output Research Articles

A Novel Four Single-Sideband M-QAM Modulation Scheme Using a Shadow Equalizer for MIMO System Toward 5G Communications.

Single-sideband (SSB) modulation through Hilbert transformation has successfully transmitted data using only half the bandwidth of the traditional scheme for the same amount of contained information. Toward this end, the four single-sideband (4-SSB) approach for high order modulation is a promising approach for the next-generation communications by applying soft-input soft-output (SISO) equalizer algorithms over orthogonal frequency division multiplexing (OFDM). However, OFDM is challenging for realizing the feasible 5G communications, compared to the emerging techniques, e.g., non-orthogonal multiple access (NOMA), orthogonal multiple access (OMA) or multiple-input multiple-output (MIMO). Since the 4-SSB is an orthogonal modulation which was successfully applied over the traditional OFDM, in this article, we propose a novel 4-SSB modulation scheme over OFDM Guard Interval (GI) and massive MIMO. Besides the carrier signal, from the receiver side, we also apply the shadow equalizer algorithm in the uncoded and coded environment using turbo codes to achieve the 4-SSB with high efficiency from low complexity and energy consumption for 5G. The evaluation results validate that our system consumes lower energy due to low complexity gained from same number of iterations without the heavy decoding as of the 4-SSB SISO based on the turbo equalizer. In addition, the 4-SSB over the OFDM GI achieves the best performance among the relevant approaches conducted in 4-SSB. The proposal then acts as a practical communication system designed to solve the inter-symbol interference (ISI) induced by additional Hilbert transform in the wireless environment toward fifth generation (5G), given that turbo code is considered as a potential channel coding scheme for 5G radio specification.

Noncoherent Detection With Polar Codes

Polar codes (PCs) have attracted significant attention in the last decade, especially after their adoption in the forthcoming 5G wireless networks. However, previous studies focused on coherent polar codes, which always rely on the strong assumption of available perfect channel state information. Instead, in this paper, we investigate the use of PCs in noncoherent systems. First, a binary differential phase shift keying (BDPSK) demodulator is concatenated with a polar decoder to form the noncoherent detector, where successive cancellation (SC) is applied. The simulation results demonstrate that the SC-based PCs for noncoherent detection have approximately a discrepancy of only 3 dB compared with the coherent counterpart in noncoherent channels. Furthermore, in order to further decrease this discrepancy, we replace the BDPSK demodulator with a soft-input soft-output (SISO) multiple symbol differential sphere decoding demodulator. Similarly, the SC-based PC decoder is replaced by the SISO belief propagation-based PC decoder, and by using this novel architecture, an iterative noncoherent detector is constructed. Benefiting from further invoking extrinsic information transfer chart tool and the dynamic window-size detection scheme, the performance of the proposed iterative noncoherent detector becomes competitive with its coherent one in practical applications, since the performance degradation is reduced to 1 dB.

Maximum Likelihood and Soft Input Soft Output MIMO Detection at a Reduced Complexity

This paper proposes an efficient pruning algorithm for MIMO detector, which not only achieves the same performance of the maximum likelihood (ML) decoder, but also massively reduces the number of visiting nodes. The proposed algorithm applies correct sorting order so that it achieves the same performance of the ML decoder. Thanks to the use of the correct ordering, both child and sibling nodes can be pruned efficiently. As a result, the number of visiting nodes is significantly reduced. To acquire properly sorted order, we propose fast sorting algorithms that generate the exact sorted sequence. Furthermore, the proposed schemes can be applied in SISO MIMO detector. The advantages of the proposed sphere decoder become more pronounced in high-order modulation schemes.

Polar coded iterative multiuser detection for sparse code multiple access system

Polar coded sparse code multiple access (SCMA) system is conceived in this paper. A simple but new iterative multiuser detection framework is proposed, which consists of a message passing algorithm (MPA) based multiuser detector and a soft-input soft-output (SISO) successive cancellation (SC) polar decoder. In particular, the SISO polar decoding process is realized by a specifically designed soft re-encoder, which is concatenated to the original SC decoder. This soft re-encoder is capable of reconstructing the soft information of the entire polar codeword based on previously detected log-likelihood ratios (LLRs) of information bits. Benefiting from the soft re-encoding algorithm, the resultant iterative detection strategy is able to obtain a salient coding gain. Our simulation results demonstrate that significant improvement in error performance is achieved by the proposed polar-coded SCMA in additive white Gaussian noise (AWGN) channels, where the performance of the conventional SISO belief propagation (BP) polar decoder aided SCMA, the turbo coded SCMA and the low-density parity-check (LDPC) coded SCMA are employed as benchmarks.

Reliability Level List Based Iterative SISO Decoding Algorithm for Block Turbo Codes

An iterative Reliability Level List (RLL) based soft-input soft-output (SISO) decoding algorithm has been proposed for Block Turbo Codes (BTCs). The algorithm ingeniously adapts the RLL based decoding algorithm for the constituent block codes, which is a soft-input hard-output algorithm. The extrinsic information is calculated using the reliability of these hard-output decisions and is passed as soft-input to the iterative turbo decoding process. RLL based decoding of constituent codes estimate the optimal transmitted codeword through a directed minimal search. The proposed RLL based decoder for the constituent code replaces the Chase-2 based constituent decoder in the conventional SISO scheme. Simulation results show that the proposed algorithm has a clear advantage of performance improvement over conventional Chase-2 based SISO decoding scheme with reduced decoding latency at lower noise levels.

Low-Complexity Single-Channel Blind Separation of Co-Frequency Coded Signals

Single-channel blind source separation (SCBSS) of uncoordinated, non-spread, co-frequency interfering signals with non-zero carrier frequency offset and timing offset, and without training sequence for channel estimation, is a challenging task. Iterative SCBSS of coded signals leads to good performance but is computationally expensive as it involves the turbo processing of multi-user per-survivor processing and soft-input soft-output channel decoding. In this letter, we propose a low-complexity SCBSS (LC-SCBSS) scheme, which reduces the computational complexity of the conventional iterative SCBSS by using interference-cancellation from the second iteration onward, and adaptive channel truncation for certain users. Simulation results show that the proposed LC-SCBSS reduces the computational complexity by more than 99%, with only a marginal degradation in performance.

Iterative equalization algorithm based on modified matrix for asynchronous MIMO OFDM

Aiming to co-antenna interference and multipath interference in the downlink multiple input multiple output orthogonal frequency division multiple multiplexing (MIMO-OFDM) asynchronous communication system, a low complexity iterative equalization algorithm based on precoding matrix is proposed. At the transmitter, the algorithm utilizes precoding matrix to spread the symbols over all the subcarriers, which relieve the influence of deep fading in part of the subcarriers. At the receiver, the algorithm adopts Soft input soft output(SISO) interference elimination algorithm based on the minimum mean square error sorted QR decomposition (MMSE-SQRD) to avoid the complexity of solving inverse matrix, which is always involved in the traditional parallel soft interference elimination algorithm based on minimum mean square error(MMSE)equalization. Utilizing a sorted QR decomposition of the channel matrix, on the other hand, the algorithm has the priority for detection transmission symbol with maximum noise-signal ratio (SNR) to improve detection accuracy. Furthermore, the error of reconstructed signals is spread by the precoding matrix, which decreases the error propagation in iteration processing. Simulation results show that the performance of the proposed algorithm is improved compared with the existing iterative interference cancellation algorithm, that is, when the system is equipped with 2 transmitters and 2 receivers and the Bit error rate is 10-3, the performance of the system is improved about 2dB.

Low Complexity Syndrome-Based Decoding Algorithm Applied to Block Turbo Codes

This paper presents a technique for reducing the decoding complexity of block turbo code with an extended Hamming code as a component code. In conventional decoding algorithms, when an input vector has a zero syndrome, complexity can be reduced by using the hard-input soft-output (HISO) algorithm. Although sufficient error correction can be achieved using hard decision decoding (HDD) of a component code, conventional methods have used the soft-input soft-output (SISO) algorithm for input vectors with a single error. However, when HDD is applied to all input vectors in which the syndrome is detected as a single error, performance loss occurs owing to the occasional presence of input vectors with triple errors. To solve this problem, we used two criteria for distinguishing between instances of single and triple errors. We maximized the applied rates of the HDD-based HISO algorithm depending on whether the criteria were satisfied. The SISO algorithm was applied when the two criteria were not met. In this case, the number of HDD usages can be reduced to half by removing duplicates or unnecessary candidate codewords. Simulation results show that the proposed algorithm can considerably reduce decoding complexity without performance loss compared with conventional algorithms.

Time Synchronization of Turbo-Coded Square-QAM-Modulated Transmissions: Code-Aided ML Estimator and Closed-Form Cramér–Rao Lower Bounds

This paper introduces a new maximum likelihood (ML) solution for the code-aided (CA) timing recovery problem in square-quadrature amplitude modulation (QAM) transmissions and derives, for the very first time, its CA Cramer–Rao lower bounds (CRLBs) in closed-form expressions. The channel is assumed to be slowly time varying so that it can be considered as constant over the observation interval. By exploiting the full symmetry of square-QAM constellations and further scrutinizing the Gray-coding mechanism, we express the likelihood function of the system explicitly in terms of the code bits’ a priori log-likelihood ratios (LLRs). The timing recovery task is then embedded in the turbo iteration loop, wherein increasingly accurate estimates for such LLRs are computed from the output of the soft-input soft-output decoders and exploited at a per-turbo-iteration basis in order to refine the ML time delay estimate. The latter is then used to better resynchronize the system, through feedback to the matched filter, so as to obtain more reliable symbol-rate samples for the next turbo iteration. In order to properly benchmark the new CA ML estimator, we also derive for the very first time the closed-form expressions for the exact CRLBs of the underlying turbo synchronization problem. Computer simulations will show that the new closed-form CRLBs coincide exactly with their empirical counterparts evaluated previously using exhaustive Monte Carlo simulations. They will also show unambiguously the remarkable performance improvements of CA estimation against the traditional nondata-aided scheme, thereby highlighting the potential performance gains in time synchronization that can be achieved owing to the decoder assistance. Over a wide range of practical signal-to-noise ratios (SNRs), CA estimation becomes even equivalent to the completely data-aided scheme in which all the transmitted symbols are perfectly known to the receiver. Moreover, the new CA ML estimator almost reaches the underlying CA CRLBs, even for small SNRs, thereby confirming its statistical efficiency in practice. It also enjoys significant improvements in computational complexity as compared to the most powerful existing ML solution, namely the combined sum-product and expectation-maximization algorithm.

Soft MIMO detection through sphere decoding and box optimization

Achieving optimal detection performance with low complexity is one of the major challenges, mainly in multiple-input multiple-output (MIMO) detection. This paper presents three low-complexity Soft-Output MIMO detection algorithms that are based mainly on Box Optimization (BO) techniques. The proposed methods provide good performance with low computational cost using continuous constrained optimization techniques. The first proposed algorithm is a non-optimal Soft-Output detector of reduced complexity. This algorithm has been compared with the Soft-Output Fixed Complexity (SFSD) algorithm, obtaining lower complexity and similar performance. The two remaining algorithms are employed in a turbo receiver, achieving the max-log Maximum a Posteriori (MAP) performance. The two Soft-Input Soft-Output (SISO) algorithms were proposed in a previous work for soft-output MIMO detection. This work presents its extension for iterative decoding. The SISO algorithms presented are developed and compared with the SISO Single Tree Search algorithm (STS), in terms of efficiency and computational cost. The results show that the proposed algorithms are more efficient for high order constellation than the STS algorithm.

Analysis of Turbo Code Behavior with Extrinsic Information Transfer Charts in High-Speed Wireless Data Services

This paper examines turbo codes that are currently introduced in many international standards and implemented in numerous advanced communication systems, and evaluates the process of extrinsic information transfer (EXIT). The convergence properties of the iterative decoding process, associated with a given turbo-coding scheme, are estimated using the analysis technique based on so-called extrinsic information transfer (EXIT) charts. This approach provides a possibility to predict the bit-error rate (BER) of a turbo code system with only the extrinsic information transfer chart. It is shown that extrinsic information transfer charts are powerful tools to analyze and optimize the convergence behavior of iterative systems utilizing the turbo principle, i.e., systems exchanging and refining extrinsic information. The idea is to consider the associated soft-input soft-output (SISO) stages as information processors, which map input a priori log likelihood ratios (LLRs) onto output extrinsic LLRs, the information content being obviously assumed to increase from input to output, and introduce them to the design of turbo systems without the reliance on extensive simulation. Compared with the other methods for generating extrinsic information transfer functions, the suggested approach provides insight into the iterative behavior of linear turbo systems with substantial reduction in numerical complexity.

Useful Mathematical Tools for Capacity Approaching Codes Design

Focus of this letter is the oldest class of codes that can approach the Shannon limit quite closely, i.e., low-density parity-check (LDPC) codes, and two mathematical tools that can make their design an easier job under appropriate assumptions. In particular, we present a simple algorithmic method to estimate the threshold for regular and irregular LDPC codes on memoryless binary-input continuous-output additive white Gaussian noise (AWGN) channels with sum-product decoding, and, to determine how close are the obtained thresholds to the theoretical maximum, i.e., to the Shannon limit, we give a simple and invertible expression of the AWGN channel capacity in the binary input-soft output case. For these codes, the thresholds are defined as the maximum noise level, such that an arbitrarily small bit-error probability can be achieved as the block length tends to infinity. We assume a Gaussian approximation for message densities under density evolution, a widely used simplification of the decoding algorithm.

Turbo Coded OFDM Combined with MIMO Antennas Based on Matched Interleaver for Coded-Cooperative Wireless Communication

A turbo coded cooperative orthogonal frequency division multiplexing (OFDM) with multiple-input multiple-output (MIMO) antennas scheme is considered, and its performance over a fast Rayleigh fading channel is evaluated. The turbo coded OFDM incorporates MIMO (2 × 2) Alamouti space-time block code. The interleaver design, and its placement always plays a vital role in the performance of a turbo coded cooperation scheme. Therefore, a code-matched interleaver (CMI) is selected as an optimum choice of interleaver and is placed at the relay node. The performance of the CMI is evaluated in a turbo coded OFDM system over an additive white Gaussian noise (AWGN) channel. Moreover, the performance of the CMI is also evaluated in the turbo coded OFDM system with MIMO antennas over a fast Rayleigh fading channel. The modulation schemes chosen are Binary Phase shift keying (BPSK), Quadrature phase shift keying (QPSK) and 16-Quadrature amplitude modulation (16QAM). Soft-demodulators are employed along with joint iterative soft-input soft-output (SISO) turbo decoder at the destination node. Monte Carlo simulated results reveal that the turbo coded cooperative OFDM system with MIMO antennas scheme incorporates coding gain, diversity gain and cooperation gain successfully over the direct transmission scheme under identical conditions.

Factor Graph Aided Multiple-Symbol Differential Detection in the Broadcasting Phase of a Network Coding Based UWB Relay System

A factor-graph-aided multiple-symbol differential detection (FG-MSDD) is proposed and its performance is analyzed and evaluated in the broadcasting phase (i.e., the downlink phase) of an ultra-wideband (UWB) two-way relay system (TWRS). In the downlink of the TWRS, the relay is transmitting network-coded information to the sources, and each source node aims to calculate a posteriori probabilities (APPs) of the information symbols from the relay node. A sampling method based on the modified autocorrelation receiver is proposed for FG-MSDD, which has a trellis structure. The trellis can be decomposed into multiple subtrellises depending on the FG factorization. Then, a methodology for APPs is derived when the forward-and-backward message passing is performed on the subtrellises. The main advantage of FG-MSDD is that it exploits soft information accurately with the aid of the bidirectional message passing. In addition, the proposed FG-MSDD, in conjunction with any soft-input soft-output (SISO) decoding scheme, is capable of obtaining an iterative detection algorithm. Various performance evaluation results obtained by means of computer simulations have verified that the proposed algorithm improves detection performance for the noncoherent UWB TWRS.

Efficient Decoding Technique for Block Product Turbo Codes

In this paper, we propose an efficient technique for an iterative soft input soft output (SISO) decoding algorithm of block turbo codes with constituent Hamming codes. Pyndiah’s iterative decoding algorithm for block turbo codes supports various code rates by using concatenation, and shows high bit error rate (BER) performance in an additive white Gaussian noise channel (AWGN) environment as the iterative decoding progresses. However, one disadvantage of this code is that the delay increases during decoding with an increasing number of iterations. By employing syndrome-based iterative SISO decoding and iterative SISO decoding using an alpha value, we could obtain high BER performance. In addition, we propose a SISO-hybrid maximum likelihood decoding (SISO-H-MLD) algorithm which achieves almost the same performance as SISO decoding while reducing the number of iterations.

On Low-Complexity Soft-Input Soft-Output Linear Equalizers

The design of low-complexity soft-input soft-output (SISO) linear equalizer (LE) for turbo equalization can be classified into two categories: the Cat-I assuming random a priori soft input (from the decoder) and the Cat-II treating the a priori input deterministic. There is a lack of systematic comparison between the two categories. In this letter, a comprehensive comparison between the two categories of SISO LE is provided for multiple-input multiple-output (MIMO) systems. It is shown the two categories are equivalent for constant-modulus modulations. For non-constant-modulus modulations, however, they are generally not the same, even though the two achieve similar performance. In terms of complexity, the Cat-I is more efficient, especially for high-order modulations.

Soft-Decision for Differential Amplify-and-Forward over Time-Varying Relaying Channel

Differential detection schemes do not require any channel estimation, which can be employed under user mobility with low computational complexity. In this work, a soft-input soft-output (SISO) differential detection algorithm is proposed for amplify-and-forward (AF) over time-varying relaying channels based cooperative communications system. Furthermore, maximum-likelihood (ML) detector for M-ary differential Phase-shift keying (DPSK) is derived to calculate a posteriori probabilities (APP) of information bits. In addition, when the SISO is exploited in conjunction with channel decoding, iterative detection and decoding approach by exchanging extrinsic information with outer code is obtained. Finally, simulation results show that the proposed non-coherent approach improves detection performance significantly. In particular, the system can obtain greater performance gain under fast-fading channels.

Low Complexity Iterative MMSE-PIC Detection for Medium-Size Massive MIMO

In medium-size massive MIMO systems, the minimum mean-square-error parallel interference cancellation (MMSE-PIC)-based soft-input soft-output (SISO) detector is often used due to its relatively low complexity and good bit error rate (BER) performance. The computational complexity of MMSE-PIC for detecting a block of data is dominated by the computation of a Gram matrix and a matrix inversion. They have computational complexity of $\mathcal{O}(K^2M)$ and $\mathcal{O}(K^3)$ , respectively, where $K$ is the number of uplink users with one transmit antenna each and $M$ is the number of receive antennas at the base station. In this letter, by using an $L$ (typically $L \leq 3$ ) terms of Neumann series expansion to approximate the matrix inversion, we reduce the total computational complexity to $\mathcal{O}(LKM)$ . Compared with alternative algorithms, which focus on reducing the complexity of the matrix inversion only, the proposed method can also avoid calculating the Gram matrix explicitly and thus significantly reducing the total complexity.

Duality of channel encoding and decoding ‐ Part I: rate‐1 binary convolutional codes

AbstractIn this paper, we revisit the forward, backward and bidirectional Bahl–Cocke–Jelinek–Raviv (BCJR) soft‐input soft‐output (SISO) maximum a posteriori probability (MAP) decoding process of rate‐1 binary convolutional codes. From this, we establish some interesting explicit relationships between encoding and decoding of rate‐1 convolutional codes. We observe that the forward and backward BCJR SISO MAP decoders can be simply represented by their dual SISO channel encoders using shift registers in the complex number field. Similarly, the bidirectional MAP decoding can be implemented by linearly combining the shift register contents of the dual SISO encoders of the respective forward and backward decoders. The dual encoder structures for various recursive and non‐recursive rate‐1 convolutional codes are derived. Copyright © 2016 John Wiley & Sons, Ltd.

Performance and Complexity Evaluation of Iterative Receiver for Coded MIMO-OFDM Systems

Multiple-input multiple-output (MIMO) technology in combination with channel coding technique is a promising solution for reliable high data rate transmission in future wireless communication systems. However, these technologies pose significant challenges for the design of an iterative receiver. In this paper, an efficient receiver combining soft-input soft-output (SISO) detection based on low-complexity K-Best (LC-K-Best) decoder with various forward error correction codes, namely, LTE turbo decoder and LDPC decoder, is investigated. We first investigate the convergence behaviors of the iterative MIMO receivers to determine the required inner and outer iterations. Consequently, the performance of LC-K-Best based receiver is evaluated in various LTE channel environments and compared with other MIMO detection schemes. Moreover, the computational complexity of the iterative receiver with different channel coding techniques is evaluated and compared with different modulation orders and coding rates. Simulation results show that LC-K-Best based receiver achieves satisfactory performance-complexity trade-offs.