Performance of multi level‐turbo coding with neural network‐based channel estimation over WSSUS MIMO channels

This paper presents the performance of the transmit diversity‐multi level turbo codes (TD‐MLTC) over the multiple‐input–multiple‐output (MIMO) channels based on the wide sense stationary uncorrelated scattering (WSSUS). The multi level‐turbo code (ML‐TC) system contains more than one turbo encoder/decoder block in its structure. At the transmitter side, the ML‐TC uses the group partitioning technique that partitions a signal set into several levels and encodes each level separately by a proper component of the encoder to improve error performance. The binary input sequence is passed through the MLTC encoder and mapped to 4‐PSK and then fed into the transmit diversity scheme for high data transmission over wireless fading channels. At the receiver side, distorted multi‐path signals are received by multiple receiver antennae. WSSUS MIMO channel parameters are estimated by using an artificial neural network and an iterative combiner. Input sequence of the first level of the MLTC encoder is estimated at the first level of MLTC decoder. Subsequently, the other input sequences are computed by using the estimated input bit streams of the previous levels. 4‐PSK two‐level turbo codes are simulated for 2T_x?1R_x and 2T_x?2R_x antenna configurations over WSSUS MIMO channels. Here, TD‐MLTC and its efficient implementations are discussed and simulation results are given. Copyright © 2008 John Wiley & Sons, Ltd.     

Multilevel/AES-LDPCC-CPFSK with channel equalization over WSSUS multipath environment

In this paper, in order to ensure secure and robust communication, a new type of data encryption and error correction mechanism called Multilevel/Advanced Encryption Standard-Low Density Parity Check Coded-Continuous Phase Frequency Shift Keying (Multilevel/AES-LDPCC-CPFSK) is carried out. Here, we have chosen AES for data encryption, LDPC codes for error correction and CPFSK for modulation. We have evaluated error performance of this scheme over Wide-Sense Stationary Uncorrelated Scattering (WSSUS) multipath channels with channel equalization. We have simulated 5-level AES, 2-level LDPC for 4CPFSK and 16CPFSK over WSSUS channels modeled by Cooperation in the field of Science & Technology, Project #207 (COST207). We have concluded that our proposed structure has promising results compared to Turbo Codes for all SNR values in WSSUS channels.     

Concatenation of space‐time block codes and turbo trellis coded modulation (ST‐TTCM) over Rician fading channels with imperfect phase

In this paper, the performance of space time‐turbo trellis coded modulation (ST‐TTCM) is evaluated over Rician and Rayleigh fading channels with imperfect phase. We modify Baum–Welch (BW) algorithm to estimate the fading and phase jitter parameters for multi‐antenna configurations. Thus, we assume that the channel parameters change slower than carrier frequency. We know that, at high data rate transmissions over wireless fading channels, space–time block codes (STBC) provide the maximal possible diversity advantage. Here, the combined effects of the amplitude and the phase of the received signal are considered, each one modelled by Rician and Tikhonov distributions, respectively. We investigate space time‐turbo trellis coded modulation (ST‐TTCM) for 8‐PSK for several Rician factor K and phase distortion factor η. Thus, our results reflect the degradations both due to the effects of the fading on the amplitude and phase noise of the received signal while the channel parameters are estimated by BW algorithm. Copyright © 2004 John Wiley & Sons, Ltd.     

Network‐coded MIMO‐NOMA systems with FEC codes in two‐way relay networks

This paper assumes two users and a two‐way relay network with the combination of 2×2 multi‐input multi‐output (MIMO) and nonorthogonal multiple access (NOMA). To achieve network reliability without sacrificing network throughput, network‐coded MIMO‐NOMA schemes with convolutional, Reed‐Solomon (RS), and turbo codes are applied. Messages from two users at the relay node are network‐coded and combined in NOMA scheme. Interleaved differential encoding with redundancy (R‐RIDE) scheme is proposed together with MIMO‐NOMA system. Quadrature phase‐shift keying (QPSK) modulation technique is used. Bit error rate (BER) versus signal‐to‐noise ratio (SNR) (dB) and average mutual information (AMI) (bps/Hz) versus SNR (dB) in NOMA and MIMO‐NOMA schemes are evaluated and presented. From the simulated results, the combination of MIMO‐NOMA system with the proposed R‐RIDE‐Turbo network‐coded scheme in two‐way relay networks has better BER and higher AMI performance than conventional coded NOMA system. Furthermore, R‐RIDE‐Turbo scheme in MIMO‐NOMA system outperforms the other coded schemes in both MIMO‐NOMA and NOMA systems.     

Bandwidth‐efficient turbo coding over Rayleigh fading channels

Introduced in 1993, turbo codes can achieve high coding gains close to the Shannon limit. In order to design power and bandwidth‐efficient coding schemes, several approaches have been introduced to combine high coding rate turbo codes with multilevel modulations. The coding systems thus obtained have been shown to display near‐capacity performance over additive white Gaussian noise (AWGN) channels. For communications over fading channels requiring large coding gain and high bandwidth efficiency, it is also interesting to study bit error rate (BER) performance of turbo codes combined with high order rectangular QAM modulations. To this end, we investigate, in this paper, error performance of several bandwidth‐efficient schemes designed using the bit‐interleaved coded modulation approach that has proven potentially very attractive when powerful codes, such as turbo codes, are employed. The structure of these coding schemes, termed ‘bit‐interleaved turbo‐coded modulations’ (BITCMs), is presented in a detailed manner and their BER performance is investigated for spectral efficiencies ranging from 2 to 7 bit/s/Hz. Computer simulation results indicate that BITCMs can achieve near‐capacity performance over Rayleigh fading channels, for all spectral efficiencies considered throughout the paper. It is also shown that the combination of turbo coding and rectangular QAM modulation with Gray mapping constitutes inherently a very powerful association, since coding and modulation functions are both optimized for operation in the same signal‐to‐noise ratio region. This means that no BER improvement is obtainable by employing any other signal constellation in place of the rectangular ones. Finally, the actual influence of the interleaving and mapping functions on error performance of BITCM schemes is discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Carrier phase recovery for turbo‐coded systems with pre‐coded GMSK modulation

A carrier phase recovery scheme suited for turbo‐coded systems with pre‐coded Gaussian minimum shift keying (GMSK) modulation is proposed and evaluated in terms of bit‐error‐rate (BER) performance. This scheme involves utilizing the extrinsic information obtained from the turbo‐decoder to aid an iterative carrier phase estimation process, based on a maximum‐likelihood (ML) strategy. The phase estimator works jointly with the turbo‐decoder, using the updated extrinsic information from the turbo‐decoder in every iterative decoding. A pre‐coder is used to remove the inherent differential encoding of the GMSK modulation. Two bandwidths of GMSK signals are considered: BT=0.5 and 0.25, which are recommended by the European Cooperation for Space Standardization (ECSS). It is shown that the performance of this technique is quite close to the perfect synchronized system within a wide range of phase errors. This technique is further developed to recover nearly any phase error in [?π,+π] by increasing the number of phase estimators and joint decoding units. This, however, will increase the complexity of the system. Copyright © 2008 John Wiley & Sons, Ltd.     

An FPGA Implementation of High‐Speed Flexible 27‐Mbps 8‐StateTurbo Decoder

In this paper, we propose a flexible turbo decoding algorithm for a high order modulation scheme that uses a standard half‐rate turbo decoder designed for binary quadrature phase‐shift keying (B/QPSK) modulation. A transformation applied to the incoming I‐channel and Q‐channel symbols allows the use of an off‐the‐shelf B/QPSK turbo decoder without any modifications. Iterative codes such as turbo codes process the received symbols recursively to improve performance. As the number of iterations increases, the execution time and power consumption also increase. The proposed algorithm reduces the latency and power consumption by combination of the radix‐4, dual‐path processing, parallel decoding, and early‐stop algorithms. We implement the proposed scheme on a field‐programmable gate array and compare its decoding speed with that of a conventional decoder. The results show that the proposed flexible decoding algorithm is 6.4 times faster than the conventional scheme.     

Blind equalization for an application of unitary space-time modulation in ISI channels

Transmit diversity schemes have gained attention due to the promise of increased capacity and improved performance. Among these schemes, unitary space-time modulation and differentially encoded unitary space-time modulation allow for simple noncoherent decoding for flat-fading channels. In this paper, a new blind equalization algorithm for these transmission schemes in intersymbol interference (ISI) channels is proposed. A matrix-type constant modulus algorithm that exploits the unitary structure of the space-time codes is developed. The equalizer is paired with a noncoherent decoder, resulting in a completely blind, low-complexity method for decoding in the presence of ISI. A noiseless convergence analysis is conducted and verified via simulation in both noiseless and noisy cases. The performance of the overall system is evaluated via simulation and semi-analytically, and the achieved performance is between that of the ideal zero-forcing and the minimum-mean squared-error equalizers.     

Performance of joint multilevel/AES‐LDPCC‐CPFSK schemes over wireless sensor networks

In wireless sensor networks, data encryption and channel coding are considered together for ensuring secure and robust communication. In order to achieve this purpose, we introduce a new joint scheme, namely ‘Multilevel/Advanced Encryption Standard‐Low Density Parity Check Coded‐Continuous Phase Frequency Shift Keying (ML/AES‐LDPCC‐CPFSK)’. AES algorithm is the most powerful and widely used symmetric key cryptography in providing secure data transmission. LDPC codes have very large Euclidean distance and use iterative decoding algorithms. In this study, we have increased error performance employing multilevel structure to AES and LDPC. In all communications systems, phase discontinuities of modulated signals result in extra bandwidth requirements. CPFSK, which is a special type of continuous phase modulation, is a powerful solution for this problem. In this paper, we simulate error performance of ML/AES‐LDPCC‐CPFSK for regular LDPC codes. Simulation results are drawn for 4CPFSK, 8CPFSK and 16CPFSK over wireless cooperative sensor networks. Using this scheme, we are able to improve bit error performance, channel throughput, security level of communication and reduction in complexity compared with related schemes such as various turbo code structures. Copyright © 2009 John Wiley & Sons, Ltd.     

EM‐based iterative receiver for coded MIMO systems in unknown spatially correlated noise

We present iterative channel estimation and decoding schemes for multi‐input multi‐output (MIMO) Rayleigh block fading channels in spatially correlated noise. An expectation‐maximization (EM) algorithm is utilized to find the maximum likelihood (ML) estimates of the channel and spatial noise covariance matrices, and to compute soft information of coded symbols which is sent to an error‐control decoder. The extrinsic information produced by the decoder is then used to refine channel estimation. Several iterations are performed between the above channel estimation and decoding steps. We derive modified Cramer–Rao Bound (MCRB) for the unknown channel and noise parameters, and show that the proposed EM‐based channel estimation scheme achieves the MCRB at medium and high SNRs. For a bit error rate of 10⁻⁶ and long frame length, there is negligible performance difference between the proposed scheme and the ideal coherent detector that utilizes the true channel and noise covariance matrices. Copyright © 2006 John Wiley & Sons, Ltd.     

A novel expression for the achievable MSE performance obtained by blind adaptive equalizers

In this paper, I propose for the noisy, real, and two independent quadrature carrier case, an approximated closed-form expression for the achievable minimum mean square error (MSE) performance obtained by blind equalizers where the error that is fed into the adaptive mechanism which updates the equalizer’s taps can be expressed as a polynomial function of the equalized output of order three like in Godard’s algorithm. The proposed closed-form expression for the achievable MSE is based on the step-size parameter, on the equalizer’s tap length, on the channel power, on the signal to noise ratio (SNR), on the nature of the chosen equalizer, and on the input signal statistics. Since the channel power is measurable or can be calculated if the channel coefficients are given, there is no need anymore to carry out any simulation with various step-size parameters, different values for the signal to noise ratio (SNR) and equalizer’s tap length for a given equalization method, and input signal statistics in order to find the MSE performance in the convergence state.     

SNR mismatch and online estimation in turbo decoding

Iterative decoding of turbo codes, as well as other concatenated coding schemes of similar nature, requires knowledge of the signal-to-noise ratio (SNR) of the channel so that proper blending of the a posteriori information of the separate decoders is achieved. We study the sensitivity of decoder performance to misestimation of the SNR, and propose a simple online scheme that estimates the unknown SNR from each code block, prior to decoding. We show that this scheme is sufficiently adequate in accuracy to not appreciably degrade the performance     

Turbo equalization via constrained-delay APP estimation with decision feedback

We consider turbo equalization for intersymbol interference (ISI) channels, wherein soft symbol decisions generated by the channel detector are iteratively exchanged with the outer error-correction decoder based on the turbo principle. Our work is based on low-complexity suboptimal soft-output channel detection using a constrained-delay (CD) a posteriori probability (APP) algorithm. Central to the proposed idea is the incorporation of effective decision-feedback schemes, which significantly reduce complexity while providing immunity against error propagation that typically plagues decision-feedback schemes. We observe that the effect of decision feedback is quite different on turbo equalization versus traditional, hard-decision-generating and noniterative equalization. In particular, we demonstrate that when the feedback scheme applied is inadequate for the given equalizer parameters and ISI condition, the extrinsic information generated by the equalizer becomes distinctly non-Gaussian, and the quality of soft information, as monitored by the trajectory of mutual information, fails to improve in the iterative process. We identify parameters of feedback-based CD-APP schemes that offer favorable complexity/performance tradeoffs, compared with existing turbo-equalization techniques.     

Near‐Optimum Blind Decision Feedback Equalization for ATSC Digital Television Receivers

This paper presents a near‐optimum blind decision feedback equalizer (DFE) for the receivers of Advanced Television Systems Committee (ATSC) digital television. By adopting a modified trellis decoder (MTD) with a trace‐ back depth of 1 for the decision device in the DFE, we obtain a hardware‐efficient, blind DFE approaching the performance of an optimum DFE which has no error propagation. In the MTD, the absolute distance is used rather than the squared Euclidean distance for the computation of the branch metrics. This results in a reduction of the computational complexity over the original trellis decoding scheme. Compared to the conventional slicer, the MTD shows an outstanding performance improvement in decision error probability and is comparable to the original trellis decoder using the Euclidean distance. Reducing error propagation by use of the MTD in the DFE leads to the improvement of convergence performance in terms of convergence speed and residual error. Simulation results show that the proposed blind DFE performs much better than the blind DFE with the slicer, and the difference is prominent at the trellis decoder following the blind DFE.     

Channel-parameter estimation for turbo trellis coded modulation in OFDM systems

In this paper, a blind maximum-likelihood channel-parameter estimation algorithm is developed for turbo trellis coded modulation (TTCM) in orthogonal frequency division multiplexing (OFDM) systems. We modify the Baum-Welch (BW) parameter estimation algorithm to provide a computationally efficient solution for error performance. The bit-error performance of the TTCM-OFDM scheme has been investigated in AWGN, Rayleigh, Rician channels with and without channel-state information (CSI) for different Doppler shifts, signal-to-noise ratios (SNR), iteration numbers, number of subcarriers, and frame sizes. Published in Russian in Radiotekhnika i Elektronika, 2007, Vol. 52, No. 3, pp. 458–468. The text was submitted by the authors in English.     

Design and Architecture of Low‐Latency High‐Speed Turbo Decoders

In this paper, we propose and present implementation results of a high‐speed turbo decoding algorithm. The latency caused by (de)interleaving and iterative decoding in a conventional maximum a posteriori turbo decoder can be dramatically reduced with the proposed design. The source of the latency reduction is from the combination of the radix‐4, center to top, parallel decoding, and early‐stop algorithms. This reduced latency enables the use of the turbo decoder as a forward error correction scheme in real‐time wireless communication services. The proposed scheme results in a slight degradation in bit error rate performance for large block sizes because the effective interleaver size in a radix‐4 implementation is reduced to half, relative to the conventional method. To prove the latency reduction, we implemented the proposed scheme on a field‐programmable gate array and compared its decoding speed with that of a conventional decoder. The results show an improvement of at least five fold for a single iteration of turbo decoding.     

Near-capacity turbo trellis coded modulation design based on EXIT charts and union bounds - [transactions papers]

Bandwidth efficient parallel-concatenated Turbo Trellis Coded Modulation (TTCM) schemes were designed for communicating over uncorrelated Rayleigh fading channels. A symbol-based union bound was derived for analysing the error floor of the proposed TTCM schemes. A pair of In-phase (I) and Quadrature-phase (Q) interleavers were employed for interleaving the I and Q components of the TTCMcoded symbols, in order to attain an increased diversity gain. The decoding convergence of the IQ-TTCM schemes was analysed using symbol-based EXtrinsic Information Transfer (EXIT) charts. The best TTCM component codes were selected with the aid of both the symbolbased union bound and non-binary EXIT charts, for designing capacity-approaching IQ-TTCM schemes in the context of 8PSK, 16QAM, 32QAM and 64QAM modulation schemes.     

SNR estimation in Nakagami-m fading with diversity combining and its application to turbo decoding

We propose an online signal-to-noise ratio (SNR) estimation scheme for Nakagami-m (1960) fading channels with L branch equal gain combining (EGC) diversity. We derive the SNR estimate based on the statistical ratio of certain observables over a block of data, and use the SNR estimates in the iterative decoding of turbo codes on Nakagami-m fading channels with L branch EGC diversity. We evaluate the turbo decoder performance using the SNR estimate under various fading and diversity scenarios (m = 0.5, 1, 5 and L = 1, 2, 3) and compare it with the performance using perfect knowledge of the SNR and the fade amplitudes.     

Trellis code‐aided high‐rate M‐QAM space‐time labeling diversity using a unitary expansion

In this paper, we present a high‐rate M‐ary quadrature amplitude modulation (M‐QAM) space‐time labeling diversity (STLD) system that retains the robust error performance of the conventional STLD system. The high‐rate STLD is realised by expanding the conventional STLD via a unitary matrix transformation. Robust error performance of the high‐rate STLD is achieved by incorporating trellis coding into the mapping of additional bits to high‐rate codes. The comparison of spectral efficiency between the proposed trellis code‐aided high‐rate STLD (TC‐STLD) and the conventional STLD shows that TC‐STLD with 16‐QAM and 64‐QAM respectively achieves a 12.5% and 8.3% increase in spectral efficiency for each additional bit sent with the transmitted high‐rate codeword. Moreover, we derive an analytical bound to predict the average bit error probability performance of TC‐STLD over Rayleigh frequency‐flat fading channels. The analytical results are verified by Monte Carlo simulation results, which show that the derived analytical bounds closely predict the average bit error probability performance at high signal‐to‐noise ratios (SNR). Simulation results also show that TC‐STLD with 1 additional bit achieves an insignificant SNR gain of approximately 0.05 dB over the conventional STLD, while TC‐STLD with 2 additional bits achieves an SNR gain of approximately 0.12 dB.     

Conventional and modified TAS/OSTBC schemes in dual‐hop fixed‐gain amplify‐and‐forward relaying systems with imperfect feedback

Modified transmit antenna selection (TAS)/orthogonal space‐time block coding (OSTBC) (M‐TAS/OSTBC) schemes have been shown to achieve superior error performance together with a reduced‐rate feedback channel in the presence of feedback errors (FEs) when compared with the conventional TAS/OSTBC (C‐TAS/OSTBC) schemes. This paper focuses on the bringing of fixed‐gain amplify‐and‐forward (FGAF) relaying schemes that employ M‐TAS/OSTBC schemes at both hops that provides reduced feedback‐rate and robust error performance in the presence of erroneous‐feedback channels. The exact expressions of the outage and error probabilities for both dual‐hop FGAF relaying schemes in Nakagami‐m fading channels have been derived and validated via Monte Carlo simulations. Additionally, with the help of high signal‐to‐noise ratio (SNR) (i.e., asymptotic) approaches and some analytical approximations, the asymptotic diversity order analysis has been carried out. Besides, by providing a simulation‐based examination on the inclusion of power allocation within the modified scheme, the additional advantages on the performance have been exhibited. The extensive investigation and comparisons to the conventional schemes have shown that M‐TAS/OSTBC schemes employed at each transmission link provide full diversity order and considerable error performance as the C‐TAS/OSTBC scheme in ideal feedback cases and also achieve more robust error performance in the presence of FEs. Thus, by using M‐TAS/OSTBC schemes, the overall performances of the dual‐hop FGAF relaying schemes have been enhanced, which would result in reductions on the average SNR requirements to achieve a specified error rate constraint. Copyright © 2015 John Wiley & Sons, Ltd.