Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix

An iterative algorithm is presented for soft-input-soft-output (SISO) decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the sum product algorithm (SPA) in conjunction with a binary parity check matrix of the RS code. The novelty is in reducing a submatrix of the binary parity check matrix that corresponds to less reliable bits to a sparse nature before the SPA is applied at each iteration. The proposed algorithm can be geometrically interpreted as a two-stage gradient descent with an adaptive potential function. This adaptive procedure is crucial to the convergence behavior of the gradient descent algorithm and, therefore, significantly improves the performance. Simulation results show that the proposed decoding algorithm and its variations provide significant gain over hard decision decoding (HDD) and compare favorably with other popular soft decision decoding methods.Comment: 10 pages, 10 figures, final version accepted by IEEE Trans. on Information Theor

Turbo Decoding and Detection for Wireless Applications

A historical perspective of turbo coding and turbo transceivers inspired by the generic turbo principles is provided, as it evolved from Shannon’s visionary predictions. More specifically, we commence by discussing the turbo principles, which have been shown to be capable of performing close to Shannon’s capacity limit. We continue by reviewing the classic maximum a posteriori probability decoder. These discussions are followed by studying the effect of a range of system parameters in a systematic fashion, in order to gauge their performance ramifications. In the second part of this treatise, we focus our attention on the family of iterative receivers designed for wireless communication systems, which were partly inspired by the invention of turbo codes. More specifically, the family of iteratively detected joint coding and modulation schemes, turbo equalization, concatenated spacetime and channel coding arrangements, as well as multi-user detection and three-stage multimedia systems are highlighted

Multi-non-binary turbo codes

International audienceThis paper presents a new family of turbo codes called multi-non-binary turbo codes (MNBTCs) that generalizes the concept of turbo codes to multi-non-binary (MNB) parallel concatenated convolutional codes (PCCC). An MNBTC incorporates, as component encoders, recursive and systematic multi-non-binary convolutional encoders. The more compact data structure for these encoders confers some advantages on MNBTCs over other types of turbo codes, such as better asymptotic behavior, better convergence, and reduced latency. This paper presents in detail the structure and operation of an MNBTC: MNB encoding, trellis termination, Max-Log-MAP decoding adapted to the MNB case. It also shows an example of MNBTC whose performance is compared with the state-of-the-art turbo code adopted in the DVB-RCS2 standard

On distributed coding, quantization of channel measurements and faster-than-Nyquist signaling

This dissertation considers three different aspects of modern digital communication systems and is therefore divided in three parts. The first part is distributed coding. This part deals with source and source- channel code design issues for digital communication systems with many transmitters and one receiver or with one transmitter and one receiver but with side information at the receiver, which is not available at the transmitter. Such problems are attracting attention lately, as they constitute a way of extending the classical point-to-point communication theory to networks. In this first part of this dissertation, novel source and source-channel codes are designed by converting each of the considered distributed coding problems into an equivalent classical channel coding or classical source-channel coding problem. The proposed schemes come very close to the theoretical limits and thus, are able to exhibit some of the gains predicted by network information theory. In the other two parts of this dissertation classical point-to-point digital com- munication systems are considered. The second part is quantization of coded chan- nel measurements at the receiver. Quantization is a way to limit the accuracy of continuous-valued measurements so that they can be processed in the digital domain. Depending on the desired type of processing of the quantized data, different quantizer design criteria should be used. In this second part of this dissertation, the quantized received values from the channel are processed by the receiver, which tries to recover the transmitted information. An exhaustive comparison of several quantization cri- teria for this case are studied providing illuminating insight for this quantizer design problem. The third part of this dissertation is faster-than-Nyquist signaling. The Nyquist rate in classical point-to-point bandwidth-limited digital communication systems is considered as the maximum transmission rate or signaling rate and is equal to twice the bandwidth of the channel. In this last part of the dissertation, we question this Nyquist rate limitation by transmitting at higher signaling rates through the same bandwidth. By mitigating the incurred interference due to the faster-than-Nyquist rates, gains over Nyquist rate systems are obtained

Turbo space-time coding for mimo systems : designs and analyses

Multiple input multiple output (MIMO) systems can provide high diversity, high data rate or a mix of both, for wireless communications. This dissertation combines both modes and suggests analyses and techniques that advance the state of the art of MIMO systems. Specifically, this dissertation studies turbo space-time coding schemes for MIMO systems. Before the designs of turbo space-time codes are presented, a fundamental tool to analyze and design turbo coding schemes, the extrinsic information transfer (EXIT) chart method, is extended from the binary/nonbinary code case to coded modulation case. This extension prepares the convergence analysis for turbo space-time code. Turbo space-time codes with symbols precoded by randomly chosen unitary time variant linear transformations (TVLT) are investigated in this dissertation. It is shown that turbo codes with TVLT achieve full diversity gain and good coding gain with high probability. The probability that these design goals are not met is shown to vanish exponentially with the Hamming distance between codewords (number of different columns). Hence, exhaustive tests of the rank and the determinant criterion are not required. As an additional benefit of the application of TVLT, with the removal of the constant modulation condition, it is proved that throughput rates achieved by these codes are significantly higher than the rates achievable by conventional space-time codes. Finally, an EXIT chart analysis for turbo space-time codes with TVLT is developed, with application to predicting frame error rate (FER) performance without running full simulation. To increase the data rate of turbo-STC without exponentially increasing the decoding complexity, a multilevel turbo space-time coding scheme with TVLT is proposed. An iterative joint demapping and decoding receiver algorithm is also proposed. For MIMO systems with a large number of transmit antennas, two types of layered turbo space-time (LTST) coding schemes are studied. For systems with low order modulation, a type of LTST with a vertical encoding structure and a low complexity parallel interference cancellation (PlC) receiver is shown to achieve close to capacity performance. For high order modulation, another type of LTST with a horizontal encoding structure, TVLT, and an ordered successive interference cancellation (OSIC) receiver is shown to achieve better performance than conventional layered space-time coding schemes, where ordering is not available in the SIC detection

Investigation of non-binary trellis codes designed for impulsive noise environments

PhD ThesisIt is well known that binary codes with iterative decoders can achieve near Shannon limit performance on the additive white Gaussian noise (AWGN) channel, but their performance on more realistic wired or wireless channels can become degraded due to the presence of burst errors or impulsive noise. In such extreme environments, error correction alone cannot combat the serious e ect of the channel and must be combined with the signal processing techniques such as channel estimation, channel equalisation and orthogonal frequency division multiplexing (OFDM). However, even after the received signal has been processed, it can still contain burst errors, or the noise present in the signal maybe non Gaussian. In these cases, popular binary coding schemes such as Low-Density Parity-Check (LDPC) or turbo codes may not perform optimally, resulting in the degradation of performance. Nevertheless, there is still scope for the design of new non-binary codes that are more suitable for these environments, allowing us to achieve further gains in performance. In this thesis, an investigation into good non-binary trellis error-correcting codes and advanced noise reduction techniques has been carried out with the aim of enhancing the performance of wired and wireless communication networks in di erent extreme environments. These environments include, urban, indoor, pedestrian, underwater, and powerline communication (PLC). This work includes an examination of the performance of non-binary trellis codes in harsh scenarios such as underwater communications when the noise channel is additive S S noise. Similar work was also conducted for single input single output (SISO) power line communication systems for single carrier (SC) and multi carrier (MC) over realistic multi-path frequency selective channels. A further examination of multi-input multi-output (MIMO) wired and wireless systems on Middleton class A noise channel was carried out. The main focus of the project was non-binary coding schemes as it is well-known that they outperform their binary counterparts when the channel is bursty. However, few studies have investigated non-binary codes for other environments. The major novelty of this work is the comparison of the performance of non-binary trellis codes with binary trellis codes in various scenarios, leading to the conclusion that non-binary codes are, in most cases, superior in performance to binary codes. Furthermore, the theoretical bounds of SISO and MIMO binary and non-binary convolutional coded OFDM-PLC systems have been investigated for the rst time. In order to validate our results, the implementation of simulated and theoretical results have been obtained for di erent values of noise parameters and on di erent PLC channels. The results show a strong agreement between the simulated and theoretical analysis for all cases.University of Thi-Qar for choosing me for their PhD scholarship and the Iraqi Ministry of Higher Education and Scienti c Research (MOHESR) for granting me the funds to study in UK. In addition, there was ample support towards my stay in the UK from the Iraqi Cultural Attach e in Londo