Symbol level decoding of Reed-Solomon codes with improved reliability information over fading channels

A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy in the School of Electrical and Information Engineering, 2016Reliable and e cient data transmission have been the subject of current research, most especially in realistic channels such as the Rayleigh fading channels. The focus of every new technique is to improve the transmission reliability and to increase the transmission capacity of the communication links for more information to be transmitted. Modulation schemes such as M-ary Quadrature Amplitude Modulation (M-QAM) and Orthogonal Frequency Division Multiplexing (OFDM) were developed to increase the transmission capacity of communication links without additional bandwidth expansion, and to reduce the design complexity of communication systems. On the contrary, due to the varying nature of communication channels, the message transmission reliability is subjected to a couple of factors. These factors include the channel estimation techniques and Forward Error Correction schemes (FEC) used in improving the message reliability. Innumerable channel estimation techniques have been proposed independently, and in combination with di erent FEC schemes in order to improve the message reliability. The emphasis have been to improve the channel estimation performance, bandwidth and power consumption, and the implementation time complexity of the estimation techniques. Of particular interest, FEC schemes such as Reed-Solomon (RS) codes, Turbo codes, Low Density Parity Check (LDPC) codes, Hamming codes, and Permutation codes, are proposed to improve the message transmission reliability of communication links. Turbo and LDPC codes have been used extensively to combat the varying nature of communication channels, most especially in joint iterative channel estimation and decoding receiver structures. In this thesis, attention is focused on using RS codes to improve the message reliability of a communication link because RS codes have good capability of correcting random and burst errors, and are useful in di erent wireless applications. This study concentrates on symbol level soft decision decoding of RS codes. In this regards, a novel symbol level iterative soft decision decoder for RS codes based on parity-check equations is developed. This Parity-check matrix Transformation Algorithm (PTA) is based on the soft reliability information derived from the channel output in order to perform syndrome checks in an iterative process. Performance analysis verify that this developed PTA outperforms the conventional RS hard decision decoding algorithms and the symbol level Koetter and Vardy (KV ) RS soft decision decoding algorithm. In addition, this thesis develops an improved Distance Metric (DM) method of deriving reliability information over Rayleigh fading channels for combined demodulation with symbol level RS soft decision decoding algorithms. The newly proposed DM method incorporates the channel state information in deriving the soft reliability information over Rayleigh fading channels. Analysis verify that this developed metric enhances the performance of symbol level RS soft decision decoders in comparison with the conventional method. Although, in this thesis, the performance of the developed DM method of deriving soft reliability information over Rayleigh fading channels is only veri ed for symbol level RS soft decision decoders, it is applicable to any symbol level soft decision decoding FEC scheme. Besides, the performance of the all FEC decoding schemes plummet as a result of the Rayleigh fading channels. This engender the development of joint iterative channel estimation and decoding receiver structures in order to improve the message reliability, most especially with Turbo and LDPC codes as the FEC schemes. As such, this thesis develops the rst joint iterative channel estimation and Reed- Solomon decoding receiver structure. Essentially, the joint iterative channel estimation and RS decoding receiver is developed based on the existing symbol level soft decision KV algorithm. Consequently, the joint iterative channel estimation and RS decoding receiver is extended to the developed RS parity-check matrix transformation algorithm. The PTA provides design ease and exibility, and lesser computational time complexity in an iterative receiver structure in comparison with the KV algorithm. Generally, the ndings of this thesis are relevant in improving the message transmission reliability of a communication link with RS codes. For instance, it is pertinent to numerous data transmission technologies such as Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), Digital Subscriber Line (DSL), WiMAX, and long distance satellite communications. Equally, the developed, less computationally intensive, and performance e cient symbol level decoding algorithm for RS codes can be use in consumer technologies like compact disc and digital versatile disc.GS201

Performance Investigation of MIMO Based CO-OFDM FSO Communication Link for BPSK, QPSK and 16-QAM under the Influence of Reed Solomon Codes

The MIMO based CO-OFDM FSO communication system is emerging as a promising approach to meet the future bandwidth requirements for seamless communication. The atmosphere being the propagation medium is a major hindrance in wide-scale acceptability of FSO technology. For seamless and error-free transmission and reception of data, a novel concept of MIMO integrated with RS code is proposed in this paper. The system performance of an RS 64 (RS (255,127)) coded MIMO-based CO-OFDM FSO communication link was investigated using BPSK, QPSK and 16-QAM under the combined effects of geometric losses, path losses and atmospheric attenuations at a hitherto un-investigated data rate of 40 Gbps and a link distance of 5 km. The modified gamma-gamma distribution was used for modeling a moderately turbulent channel. With link length varying over a range of 1 to 5 km, error correction was maximum in 16-QAM as compared to BPSK and QPSK, with 150 to 167 corrected errors. In terms of PAPR, PSK was more apt than QAM, but with a compromise in BER. The geometric losses were reduced with link length due to an increase in error correction capability for all three modulation cases, with the least losses occurring in 16-QAM. At the target bit error rate (BER), the signal to noise ratio (SNR) required for BPSK and QPSK was higher by 3.98 dB and 6.14 dB compared to 16-QAM

Improved distance metric technique for deriving soft reliability information over Rayleigh Fading Channel

This paper presents an improved Distance Metric (DM) technique for deriving soft reliability information over Rayleigh fading channel. We compared this proposed DM technique with the conventionally used DM technique in the literature. The conventional DM method derives the soft reliability information from the output received symbols while the proposed DM method derives the soft reliability information from the Channel State Information (CSI) which result due to variations in the channel gain. Performance analysis of these DM methods are verified over flat Rayleigh fading channels, and on time-varying frequency-selective Rayleigh fading channels using rectangular M-QAM and OFDM systems respectively. Also, two channel estimation techniques are used to derived the CSI assuming different normalized Doppler frequency and frame length size. The performance of the conventional and proposed soft reliability derivation methods are documented through computer simulations assuming Koetter and Vardy, Reed-Solomon (KV-RS) soft decision decoding algorithm as the Forward Error Correction (FEC) scheme. From the computer simulation results, the proposed DM method offers significant improvement in Codeword Error Rate (CER) performance in comparison with the conventional DM method with no significant increase in computational delay and time complexity.Keywords: CSI, cubic estimators, DM, fading channels, KV-RS decoder, LMMSE, OFDM, R-matrix, 16QA

Repeat-Accumulate構造に基づく直列連接信号符号

電気通信大学201

Self-concatenated code design and its application in power-efficient cooperative communications

In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions

Comparison of code rate and transmit diversity in MIMO systems

A thesis submitted in ful lment of the requirements for the degree of Master of Science in the Centre of Excellence in Telecommunications and Software School of Electrical and Information Engineering, March 2016In order to compare low rate error correcting codes to MIMO schemes with transmit diversity, two systems with the same throughput are compared. A VBLAST MIMO system with (15; 5) Reed-Solomon coding is compared to an Alamouti MIMO system with (15; 10) Reed-Solomon coding. The latter is found to perform signi cantly better, indicating that transmit diversity is a more e ective technique for minimising errors than reducing the code rate. The Guruswami-Sudan/Koetter-Vardy soft decision decoding algorithm was implemented to allow decoding beyond the conventional error correcting bound of RS codes and VBLAST was adapted to provide reliability information. Analysis is also performed to nd the optimal code rate when using various MIMO systems.MT201

Digital VLSI Architectures for Advanced Channel Decoders

Error-correcting codes are strongly adopted in almost every modern digital communication and storage system, such as wireless communications, optical communications, Flash memories, computer hard drives, sensor networks, and deep-space probes. New and emerging applications demand codes with better error-correcting capability. On the other hand, the design and implementation of those high-gain error-correcting codes pose many challenges. They usually involve complex mathematical computations, and mapping them directly to hardware often leads to very high complexity. This work aims to focus on Polar codes, which are a recent class of channel codes with the proven ability to reduce decoding error probability arbitrarily small as the block-length is increased, provided that the code rate is less than the capacity of the channel. This property and the recursive code-construction of this algorithms attracted wide interest from the communications community. Hardware architectures with reduced complexity can efficiently implement a polar codes decoder using either successive cancellation approximation or belief propagation algorithms. The latter offers higher throughput at high signal-to-noise ratio thanks to the inherently parallel decision-making capability of such decoder type. A new analysis on belief propagation scheduling algorithms for polar codes and on interconnection structure of the decoding trellis not covered in literature is also presented. It allowed to achieve an hardware implementation that increase the maximum information throughput under belief propagation decoding while also minimizing the implementation complexity