Reliable communication is an important part of everyday living. When transmitting a message over a physical channel, noise is introduced that causes errors in the message. These errors can be inversion errors or synchronization errors. The aim of this thesis is to investigate coding techniques to minimise the effect of synchronization errors that occurred in a transmitted message. Watermarks are inserted into the encoded sequence. A neural network system is implemented before the decoder to detect the watermark and regain synchronization. / Prof. H. C. Ferreira

Cellular Digital Packet Data (CDPD) is a new wireless packet data communications system which was developed by a consortium of U.S. cellular service providers to augment their voice communications systems. The main goal of the CDPD system design was to provide wireless packet data connectivity to mobile data communications customers. This thesis presents fundamental information required to successfully implement CDPD base station or mobile equipment. This information includes an introduction to the operation of data networks, a discussion of Gaussian Filtered Minimum Shift Keying (GMSK), and a detailed analysis of Reed-Solomon error correction codes. / Master of Science

Mass., Massachusetts Inst. of Technology, Diss.--Cambridge, 2001. / Literaturverz. S. [337] - 347.

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M.Ing. (Electrical and Electronic Engineering) / In this study, the problem of correcting burst of adjacent deletions by adapting product codes was investigated. The first step in any digital transmission is to establish synchronization between the sending and receiving nodes. This initial synchronization ensures that the receiver samples the information bits at the correct interval. Unfortunately synchronization is not guaranteed to last for the entire duration of data transmission. Though synchronization errors rarely occur, it has disastrous effects at the receiving end of transmission. These synchronization errors are modelled as either insertions or deletions in the transmitted data. In the best case scenario, these errors are restricted to single bit errors. In the worst case scenario, these errors lead to bursts of bits being incorrect. If these synchronization errors are not detected and corrected, it can cause a shift in the transmitted sequence which in turn leads to loss of synchronization. When a signal is subjected to synchronization errors it is difficult accurately recover the original data signal. In addition to the loss of synchronization, the information transmitted over the channel is also subjected to noise. This noise in the channel causes inversion errors within the signal. The objective of this dissertation is to investigate if an error correction scheme can be designed that has the ability to detect and correct adjacent bursts of deletions and random inversion errors. This error correction scheme needed to make use of a product code matrix structure. This product matrix needed to incorporate both an error correction and synchronization technique. The chosen error correcting techniques were Hamming and Reed-Solomon codes. The chosen synchronization techniques for this project were the marker technique or an adaptation of the Hamming code technique. In order to find an effective model, combinations of these models were simulated and compared. From the research obtained and analyzed in this document it was found that, depending on the desired performance, complexity and code rate, an error correction scheme can be used in the efficient correction of bursts of adjacent deletions by adapting product codes.

Masters Report A report submitted in ful llment of the requirements for the degree of Master of Science (50/50) in the Centre for Telecommunication Access and Services (CeTAS) School of Electrical and Information Engineering Faculty of Engineering and the Built Environment February 2017 / Bounded distance decoding of Reed Solomon (RS) codes involves nding a unique codeword if there is at least one codeword within the given distance. A corrupted message having errors that is less than or equal to half the minimum distance cor- responds to a unique codeword, and therefore will decode errors correctly using the minimum distance decoder. However, increasing the decoding radius to be slightly higher than half of the minimum distance may result in multiple codewords within the Hamming sphere. The list decoding and syndrome extension methods provide a maximum error correcting capability whereby the radius of the Hamming ball can be extended for low rate RS codes. In this research, we study the probability of having unique codewords for (7; k) RS codes when the decoding radius is increased from the error correcting capability t to t + 1. Simulation results show a signi cant e ect of the code rates on the probability of having unique codewords. It also shows that the probability of having unique codeword for low rate codes is close to one. / MT2017

A dissertation submitted in fulfilment of the requirements for the degree of Master of Science in the Centre for Telecommunication Access and Services, School of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg, 2016 / Reed-Solomon codes are very popular codes used in the field of forward error correction due to their correcting capabilities. Thus, a lot of research has been done dedicated to the development of decoding algorithms for this class of code. [Abbreviated Abstract. Open document to view full version]

With the approach of the era of digital TV system around the world, how to grasp the design techniques of the receiver of the DVB-T has become a very important topic. The goal of this thesis is to pursue a highly optimized VLSI architecture compatible to the channel decoding standard of the DVB-T protocol. The channel decoding scheme adopted in DVB-T is based on the concatenated code; which is comprised of an inner Viterbi decoder, outer Reed-Solomon decoder and inner and outer de-interleaver modules. These modules all require a significant amount of data storage space, therefore the main feature of the proposed channel decoder architectures is to realize the data storage based on RAM instead of registers. This approach can lead to the reduction of silicon area and the dynamic power dissipation compared with the shift register based architecture. In order to achieve this, in the design of Viterbi module, the popular register-exchange and trace-back techniques used for the detection of the survivor path has been combined for the survivor memory management unit. As for the design of Reed-Solomon decoder, it is designed based on the modified inverse-free Berlekamp-Massey algorithm. A novel finite field constant multiplier architecture has been proposed which can reduce the required gate count of the multipliers by 20%. For outer convolutional deinterleaver, a specific address generator has been designed such that the data deinterleaver path can be merged and implemented as two memory blocks. For inner symbol deinterleaver, a lookahead technique has been applied to the design of address generator and deinterleaver memory has been reduced by a half compared with those in the literature. These four modules have been verified and integrated as robust channel decoder silicon IP. The related models used for IP integration and verification have also been provided. The prototyping on the FPGA has been tested to satisfy the requirement of the spec.

Reed-Solomon codes are a class of maximum distance separable error correcting codes with known fast error correction algorithms. They have been widely used to assure data integrity for stored data on compact discs, DVDs, and in RAID storage systems, for digital communications channels such as DSL internet connections, and for deep space communications on the Voyager mission. The recent explosion of storage needs for "Big Data'' has generated renewed interest in large storage systems with extended error correction capacity. Reed-Solomon codes have been suggested as one potential solution. This dissertation reviews the theory of Reed-Solomon codes from the perspective taken in Reed and Solomon's original paper on them. It then derives the Welch-Berlekamp algorithm for solving certain polynomial equations, and connects this algorithm to the problem of error correction. The discussion is mathematically rigorous, and provides a complete and consistent discussion of the error correction process. Numerous algorithms for encoding, decoding, erasure recovery, error detection, and error correction are provided and their computational cost is analyzed and discussed thus allowing this dissertation to serve as a manual for engineers interested in implementing Reed-Solomon coding.

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