3. Electronic Theses and Dissertations (ETDs) - All submissions

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Subject: search.filters.subject.Reed-Solomon codes

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    Improving the convergence rate of the iterative parity check transformation algorithm decoder for Reed-Solomon codes
    (2018) Brookstein, Peter C.
    This masters by research dissertation contributes to research in the field of Telecommunications, with a focus on forward error correction and improving an iterative Reed-Solomon decoder known as the Parity-check Transformation Algorithm (PTA). Previous work in this field has focused on improving the runtime parameters and stopping conditions of the algorithm in order to reduce its computational complexity. In this dissertation, a di↵erent approach is taken by modifying the algorithm to more e↵ectively utilise the soft-decision channel information provided by the demodulator. Modifications drawing inspiration from the Belief Propagation (BP) algorithm used to decode Low-Density Parity-Check (LDPC) codes are successfully implemented and tested. In addition to the selection of potential codeword symbols, these changes make use of soft channel information to calculate dynamic weighting values. These dynamic weights are further used to modify the intrinsic reliability of the selected symbols after each iteration. Improvements to both the Symbol Error Rate (SER) performance and the rate of convergence of the decoder are quantified using computer simulations implemented in MATLAB and GNU Octave. A deterministic framework for executing these simulations is created and utilised to ensure that all results are reproducible and can be easily audited. Comparative simulations are performed between the modified algorithm and the PTA in its most e↵ective known configuration (with =0 .001). Results of simulations decoding half-rate RS(15,7) codewords over a 16-QAM AWGN channel show a more than 50-fold reduction in the number of operations required by the modified algorithm to converge on a valid codeword. This is achieved while simultaneously observing a coding gain of 1dB for symbol error rates between 102 and 104.
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    Analysis of bounded distance decoding for Reed Solomon codes
    (2017) Babalola, Oluwaseyi Paul
    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.
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    Symbol level decoding of Reed-Solomon codes with improved reliability information over fading channels
    (2016) Ogundile, Olanyika Olaolu
    Reliable 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.
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    Modifications to the symbol wise soft input parity check transformation decoding algorithm
    (2016) Genga, Yuval Odhiambo
    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]
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