Study On The High Performance Encoding And Decoding Methods And Its Relative Techniques Of Reed-Solomon Codes

The error-control technique is one of the key techniques to preserve the image data integrity of large-scale solid-state recorder system in space application. Because of their ability to correct both burst errors and random errors, especially the burst errors. RS codes were widely used in the error-control schemes of data recording system. In this thesis, on the basis of the encoding-decoding algorithms, their implementing paths and their relative technologies developed in these fields, some guiding achievements for the fttture engineering applications were obtained through much systematic and profound work. The thesis mainly expounded as foIlowin~s: Firstly, the effective multiplication and inversion algorithms over finite field with the aspects of low apace and time complexity and their implementations suiting for RS codes were studied. Based on the Weakly-Dual-Basis (WDB) the optimum WDB was obtained and the bit-parallel multiplier was designed using the optimum WDB. The encoder or decoder constructed by the multiplier can implement the transitions between the basis simply and also can achieve high data throughput. The fast inversion algorithm based on Massev-Omura multiplier and its VLSI implementation with parallel inputting-outputting architecture were the good choice of inversion methods over finite field. The above algorithms have the characters of [ow space and time complexity, regular architecture and simple control signals. Secondly, the effective encoding and decoding methods and their implementing architectures were studied in detail. Based on the bit-parallel multipliers in optimum WDB over finite field and utilizing the modified systolic RS encoding algorithm, the RS encoder was designed. And the encoder can achieve very high data throughput and the complexity is also very low. Also based on the bit-parallel multipliers in optimum WDB over finite field and utilizing the obtained modified BM algorithm. the module decoder was designed. The frequency-domain decoding method based on modified Euclid algorithm and its parallel pipeline architecture were also presented. All of these decoding methods have the aspects of regular architecture, low decoding error probability and high data throughput. And they are suited for high application Situations. Thirdly, the data interleaving and unscrambling techniques related with the encoding-decoding methods of RS codes were also discussed. Based on the principles of encoding delay and storage capacity, the optimum interleaver and unsrcamber were achieved. In the end. some theoretical analysis and computer simulating experiments for the error-correcting performance of studied encoding and decoding algorithms were carried. The simulating experiments indicated: the incorporation of the encoding- decoding algorithms and their relative techniques obtained by study can correct the errors in image data. And the speed, decoding error probability and hardware implementing complexity also have new developments, and them can meet the requirements presented by the engineering projects.