Research On Reed-solomon Codes

Reed-Solomon (RS) codes are non-binary cyclic error correcting codes discovered in 1960 by Reed and Solomon. They have been widely used in commercial applications such as wireless communications and storage systems. They have been employed in various digital communication standards including the third-generation wireless standard (3G), terrestrial digital multimedia broadcasting (T-DMB) and digital video broadcasting (DVB). It is not only a kind of linear block code, but also a non-binary code, so it has two features, that is, it can correct both random and burst errors. And the latter one is its key feature and the reason why it is widely used. RS codes can be encoded easily, but its decoding algorithm is very complex. Thus, the research of the RS codes, especially its decoding algorithm is always a hot topic. At present , hard decision decoder is used in real applications.As we know, the performance of the hard decision algorithms is far away from that of soft decision decoding because they don't make full use of the channel's information. However, the soft decoding algorithms are of high complexity , which limits their application. Thus, the research of the decoding algorithms, especially soft decision algorithms has important theoretical significance and practical value.This paper goes along the development of RS codes, and discusses the principle of coding and decoding of RS codes, including both hard and soft decision algorithm step by step. The emphasis is on the decoding algorithms. Generally speaking, in hard decision decoding, we take HDD-BM for example, and realize the simulation of encoding and decoding process, then compare the decoding performance between the codes who have the same code length while different code rates. With respect to soft decision decoding, we discuss the proposed classical algorithms, such as generalized minimum distance decoding(GMD), CHASE algorithm and CGA algorithm, which is the combination of GMD and CHASE. Besides, we discuss a new algorithm named sphere decoding (SD).Then we realize the simulation and analysis their decoding performance.This paper focuses on GMD and SD algorithms ,and tries to give an easier way to find the right code from candidate codes for GMD algorithm.The simulation results indicate that the proposed method reduces the decoding complexity effectively. With regard to SD algorithm, this paper tries to combine it with GMD algorithm, and proposed a concatenated algorithm, we call it GMD-SD concatenated algorithm.According to the simulation results, by concatenating with GMD algorithm to short codes, SD algorithm enhances the error-correcting performance efficiently at a smaller parameter.So this algorithm overcomes the defects of SD algorithm, that is, room for improvement in performance is limited and decoding process becomes highly complex by increasing the parameter's value.