| Error correction coding is an indispensable part of communication systems to ensure the information reliable transport. RS codes can be corrected random errors and burst-correcting errors, which are the maximum distance separable codes, widely used in digital communication systems, storage systems.At present, high speed, low latency, regular structure of RS codes are employed in the existing system to improve error-correcting ability; At the same time, with more coding gain, the soft decision decoding algorithm of RS codes is studing on hot. The article works around the hard-decision of RS codes implemented and the performance of soft-decision algorithm and cascade codes. Main research contents are as follows:Firstly, with the method of IP core design method, the article presents a high-speed architecture for the implementation of RS encoder and decoder, using pipeline structure to improve data throughput. GF multiplier is the most complicated structure and delay's largest operation of the finite field operations. In this article, we adopt the techniques based on the natural foundation under constant multiplier, relatively simple structure, easy to implement logical operation unit. The RS decoder can be implemented using RiBM algorithm to solve a key equation. The algorithm eliminates the speed bottleneck which is in the iterative computation of discrepancies via a fully systolic array architecture, a series of identical processors to calculate the error location polynomial and error polynomial. The structure is easy realization of hardware. With Quartus II we did the RS(31, 19) hardware implementation and simulation of encoding and decoding, and download to FPGA for verification. Through the results of the experiment, The capacity of error correction of RS(31,19) codes is 6.After, RS codes perform better when the signal to noise ratio is high, while the Turbo codes have better performance in low signal to noise ratio channel. In order to make full use of this fact and improve the anti-error performance of the system, RS code and Turbo code were serially concatenated, and a cascaded OFDM WiMAX system was set up to analyze the bit error rate (BER) performance in different modulation modes based on white Gaussian noise and fading channel. The algorithm for soft decision of high order modulation is max-log likelihood ratio (MAX-LLR). It is proved that this system has a 2-3dB coding gain compared with the RS code concatenating convolution code. Also, the iterations of Turbo code are reduced, and the phenomenon of error floor is avoided. Therefore, the complexity and delay of this system is reduced effectively.The final, we study soft decision RS decoding algorithms which can improve the system coding gain by making full use of the reliability information from channel. Based on algebraic soft-decision decoding of RS codes-KV algorithms consist of three steps: multiplicity assignment, interpolation and factorization. The multiplicity assignment step affects the overall error-correcting performance and complexity. We adopt the multiplicity assignment in the Gross algorithm, and apply the re-encoding techniques to reduce the complexity. The system performance is little effect. We also research based on unreliable position Chase algorithm in the front-end of the KV algorithm. The method can achieve a good performance and complexity tradeoff. Employing a backward interpolation technology can make full use of the intermediate result of interpolation, further reducing complexity, and 0.5dB coding gain. |
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