A Simple Method for Performance Analysis of Reed-Solomon Codes over Memoryless Channel
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In this paper we investigate the bit error probability of nonbinary block codes, called Reed-Solomon codes, when they are used for error correction over the memoryless channel with cross-over probability p. First, we derive a general formula of the error correction probability for nonbinary block codes using the weight function of MDS (Maximum Distance Separable) codes. Then because the numerical approach for the derived formula assumed the UDSC (Uniform Discrete Symmetric Channel), the weight function of MDS codes is used for adjustment of the BER (Bit Error Rate) and SER (Symbol Error Rate). But, because the weights of the Reed-Solomon code are very large, the computation of them is almost impossible. Therefore, we propose a new approach using relations of the number of syndrome and arbitrary distribution to obtain the BER performance. Then the BER performance of our numerical approach is similar to simulation results.
Abstract
In this paper we investigate the bit error probability of nonbinary block codes, called Reed-Solomon codes, when they are used for error correction over the memoryless channel with cross-over probability p. First, we derive a general formula of the error correction probability for nonbinary block codes using the weight function of MDS (Maximum Distance Separable) codes. Then because the numerical approach for the derived formula assumed the UDSC (Uniform Discrete Symmetric Channel), the weight function of MDS codes is used for adjustment of the BER (Bit Error Rate) and SER (Symbol Error Rate). But, because the weights of the Reed-Solomon code are very large, the computation of them is almost impossible. Therefore, we propose a new approach using relations of the number of syndrome and arbitrary distribution to obtain the BER performance. Then the BER performance of our numerical approach is similar to simulation results.