Parameter Identification of Reed-Solomon Codes Based on Probability Statistics and Galois Field Fourier Transform

The parameter identification of channel codes plays a significant role in the fields of adaptive modulation and coding (AMC) as well as non-cooperative communications. In this paper, an algorithm based on probability statistics and Galois field Fourier transform (PS-GFFT) is proposed to identify the parameters of the Reed-Solomon (RS) codes. A threshold obtained by the probability statistics is used to skip wrong parameters within a candidate set, while GFFT is applied to reduce the error identification probability. Meanwhile, the upper bound on correct recognition rate of RS codes has been derived and proved, which quantifies the influence of the received codewords' length, the bit-error-rate of codewords, and the number of bits per symbol on the accuracy of parameters estimation. To the best of our knowledge, the upper bound, which is of great significance in evaluating the performance of recognition algorithms, is provided in this paper for the first time. The numerous simulation results illustrate that the proposed algorithm has better recognition performance than the existing RS codes recognition algorithms. Specifically, the correct recognition probability of the RS codes whose length is no more than 255 can be over 90% when the bit error rate of codewords is below 3 * 10
^-3
, while the conventional algorithms have the best correct recognition probability of 10%. Furthermore, it is observed that the correct recognition rate of our proposed algorithm is close to the derived upper bound, especially for long code length, which further verifies the superiority of our proposed algorithm.