Blind Recognition of RS Codes Based on Soft Decision
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摘要: 针对现有RS码识别算法需要对码字符号在不同域之间进行转化，且容错性能较差的问题，该文提出一种直接利用软判决序列完成RS码识别算法。算法首先从RS码定义出发，给出了RS码校验关系从GF(2m)到GF(2)上的等价转换方式，从而避免了不同域下复杂的符号转化；其次引入了能够衡量校验关系成立大小的平均校验符合度概念，然后基于其统计特性以及极大极小判决准则，遍历可能的码长以及对应的m级本原多项式，进行初始码根校验匹配，从而完成码长以及本原多项式识别；最后利用识别出的码长以及本原多项式，构建本原多项式下GF(2m)，进行连续码根匹配判决，最终完成码生成多项式识别。仿真结果表明：推导的平均校验符合度统计特性与实际情况一致，算法能在低信噪比下有效完成参数识别；同时该算法具有较好的低信噪比适应能力，在信噪比为6 dB条件下，工程中常见的RS码识别率均能达到90%以上。与现有算法相比，该文算法性能明显好于硬判决算法，且比传统算法提升1 dB以上性能。Abstract: To solve the problem that the existing algorithms for recognition of RS codes need to transform the code characters among different domains and poor performance, a new algorithm based on soft decision is proposed. Firstly, starting from the definition of RS codes, the equivalent conversion mode of the check relation of RS code from GF (2m) to GF (2) is given, which avoids the complex symbol transformation in different domains. Secondly, the average check conformity which can measure the validity of the check relationship is introduced and based on its statistical characteristics and minimax decision criteria, the possible code length and corresponding m-level primitive polynomials are traversed to match the initial code root, as the results, the code length and primitive polynomial are recognized. Finally, under the identified code length and the primitive polynomial, the GF (2m) is constructed, and the continuous code root matching decision is made, then the generation polynomial is recognized. The simulation results show that the derived statistical characteristics of the average check conformity are consistent with the actual situation, and the proposed algorithm can effectively recognize parameter under low Signal-to-Noise Ratio (SNR). At the same time, the proposed algorithm has good adaptability to low SNR. At SNR of 6 dB, the recognition rate of common RS codes in engineering can reach more than 90%. Compared with the existing methods, the performance of this algorithm is better than hard-decision algorithm, besides, it is improved by more than 1 dB compared by traditional algorithms.
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Key words:
- RS code /
- Soft decision /
- Average check conformity /
- Minimax criterion /
- Code root matching
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表 1 RS码编码器参数设定
m 码长 本原多项式 生成多项式 H1下测试元素 H0下测试元素 4 15 x4+x+1 ${\alpha ^3}{x^4} + {\alpha ^{11}}{x^3} + {\alpha ^{14}}{x^2} + {\alpha ^6}x + {\alpha ^8}$ ${\alpha ^2}$ ${\alpha ^5}$ 5 31 x5+x2+1 ${\alpha ^4}{x^2} + {\alpha ^{20}}x + \alpha $ $\alpha $ ${\alpha ^3}$ 6 63 x6+x+1 ${\alpha ^5}{x^4} + {\alpha ^{19}}{x^3} + {\alpha ^{36}}{x^2} + {\alpha ^{14}}x + {\alpha ^{58}}$ ${\alpha ^3}$ ${\alpha ^6}$ 
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表 2 不同码长的RS码编码器参数
m 码长 本原多项式 生成多项式 纠错能力 4 15 x4+x+1 ${\alpha ^3}{x^4} + {\alpha ^{11}}{x^3} + {\alpha ^{14}}{x^2} + {\alpha ^6}x + {\alpha ^8}$ 2 5 31 x5+x2+1 ${\alpha ^4}{x^4} + {\alpha ^{23}}{x^3} + {\alpha ^{13}}{x^2} + {\alpha ^{18}}x + {\alpha ^{25}}$ 2 6 63 x6+x+1 ${\alpha ^5}{x^4} + {\alpha ^{19}}{x^3} + {\alpha ^{36}}{x^2} + {\alpha ^{14}}x + {\alpha ^{58}}$ 2 7 127 x7+x+1 ${\alpha ^6}{x^4} + {\alpha ^{23}}{x^3} + {\alpha ^{69}}{x^2} + {\alpha ^{18}}x + {\alpha ^{123}}$ 2 8 255 x8+x4+x3+x2+1 ${\alpha ^7}{x^4} + {\alpha ^{78}}{x^3} + {\alpha ^{248}}{x^2} + {\alpha ^{73}}x + {\alpha ^{252}}$ 2
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