基于快速码根检验的RS码综合识别算法

doi:10.11959/j.issn.1000-436x.2022219

摘要/Abstract

摘要：

针对 RS（Reed-Solomon）码识别算法存在的计算量大和漏警概率高的问题，提出了一种基于快速码根检验的RS码综合识别算法。首先，在二元域中求解校验关系，利用快速码根检验算法依次遍历参数；然后，利用组合码根的分布特性，对级数、本原多项式以及纠错能力进行联合判定；最后，赋予长短码不同的置信权重，将通过判定的待定参数进行综合衡量，选择最优参数，并计算生成多项式。所提算法不需要信噪比等先验信息，具有较好的适应性。仿真结果表明，所提算法在较低复杂度下可以有效地降低漏警概率，与常规的硬判决算法相比，所提算法性能较好，可以较快地完成编码参数识别。

关键词: RS码, 快速码根检验, 置信权重, 综合识别, 漏警概率, 盲识别

Abstract:

In order to solve the problem of high computation and high missed alarm probability of RS (Reed-Solomon) codes for recognition, comprehensive recognition algorithm of RS codes based on fast code root trial was proposed.Firstly, the check relationship was solved in binary equivalently and fast code root trial was used to check parameters in sequence.Secondly, according to distribution characteristics of the combined code roots, m-level primitive polynomial field and error correction ability was associatively determined.Finally, the short codes and long codes were given different confidence weights and the determined parameters were comprehensively analyzed.The optimal parameter was selected and the generate polynomial was calculated.The proposed algorithm did not need prior information such as signal-to-noise ratio (SNR), and had good adaptability.The simulation results show that the proposed algorithm can effectively reduce the missed alarm probability under the condition of low complexity.Compared with the conventional hard decision algorithm, the performance of the proposed algorithm is improved, and the parameter recognition of RS codes can be completed quickly.

Key words: RS code, fast code root trial, confidence weight, comprehensive recognition, missed alarm probability, blind recognition

中图分类号:

TN911.7

张晓林, 李修桥, 孙溶辰. 基于快速码根检验的RS码综合识别算法[J]. 通信学报, 2022, 43(11): 117-126.

Xiaolin ZHANG, Xiuqiao LI, Rongchen SUN. Comprehensive recognition algorithm of RS code based on fast code root trial[J]. Journal on Communications, 2022, 43(11): 117-126.

图/表 13

图1

图2

图3

图4

表1

RS码参数设置、本原多项式和生成多项式"

n	k	本原多项式 p(x)	生成多项式g(x)
7	5	x ³+x+1	$x^{2} + α^{4} x + α^{3}$
31	27	x⁵+x²+1	$x^{4} + α^{24} x^{3} + α^{19} x^{2} + α^{29} x + α^{10}$
127	119	x⁷+x³+x²+x+1	$\begin{array}{l} x^{8} + α^{102} x^{7} + α^{28} x^{6} + α^{88} x^{5} + α^{19} x^{4} + \\ α^{97} x^{3} + α^{46} x^{2} + α^{2} x + α^{36} \end{array}$

表1

表2

(31,27)RS码识别待定参数"

m_x	n_x	本原多项式 p_x(x)	连续码根的非零偶数值分布向量 $d$	Th₁	Th₂	检验元素	阈值差值Δth_i	k_x
4	15	$p_{x} (x) = x^{4} + x + 1$	(4,1,0,0,0,0,0)	10	1	α,α ²,α³,α⁴	Δth ₁=d₄-Th₂=0	11
5	31	$p_{x} (x) = x^{5} + x^{4} + x^{3} + x^{2} + 1$	(5,0,0,0,0,0,0,0,0,0,0,0,0,0,0)	4	1	α,α ²	Δth ₂=d₂-Th₁=1	29
5	31	$p_{x} (x) = x^{5} + x^{2} + 1$	(1,4,0,0,0,0,0,0,0,0,0,0,0,0,0)	4	1	α,α ²,α³,α⁴	Δth ₃=d₄-Th₂=3	27

表2

表3

不同m下的 w τ ¯ , δ ¯ m "

m	列大小	$w_{\bar{τ}, \bar{δ}}^{m}$
3	21	12
4	60	31.9
5	155	80
6	378	190.5
7	889	448
8	2 040	1 016.3

表3

图5

图6

图7

图8

图9

图10

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