一種軟判決下的RS碼識(shí)別算法

吳昭軍; 張立民; 鐘兆根; 劉傳輝

doi:10.11999/JEIT190690

一種軟判決下的RS碼識(shí)別算法

doi: 10.11999/JEIT190690

1.
海軍航空大學(xué)信息融合研究所煙臺(tái) 264001
2.
海軍航空大學(xué)航空基礎(chǔ)學(xué)院煙臺(tái) 264001

基金項(xiàng)目: 國家自然科學(xué)基金(61179016)；泰山學(xué)者工程專項(xiàng)(ts201511020)

詳細(xì)信息

作者簡介:
吳昭軍：男，1992年生，博士生，研究方向?yàn)樾诺谰幋a識(shí)別

張立民：男，1966年生，教授，博士生導(dǎo)師，研究方向?yàn)樾l(wèi)星信號(hào)處理及應(yīng)用

鐘兆根：男，1984年生，博士，講師，研究方向?yàn)閿U(kuò)頻信號(hào)處理

劉傳輝：男，1984年生，博士，講師，研究方向?yàn)楹娇胀ㄐ畔到y(tǒng)與網(wǎng)絡(luò)

通訊作者:
張立民　iamzlm@163.com

中圖分類號(hào): TN911.7
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出版歷程
- 收稿日期: 2019-09-05
- 修回日期: 2020-04-16
- 網(wǎng)絡(luò)出版日期: 2020-04-23
- 刊出日期: 2020-09-27

Blind Recognition of RS Codes Based on Soft Decision

1.
Department of Information Fusion, Naval Aviation University, Yantai 264001, China
2.
School of Aviation Basis, Naval Aviation University, Yantai 264001, China

Funds: The National Natural Science Foundation of China (61179016), The Taishan Scholar Special Foundation (ts201511020)

摘要

摘要: 針對(duì)現(xiàn)有RS碼識(shí)別算法需要對(duì)碼字符號(hào)在不同域之間進(jìn)行轉(zhuǎn)化，且容錯(cuò)性能較差的問題，該文提出一種直接利用軟判決序列完成RS碼識(shí)別算法。算法首先從RS碼定義出發(fā)，給出了RS碼校驗(yàn)關(guān)系從GF(2^m)到GF(2)上的等價(jià)轉(zhuǎn)換方式，從而避免了不同域下復(fù)雜的符號(hào)轉(zhuǎn)化；其次引入了能夠衡量校驗(yàn)關(guān)系成立大小的平均校驗(yàn)符合度概念，然后基于其統(tǒng)計(jì)特性以及極大極小判決準(zhǔn)則，遍歷可能的碼長以及對(duì)應(yīng)的m級(jí)本原多項(xiàng)式，進(jìn)行初始碼根校驗(yàn)匹配，從而完成碼長以及本原多項(xiàng)式識(shí)別；最后利用識(shí)別出的碼長以及本原多項(xiàng)式，構(gòu)建本原多項(xiàng)式下GF(2^m)，進(jìn)行連續(xù)碼根匹配判決，最終完成碼生成多項(xiàng)式識(shí)別。仿真結(jié)果表明：推導(dǎo)的平均校驗(yàn)符合度統(tǒng)計(jì)特性與實(shí)際情況一致，算法能在低信噪比下有效完成參數(shù)識(shí)別；同時(shí)該算法具有較好的低信噪比適應(yīng)能力，在信噪比為6 dB條件下，工程中常見的RS碼識(shí)別率均能達(dá)到90%以上。與現(xiàn)有算法相比，該文算法性能明顯好于硬判決算法，且比傳統(tǒng)算法提升1 dB以上性能。
- RS碼 /
- 軟判決 /
- 平均校驗(yàn)符合度 /
- 極大極小準(zhǔn)則 /
- 碼根匹配
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 (2^m) 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 (2^m) 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.
- RS code /
- Soft decision /
- Average check conformity /
- Minimax criterion /
- Code root matching

HTML全文

圖 1 校驗(yàn)符合度統(tǒng)計(jì)特性對(duì)比

下載: 全尺寸圖片幻燈片

圖 2 碼長對(duì)算法識(shí)別性能影響

下載: 全尺寸圖片幻燈片

圖 3 碼塊數(shù)目對(duì)算法影響

下載: 全尺寸圖片幻燈片

圖 4 5種算法對(duì)比

下載: 全尺寸圖片幻燈片

表 1 RS碼編碼器參數(shù)設(shè)定

m	碼長	本原多項(xiàng)式	生成多項(xiàng)式	H₁下測試元素	H₀下測試元素
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	${\alpha ^5}{x^4} + {\alpha ^{19}}{x^3} + {\alpha ^{36}}{x^2} + {\alpha ^{14}}x + {\alpha ^{58}}$	${\alpha ^3}$	${\alpha ^6}$

下載: 導(dǎo)出CSV

表 2 不同碼長的RS碼編碼器參數(shù)

m	碼長	本原多項(xiàng)式	生成多項(xiàng)式	糾錯(cuò)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

下載: 導(dǎo)出CSV

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