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研究生:周聖翔
研究生(外文):Sheng-Hsiang Chou
論文名稱:里德所羅門碼之非二進制信念傳遞解碼演算法之研究
論文名稱(外文):A Nonbinary Belief Propagation Based Decoding Algorithm for RS Codes
指導教授:鄭立德
指導教授(外文):Li-Der Jeng
學位類別:碩士
校院名稱:中原大學
系所名稱:電子工程研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2011
畢業學年度:99
語文別:中文
論文頁數:41
中文關鍵詞:跳頻展頻部分頻帶干擾可靠度演算法非二進制
外文關鍵詞:reliabilitypartial band noise jammingalgorithmnon-binary
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跳頻展頻[1](Frequency-Hopping Spread Spectrum,FH-SS) 技術因具有抗干擾、多重進接等特性,已經廣泛地被應用於無線通訊系統中,尤其是在軍事用途上。近年來,跳頻技術結合M-ary頻率鍵移(M-ary Frequency Shift Keying,MFSK)的系統已經廣泛地被運用在一般的通訊系統上。一般而言,跳頻系統可分為兩種:一種稱快跳頻(Fast Frequency-Hopping,FFH)系統,而另一種則是慢跳頻(Slow Frequency-Hopping,SFH)系統。對於慢跳頻系統而言,為了達到符合規格的抗干擾能力,通常需要額外的機制來強化它,常用的一種方式就是利用正向錯誤更正碼(Forward Error-Correction coding,FEC)。近年來,部分頻帶干擾[4](Partial Band Noise Jamming,PBNJ)以及帶頻多波道單音干擾環境結合里德-所羅門(Reed-Solomon)碼的應用在慢跳頻系統裡的效能已被廣泛研究,不過主要都僅限於錯誤率的分析,而[8]利用一般的通訊方法或結合正向錯誤更正碼來提升抗干擾效能。OSD(Order Statistic Decoding)[2]演算法是一種有效改善系統複雜度的演算法,而先前研究只考慮二進制(binary)訊號,並無直接使用非二進制訊號的研究。
  因此,本論文提出可使用於非二進制訊號的處理方法,來改善系統效能。在正向錯誤更正碼的解碼部分,本論文選用里德-所羅門碼,在系統部分調變改用了非同調MFSK搭配SHF,通道環境添加了PBNJ,且在接收端新增了可靠度(Reliability)的計算方法。可靠度比較了兩種方法,最佳化解碼使用聯合機率密度函數(joint Probability Density Function ,joint PDF)的方式,次佳的則使用較簡單的計算方式。本論文比較不同解碼方法的計算,使用最佳與次佳的解碼方法(Decoding Metric),其中最佳化的採用PDF來計算距離,次佳的則利用通道輸出比值做計算。希望藉由提出的方法達到不須額外進行訊號轉換,可以直接使用演算法進行解碼,以達到節省系統運算時間,提升系統效能。模擬結果顯示,本論文所提出的方法,確實能將非二進制的訊號不需另外轉換而使用演算法進行解碼並且獲得不錯的效能提升。

Owing to the advantage of anti-jam (AJ) capability and multiple access property, frequency-hopping spread spectrum (FH-SS) combined with M-ary Frequency Shift Keying (MFSK) has been widely applied in wireless communication systems. The initial application of FH-SS techniques are developed in military communication systems. In general, there are two classes of frequency-hopping systems. One is the fast frequency-hopping (FFH) system, and the other is the slow frequency-hopping (SFH) system.
For SFH systems, a good forward error correcting coding (FEC) is essential to acquire a satisfactory AJ capability. In the recent years, SFH systems and Reed-Solomon code systems under Partial Band Noise Jamming (PBNJ) and Band Multi-tone Jamming (BMTJ) environment are studied extensively. But most of them only focused on the error probability in the general communication systems. None of them has utilized the property of transmitted data, such as the correlations among image pixels.
In this paper, we propose a non-binary belief propagation based decoding algorithm for RS codes under Additive White Gaussian Noise (AWGN) and PBNJ. Our method utilizes the property of the transmitted data, such as non-binary data. Otherwise, we also employ the Forward Error-correction Coding (FEC). Consequently, we combine the property and FEC with the non-binary Order Statistic Decoding algorithm to enhance the entire system performance. By evaluating the Symbol Error probability Ratio(SER) values of the transmitted non-binary data, the simulation results show that the performance of our system is better than MFSK system and RS code algebra decoding.

目錄
中文摘要...............I
Abstract...............III
誌謝...............IV
目錄...............V
圖目錄...............VI
CHAPTER 1 簡介...............1
1.1 動機……………………………………………………………………….1
1.2 大綱…………………………………………………………………….....2
CHAPTER 2 跳頻系統與通道模型...............4
2.1 跳頻展頻系統簡介……………………………………………………. ...4
2.2 部分頻帶雜訊干擾模型………………………………………………. ...8
2.3 MFSK系統效能之分析…………………………………………………10
CHAPTER 3 里德-所羅門碼(REED-SOLOMON CODE)...............12
3.1 RS CODE簡介…………………………………………………………....12
3.2 RS CODE數學定義……………………………………………………....12
3.3 RS CODE編碼…………………………………………………………....14
3.4 RS CODE解碼…………………………………………………………....16
CHAPTER 4 二進制OSD演算法...............20
4.1 OSD演算法簡介………………………………………………………..20
4.2 二進制生成矩陣………………………………………………………...20
4.3 排序方式………………………………………………………………...21
4.4 更正機制………………………………………………………………...22
CHAPTER 5非二進制OSD演算法………………………………………………24
5.1 系統架構………………………………………………………………...24
5.2 非二進制生成矩陣……………………………………………………...26
5.3 可靠度計算……………………………………………………………...27
5.4 非二進制解碼方法……………………………………………………...28
CHAPTER 6 模擬結果...............30
CHAPTER 7 結論...............33
參考文獻...............34

圖目錄
圖2.1:  同調跳頻系統之傳送機...............6
圖2.2:  同調跳頻系統之接收機...............6
圖2.3:  4FSK慢跳頻系統之訊號傳送方式...............7
圖2.4:  部分頻帶雜訊干擾與可加性白色高斯雜訊之功率密度頻譜...............9
圖3.1:  使用P(x)=x^8+x^4+x^3+x^2+1所產生之元素...............13
圖3.2:  Berlekamp-Massey Algorithm...............18
圖5.1:  使用里德-所羅門碼之非二進制OSD演算法系統方塊圖...............24
圖6.1:  使用非同調包線檢測器計算與16FSK在使用 里德-所羅門碼下的錯誤率比較...............31
圖6.2:  使用非同調能量檢測器計算與16FSK在使用 里德-所羅門碼下的錯誤率比較...............31
圖6.3:  使用機率密度函數計算與16FSK在使用 里德-所羅門碼下的錯誤率比較...............32
圖6.4:  三種方法與16FSK在使用 里德-所羅門碼下的錯誤率比較...............32
[1]M. B. Pursley and W. E. Stark, “Performance of Reed-Solomon coded frequency-hop spread-spectrum communications in partial-band interference.” IEEE Trans. Commun., vol. COM-33, pp. 767-774, Aug. 1985.
[2]Marc P. C. Fossorier and Shu Lin “Soft-decision decoding of linear block codes based on ordered statistics” IEEE Transactions on information Theory, VOL. 41, NO. 5, SEPTEMBER 1995
[3]Jing Jiang, Krishna R. Narayanan “Iterative Soft Decoding of Reed–Solomon Codes” Communications Letters, IEEE . vol. 8, pp. 244-246, Dec. 2004
[4]J. H. Kang and W. E. Stark, ”Turbo codes for coherent FH-SS with partial band interference”, IEEE Trans. Commun., vol. 1, pp.5-9, Nov. 1996
[5]J. H. Kang and W. E. Stark, ”Turbo codes for noncoherent FH-SS withpartial-band interference,” IEEE Trans. Commun., vol. 46, pp. 1451-1458, Nov. 1998.
[6]C. D. Frank and M. B. Pursley, ”Tradeoffs in concatenated coding for frequency-hop packet radio with partial-band interference.” IEEE Military Communications Conference Record, vol. 1, pp. 125-129, October 1992.
[7]C. D. Frank and M. B. Pursley, ”Concatenated coding alternatives for frequency-hop packet radio.” IEICE Transactions on Communications, vol. E76-B, no. 8, pp. 863-873, August 1993.
[8]Yu T. Su, Li-Der Jeng, “Antijam capability analysis of RS-coded slow frequency-hopped systems”, IEEE Trans. Commun., vol. 48, No. 2. Feb, 2000.
[9]A. J. Viterbi, “A robust ratio-threshold technique to mitigate tone and partial band jamming in coded MFSK systems,” in 1982 IEEE Conf. Rec. MILCOM, 1982, pp. 22.4.1–22.4.5.
[10]M. B. Pursley, “Reed Solomon codes in frequency hop communications,” in Reed Solomon Codes and Their Applications, S. B. Wicker and V. K. Bhargava, Eds. Piscataway, NJ: IEEE Press, 1994, ch. 8.
[11]D. Chase, “A class of algorithms for decoding block codes with channel measurement information” IEEE Trans. Inform. Theory, vol. IT-18, pp. 170-182, Jan. 1972.
[12]M. K. Simon, J. K. Omura, R. A. Scholtz, and B. K. Levitt, Spread Sprectrum Communications, Vol. I, Computer Science Press, Inc., Rockville, Md., 1985.
[13]J. G. Proakis, Digital Communication, New York: McGraw-Hill, 4th ed., 2001
[14]Rafael C. Gonzalez , Richard E. Woods , ”Digital Image Processing (3rd Edition)”


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