臺灣博碩士論文加值系統

由於多媒體通訊的廣泛應用，網際網路的普及以及客戶寬頻化的需求，使得傳輸系統容量不斷提昇。密集波長分波多工(Dense Wavelength Division Multiplexing, DWDM)技術，為利用一對光纖芯線傳送多個波長光信號，以達到提昇傳輸系統容量的方法。DWDM結合光放大器能提供長距離、高容量傳輸系統。不管未來的全光網路(all optical network)或者目前的高速率同步數位網路(Synchronization Digital Hierarchy,SDH)都將被廣泛的應用。
傳統的串列編碼系統(serial coding)將配位檢查位元(parity check bits) 加入資料序列中，這樣將提昇系統的傳送速率較難為設計者所接受。同步數位網路(SDH or SONET)的前向誤碼更正(Forward Error Correction, FEC)係將配位檢查位元置於SDH or SONET碼框(frame)未被使用的贅位元(overhead bits)中。雖然此法未改變系統速率而且證明在分散限制(dispersion-limited)的光纖系統中大大改善了系統的效能(performance)。但是將配位檢查位元置於某些指定的贅位元中，將使得編/解碼時信號處理的複雜度增加。這樣不但限制它的傳送速率，而且擴充到高容量、具有多個光波長通道WDM系統中，需要巨大數量的編/解碼器是可理解的。
基於WDM系統各波長通道間自然並列(parallel)的特性，將配位檢查位元置於增加的波長(通道)中已在[4]和[7]中被提出，而且在[7]中建議採用乘積碼(product codes) ，以一組編/解碼器及兩個增加的波長(通道)來更正編碼區塊(encoded block)中任一波長的單一誤碼。應用於WDM系統中，此法不但簡單、明確易於實現，而且資料字元在編碼、傳送、解碼全部是並列(parallel)方式，是一種既簡單又有效率的方法。
因此本文將基於前面的論點，在不改變位元速率之下，以標準的位元速率、二維(two-dimension)、全並列的編碼法則，使用增加的四個配位檢查波長(通道)來實現WDM系統兩個隨機比次誤碼(double random errors)的更正能力。此外，在WDM系統中對於任意單一波長以及多個相鄰波長通道的突發誤碼(burst errors)的更正能力也一併提出建議的解決方案。本文也將與其它WDM編碼系統的效能做一分析比較，最後並對更正多個隨機誤碼提出建議的解決方法。

The capacity of transmission system increase due to the widely use of broadband applications by customers. In order to enhance transmission systems capacity, DWDM utilize one pair of optical fiber to transmit multi-wavelength signals. WDM with OA (Optical Amplifier) could offer long distance, high capacity transmission system. Either the ″All Optical Network″ in the future or the ″Synchronization Digital Hierarchy″ nowadays will be the trend of fiber communication development.
In conventional serial coding systems, coding-induced
parity-check bits are added to the encoded data sequences so that the system bit rate is inevitably increased. In practical lightwave systems, the change of system bit rate is generally unacceptable. FEC for SONET or SDH put parity-check bits in unassigned overheads of the frame. System bit rate thereby is unchanged. The results show that the performance of a dispersion-limited lightwave system is improved drastically. However, as parity-check bits are put on some specific overheads, the required signal processing in the encoder/decoder becomes complicated, resulting in limiting its operating speed. Extending to high-capacity WDM systems with many high-speed wavelength channels, numerous encoder/decoders will be necessary.
Taking advantage of the parallel nature of WDM systems, putting parity-check bits in additional wavelength channels was proposed by [4] and [7]. In [7] based on product codes, it required only one encoder/decoder and two additional wavelength channels to correct one error in any all of wavelength channels. The implementation of the scheme is straightforward and simple since the codeword can be encoded, transmitted and decoded all in parallel. Therefore, the resulting coding scheme is simple and efficient.
In this thesis we presented a modified interchannel WDM coding system with four parity-check wavelength channels which will provide a double-error correction capability to the systems. Correcting burst-errors scheme in any all of wavelength channels and adjacent wavelength channels are also proposed. The performance with other coding schemes are analyzed and compared. Finally, the generalization of interchannel coding in WDM lightwave systems to arbitrary error-correction capability has also been given.

第一章 簡介 1
1.1提昇傳輸系統容量的方法 1
1.1.1空間分波多工(SDM) 1
1.1.2時間分波多工(TDM) 2
1.1.3密集波長分波多工(DWDM) 3
1.2分波多工(WDM)系統的錯誤更正碼 4
第二章 波長分波多工(WDM)通道間隨機誤碼之編碼 13
2.1隨機誤碼之通道模型 13
2.2 WDM通道間隨機誤碼之編碼 14
2.3傳送的碼框架構 17
2.4 WDM通道間隨機誤碼之解碼 19
2.4.1 WDM隨機誤碼解碼演算法 21
2.4.2 正交的限制 22
第三章WDM通道間突發誤碼之編碼 23
3.1突發誤碼的通道模型 23
3.2 突發誤碼長度之定義 24
3.3 WDM系統任意單一波長突發誤碼編碼原則 25
3.4 WDM系統任意相鄰n個波長的突發誤碼更正 27
3.5任意單一波長突發誤碼編碼碼框及架構 32
3.5.1任意單一波長突發誤碼更正碼之碼框 32
3.5.2任意單一波長突發誤碼編碼架構 33
3.6任意單一波長突發誤碼解碼的演算法 34
3.7任意單一波長突發誤碼解碼架構 35
第四章WDM通道編碼之效能分析 39
4.1 WDM通道間隨機誤碼編碼效能分析 39
4.2 WDM通道間突發誤碼編碼效能分析 43
第五章 WDM通道編碼總論 47
5.1隨機誤碼更正碼 47
5.2 WDM任意單一波長突發誤碼更正碼 49
5.2.1突發誤碼長度( =4)的單一波長突發誤碼更正編碼 49
5.2.2突發誤碼長度( =5)的單一波長突發誤碼更正編碼 51
5.3 WDM任意m個相鄰波長突發誤碼( )更正碼 52
5.4 WDM任意m個相鄰波長突發誤碼( )更正之解碼 54
5.5 WDM誤碼更正並列編碼之比較 54
第六章 結論 56
參考資料 58
附錄A 突發誤碼更正碼在吉爾伯特─艾力歐特通道
(Gilbert─Elliott Channel)的性能分析 61
A.1 GE通道模型(Gilbert─Elliott Channel Model) 61
A.2 突發誤碼更正編碼分析 62
A.3 確定通道(Certain Channel)的簡化分析 65

[1] W.D. Grover,“ Forward error correction in dispersion-limited lightwave system,” J.Lightwave Technol., vol. 6, no. 5, pp. 643-654, May 1998.
[2] W.D. Grover and T.E. Moore,“Design and characterization of an error-correcting code for the SONET STS-1 tributary,” IEEE Trans. Commun., vol. 38, no. 4, pp. 467-476, Apr. 1990.
[3] S. Lin and D.J. Costello, Jr., Error Control Coding: Fundamental and Applications, Englewood Cliffs, NJ: Prentice-Hall, 1983.
[4] S.-K Shao and M.-S Kao,“WDM coding for high-capacity lightwave systems,“J. Lightwave Technol., vol. 12, no. 1, pp. 137-148, Jan.1994.
[5] M.-S Kao, S.-K Shao and H.-Y. Chen,“ WDM coding system with single parity-check channel,” J. Lightwave Technol., vol. 12, no.10, pp. 1827-1834, Oct. 1994.
[6] T. Rao and E. Fujiwara, Error-Control Coding for Computer Systems, Englewood Cliffs, NJ: Prentice-Hall, 1989.
[7] M.-S Kao, H.-Y. Chen and D. Lin, “A product-coded WDM coding system,”IEEE Trans. Commun., vol. 44, no. 1, pp. 43-46, Jan.1996.
[8] C.A. Brackett,“ Dense wavelength division multiplexing networks: Principles and applications,” IEEE J. Select. Areas Commun., vol. 8, no. 6, pp. 948-964, Aug. 1990.
[9] P.E. Green,“ The future of fiber-optic computer networks,”IEEE Computer, vol. 24, no. 9, pp. 78-87, Sept. 1991.
[10] P. Urquhart,“ Review of rare earth doped fiber lasers and amplifiers,“ IEE Proc. J, vol. 135, no. 6, pp. 385-407, Dec. 1988.
[11] Cf.,“Special issue on optical amplifiers,” J. Lightwave Technol., vol. 9, no.2, Feb. 1991.
[12] J. L. Massey, Threshold Decoding, Cambridge, MA: M.I.T. Press, 1963.
[13] G. Clark and J. Gain, Error-Correction Coding for Digital Communications, New York: Plenum, Mar. 1988.
[14] A. Murad and T. Fuja, “Distributed decoding of cyclic block codes using a generalization of majority-logic decoding,”IEEE Trans. Inform. Theory, vol. 39, no. 5, pp. 1535-1545, Sept. 1993.
[15] ITU-T G.692(former G.MCS),“Optical interfaces for multichannel systems with optical amplifiers”.
[16] G. Sharma and A.A. Hassan,“Performance Evaluation of Burst-Error-Correcting Codes on a Gilbert-Elliott Channel,” IEEE Trans. Commun., vol. 46, no.7, pp. 846-849, July.1998.
[17] X.Wei and A.N.Akansu“ On Parallel Iterative Decoding of Product Codes” IEEE Trans. Commun, pp.2483-2486, Mar. 2001.
[18] G.-C.Yang and W.C. Kwong, Prime Codes With Applications to CDMA Optical and Wireless Networks, Artech House, Feb. 2002.