近年來隋著硬體設計的進步,LDPC碼已廣泛被運用於通訊系統上,像是IEEE 802.11n及802.16e 標準使用准迴旋式的低密度奇偶檢查碼(QC-LDPC).而解碼部份,普遍性的使用和-積演算法(Sum-Product Algorithm,SPA)去做解碼的動作,由於現在趨勢是希望吞吐量(throughput)能快則快,所以我們在錯誤更正碼這塊希望能加強解碼的速度.連續排程解碼(Sequential Scheduling)是普遍性用來加速解碼的方式,如分層訊息傳輸(LBP),但由於解碼順序是固定的,所以為了將解碼效率達到極致,所以有人利用動態排程(Informed Dynamic Scheduling,IDS)的方式,針對當下解碼過程中的一些資訊來作為解碼排程的依據,而差值的訊息傳輸(RBP)及差值節點化的訊息傳輸(NW-RBP)是已被提出來不錯的方法,利用動態排程方式來加快收斂速度,但各有其優缺點,RBP擁有加速收斂的優點,但收斂到的錯誤率較高,而NW-RBP收斂速度比RBP慢,但收斂到的錯誤率比RBP好很多.本篇論文主要是針對他們的優缺點去做深入的探討,並作些微的修正,希望能達到結合兩者優點的效能.模擬結果顯示,我們成功的提出QUE的方法將兩者優點結合,收斂速度和即快的RBP相同並超越整體RBP及NW-RBP的錯誤率.另外,我們也將動態排程的主題延伸至不均等的錯誤率保護(Unequal Error Protection,UEP)的部份,希望利用調整常見的動態排程(RBP)的解碼先後順序,來達到不同程度上的UEP效果,而在不同的嘗試下,我們成功的利用動態排程結合APP上的限制來達到不同程度的UEP效果.

In recent years, quasi-cyclic low-density parity-check code (QC-LDPC) is
popularly used in IEEE 802.11n and 802.16e standard. In decoder part, Sum-
Product Algorithm was generally used for decoding. The current issue is fo-
cused on the throughput. If the throughput increases, the convergence of
decoding was also increased. Sequential scheduling is a general way to speed
up the convergence. LBP is one of them. But sequential scheduling was ‾xed
the decoding process. It does not optimize the decoding process. To limit the
convergence, informed dynamic scheduling (IDS) was proposed for fast conver-
gence. IDS was used the decoding information to decided the next decoding
step. Residual belief propagation (RBP) and Node-wise RBP (NW-RBP) were
proposed in dynamic decoding process. But they have their own advantages
and disadvantages. In this thesis, we proposed QUE-RBP method to combine
their advantages and exceed the performance of NW-RBP. In another topic,
we combine IDS with unequal error protection (UEP). We want to change the
decoding process of RBP to make di□erent UEP levels. In many tests, we
successfully use IDS and limit the APP to make di□erent UEP levels.

[1] C. E. Shannon, A mathematical theory of communication,Bell Syst.
Tech. J. , vol.27 ,pp. 379-423 and 623-656, 1948.
[2] C.Berrou, A. Glavieux, and P.Thitimajshima,"Near Shannon limit error-
correcting coding and decoding:turbo-codes(1)," in Proc. IEEE Int.
Conf. on Communications pp. 1064-1070, May 1993.
[3] T. Richardson and R. Urbanke, "E±cient encoding of low-density parity-
check codes," IEEE Trans. Inf. Theory, vol.47, no. 2, pp. 498-519, Feb.
2001.
[4] B. Masnick and J. Wolf, "On linear unequal error protection codes,"
IEEE Trans. Inform. Theory, vol. 3, pp. 600-607, Oct. 1967.
[5] D. J. C. Mackay, "Good Error-Correcting Codes Based on Very Sparse
Matrices," IEEE Trans. Inform. Theory, vol. 45, no. 3, pp.399-432,
March 1999.
[6] G. Elidan, I. McGraw, and D. Koller. Residual belief propaga-
tion:informed scheduling for asynchronous message passing. In Proc.
22nd Conference on Uncertainty in Arti‾cial Intelligence,MIT, Cam-
bridge, MA, July 2006.
68
[7] R. G. Gallager, Low-Density Parity-Check Codes. Cambridge, MA: MIT
Press, 1963.
[8] X. Yang, D. Yuan, P. Ma, and M. Jiang, "New research on unequal error
protection (UEP) property of irregular LDPC codes," in Proceedings of
IEEE Consumer Communications and Networking Conference (CCNC
'04), pp. 361-363, Las Vegas, Nev, USA, January 2004.
[9] N. Rahnavard, H. Pishro-Nik, and F. Fekri, "Unequal error protection
using partially regular LDPC codes," IEEE Transactions on Communi-
cations, vol. 55, no. 3, pp. 387-391, 2007.
[10] A. Casado, M. Griot, and R. D. Wesel, "Informed dynamic scheduling
for belief-propagation decoding of LDPC codes," in Proc. IEEE Inter-
national Conference on Communications, 2007.
[11] X. -Y. Hu, E. Eleftheriou, and D. M. Arnold, Regular and Irreg-
ular Progressive Edge-Growth Tanner Graphs, Submitted to IEEE
Trans.Inform. Theory, 2002.
[12] C. Poulliat, D. Declercq, and I. Fijalkow, Enhancement of unequal er-
ror protection properties of LDPC codes,IEURASIP Journal on Wire-
less Communications and Networking, vol. 2007, pp. Article ID 92659, 9
pages, 2007. doi:10.1155/2007/92659.