本文關(guān)鍵詞：原模圖LDPC碼的準(zhǔn)循環(huán)擴(kuò)展算法研究　出處：《東北大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

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【摘要】：低密度奇偶校驗(yàn)(Low Density Parity Check, LDPC)碼性能逼近香農(nóng)容限并具有較低的譯碼復(fù)雜度,為此受到越來越多的關(guān)注。在此基礎(chǔ)上,美國(guó)噴氣推進(jìn)(Jet Propulsion Laboratory, JPT)實(shí)驗(yàn)室提出了原模圖LDPC碼,此種編碼技術(shù)因具有編譯碼復(fù)雜度低和誤碼性能良好等特點(diǎn),而成為一類重要的LDPC碼,并已成為衛(wèi)星數(shù)字電視傳輸標(biāo)準(zhǔn)(Digital Video Broadcasting-Satellite 2 DVB-S2) 以及 CCSDS (Consultative Committee for Space Data Systems, CCSDS)深空通信等通信標(biāo)準(zhǔn)中的信道編碼方案。眾所周知原模圖準(zhǔn)循環(huán)擴(kuò)展算法(簡(jiǎn)稱為PQCE算法)不僅影響構(gòu)造原模圖LDPC碼的誤碼性能,而且還決定著原模圖LDPC碼的編譯碼器的硬件實(shí)現(xiàn)復(fù)雜度,但PQCE算法中仍有許多問題有待于研究,所以研究PQCE算法具有重要意義。本文的主要工作如下：(1)介紹了原模圖LDPC碼的研究背景、意義和研究現(xiàn)狀,然后闡述了其基本理論、編譯碼方法、以及PEXIT (Protograph EXIT, PEXIT)圖。(2)針對(duì)利用現(xiàn)有PQCE算法構(gòu)造的校驗(yàn)矩陣中存在大量短環(huán)和較慢收斂速度問題,提出了PEG-PH-PQCE算法。該算法首先利用PEG (Progressive Edge Growth, PEG)去重邊擴(kuò)展算法獲得基矩陣完成原模圖的第一步擴(kuò)展；然后利用PH準(zhǔn)循環(huán)擴(kuò)展算法完成第二步擴(kuò)展,即通過PEG準(zhǔn)循環(huán)擴(kuò)展算法得到初始指數(shù)矩陣,之后利用登山(HillClimbing, HC)算法優(yōu)化初始指數(shù)矩陣,最終獲得性能較好的校驗(yàn)矩陣。仿真實(shí)驗(yàn)表明該算法構(gòu)造的校驗(yàn)矩陣中短環(huán)數(shù)量少、算法收斂速度快。(3)針對(duì)利用現(xiàn)有PQCE算法構(gòu)造的原模圖LDPC碼環(huán)之間的連通度較低問題,提出了PE-IPEG-PQCE算法。該算法首先通過PEG去重邊擴(kuò)展算法獲得初始基矩陣和邊交換操作優(yōu)化初始基矩陣中的環(huán)分布,完成原模圖的第一步擴(kuò)展；然后引入ACE和短環(huán)數(shù)量作為標(biāo)準(zhǔn)擴(kuò)展樹圖,給出了PEG準(zhǔn)循環(huán)擴(kuò)展算法,利用此算法完成第二步擴(kuò)展,并能夠獲得到連通度較高的校驗(yàn)矩陣。仿真實(shí)驗(yàn)表明所提算法不僅能夠有效地增大環(huán)之問的連通度而且能夠減少短環(huán)數(shù),從而提高了原模圖LDPC碼的誤碼性能。
[Abstract]:The performance of low Density Parity check (LDPC) codes approximates Shannon's tolerance and has low decoding complexity. More and more attention has been paid to this. On this basis, Jet Propulsion Laboratory of the United States is promoted. The prototype LDPC code is proposed by JPTLab. This coding technique is a kind of important LDPC codes because of its low complexity and good error-code performance. Digital Video Broadcasting-Satellite 2 DVB-S2) has become the standard of satellite digital TV transmission. And Committee for Space Data Systems. As we all know, the quasi-cyclic expansion algorithm (PQCE algorithm) not only affects the error performance of constructing the original mode map LDPC code, but also the channel coding scheme in the communication standards such as deep space communication. And it also determines the complexity of the hardware implementation of the LDPC code, but there are still many problems in the PQCE algorithm to be studied. So it is of great significance to study the PQCE algorithm. The main work of this paper is as follows: 1) introduce the background, significance and research status of the primitive LDPC code, and then explain its basic theory. Encoding and decoding methods, and PEXIT / Protograph EXIT. In view of the check matrix constructed by using the existing PQCE algorithm, there are a large number of short rings and slow convergence rate problems. A PEG-PH-PQCE algorithm is proposed, which uses PEG Progressive Edge Growth at first. The peg) algorithm obtains the first step extension of the base matrix to complete the original mode graph. Then the PH quasi-cyclic expansion algorithm is used to complete the second step expansion, that is, the initial exponential matrix is obtained by the PEG quasi-cyclic expansion algorithm, and then the climbing algorithm is used. HCI) algorithm optimizes the initial exponential matrix and finally obtains a good performance check matrix. The simulation results show that the number of short loops in the algorithm is less. The convergence rate of the algorithm is fast. (3) aiming at the problem of low connectivity between LDPC code rings of primitive mode graph constructed by existing PQCE algorithm. In this paper, PE-IPEG-PQCE algorithm is proposed. Firstly, the initial basis matrix and the edge exchange operation are obtained by using the PEG resetting extension algorithm to optimize the ring distribution in the initial base matrix. Complete the first step extension of the original mode diagram; Then the ACE and the number of short rings are introduced as the standard extension tree graph, and the PEG quasi-cyclic expansion algorithm is given, and the second step is completed by using this algorithm. The simulation results show that the proposed algorithm can not only increase the connectivity of rings but also reduce the number of short rings. Thus, the error performance of the original mode diagram LDPC code is improved.
【學(xué)位授予單位】：東北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：TN911.22

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