LDPC編碼算法研究

通信工程論文編號:TX353  論文字數:17120,頁數:36

目錄

摘要 I
ABSTRACT II
第1章 緒論 1
 1.1數字通信與信道編碼 1
 1.2糾錯碼的發展 1
 1.3 LDPC碼發展歷史和現狀 3
 1.4本文主要工作 7
第2章 LDPC碼的定義及編碼原理 8
 2.1 LDPC碼的定義及Tanner圖 8
 2.1.1 LDPC碼的定義及其描述 8
 2.1.2 LDPC碼的Tanner圖表示 9
 2.2 LDPC碼的編碼 11
 2.2.1 直接編碼 12
 2.2.2 快速編碼 12
 2.2.3 構造半隨機校驗矩陣H的編碼 14
 2.2.4 具有循環碼特性的LDPC碼的編碼 15
 2.2.5 基于刪除信道LDPC碼迭代譯碼算法的編碼 15
 2.3 LDPC碼的譯碼 15
第3章 LDPC碼的校驗矩陣的構造 16
 3.1 Gallager構造法 16
 3.2 Mackay構造法 17
 3.3超輕構造法 20
 3.4完全隨機構造法 20
 3.5 Hu Xiao-Yu的PEG方法 21
 3.6 Bit-filling和Extended Bit-filling方法 23
 3.7非正則LDPC碼的構造方法 23
 3.8其他的構造方法 24
第4章 LDPC碼性能仿真 27
 4.1不同碼長仿真圖 27
 4.2不同碼率仿真圖 28
第5章 結束語 30
致謝 31
參考文獻 32

摘要

 低密度奇偶校驗碼（Low-Density-Parity-Check codes，簡稱LDPC碼）是當前通信領域的熱門研究課題之一，是第四代移動通信系統的信道編碼技術中強有力的競爭者。LDPC碼具有優秀的譯碼性能，迭代的概率譯碼算法使得LDPC碼可以達到接近香農限的性能，而且譯碼的復雜度較低；譯碼算法本質上是并行算法，有利于硬件的并行實現，減少譯碼延時；它能夠在迭代運行的過程中確定碼字是否已譯出，以決定譯碼過程能否結束，減少迭代次數；同時其譯碼錯誤是可以檢測的；譯碼后的誤碼率可以隨著信噪比的增加而任意減小，沒有誤碼率下降減速的error floor現象。LDPC碼編碼的復雜度較高，同時在碼長較長時，由于必須在接收到所有的信息比特后才能夠進行編碼，這就會給編碼帶來一定的延時。
 本文對LDPC碼進行了系統的研究。首先介紹了LDPC碼的定義和編譯碼原理，然后闡述了多種校驗矩陣的構造方法；最后采用Gallager構造法構造LDPC碼，并在MATLAB中進行仿真，給出了不同碼長和不同碼率的LDPC碼在高斯白噪聲信道下的誤碼率性能的仿真結果。
 

關鍵詞：LDPC碼，編碼，Gallager構造

ABSTRACT

 Low-Density-Parity-Check-Codes is currently one of the pop researches in communication field. It is the powerful competition in the 4th generation of mobile communication system. The decoding performance of LDPC is excellent and can be near the Shannon limit by iterative probability decoding algorithm. It has low complexity, the decoding algorithm is essentially parallel, so it is suitable to realize on hardware in parallel and reduce the decoding delay time. It can make certain that if the codes are decoded in the iterative decoding process and if the process can be finished in order to reduce iterative times, at the same time the decoding error can be detected. Bit error rate(BER) after decoding can be decreased arbitrarily along with the increase of Signal-to-Noise rate(SNR), and the error floor phenomenon can not occur. The complexity of encoding is high. Because the encoding process begins after receiving all needed signal bits, it brings certain delay time while the length of the codes is very long.
 This paper gives a systematic investigation of LDPC codes. First, the definition of LDPC codes and the encoding methods are introduced. Then some parity check matrix construction methods of LDPC codes are illustrated; Finally, Gallager construction LDPC codes are simulated on MATLAB. The simulation results of BER performance of different length and rate for additive white Gaussian noise channels are presented.

Keywords: LDPC codes, encode, Gallager construction