發(fā)布時(shí)間：2018-04-30 15:24

  本文選題：QC-LDPC碼 + 序列構(gòu)造��； 參考：《揚(yáng)州大學(xué)》2017年碩士論文

【摘要】：隨著信息技術(shù)的高速發(fā)展,人們對(duì)信息傳輸?shù)囊笤絹?lái)越高,推動(dòng)著現(xiàn)代編碼理論的研究。作為一類(lèi)具有逼近Shannon極限性質(zhì)的優(yōu)異碼,低密度奇偶校驗(yàn)(LDPC)碼近二十年來(lái)一直是信道編碼研究的熱點(diǎn),在諸多領(lǐng)域發(fā)揮著不可替代的作用。LDPC碼是一類(lèi)特殊的線(xiàn)性分組碼,其校驗(yàn)矩陣具有稀疏性,因而有優(yōu)良的譯碼性能。其研究方向包括校驗(yàn)矩陣的構(gòu)造、編譯碼算法的優(yōu)化以及性能分析。準(zhǔn)循環(huán)低密度奇偶校驗(yàn)(QC-LDPC)碼作為一類(lèi)重要的LDPC碼,校驗(yàn)矩陣具有準(zhǔn)循環(huán)性,不需要占用大量的存儲(chǔ)空間,編譯碼復(fù)雜度較低,因此對(duì)信道編碼研究有重要意義。論文主要給出了兩大類(lèi)QC-LDPC碼的校驗(yàn)矩陣構(gòu)造方式。第一類(lèi)源自范德蒙德矩陣,以一個(gè)給定序列為基礎(chǔ),先構(gòu)造出相應(yīng)的母矩陣,之后用循環(huán)置換矩陣擴(kuò)張構(gòu)造出圍長(zhǎng)最小為6的校驗(yàn)矩陣,得到QC-LDPC碼。隨后對(duì)矩陣元素進(jìn)行降冪處理,得到碼長(zhǎng)更加靈活方便的校驗(yàn)矩陣,同時(shí)去除了其中長(zhǎng)度為6的環(huán)。最后在保證擴(kuò)張矩陣階數(shù)較小的情況下給出逐步最小值算法,還將計(jì)算結(jié)果與Fossorier在2004年給出的構(gòu)造進(jìn)行比較。在行數(shù)為2和行、列數(shù)均為3情況下,得到的擴(kuò)張矩陣階數(shù)較小。行數(shù)為3,列數(shù)為7或8兩者相同。在母矩陣較小的情況下,利用我們提出的算法得到的擴(kuò)張矩陣階數(shù)接近Fossorier用計(jì)算機(jī)窮舉搜索得到的極限值。第二類(lèi)基于前人對(duì)歐氏幾何(EG)LDPC碼的研究,為提高校驗(yàn)矩陣圍長(zhǎng)提供了一種新穎的方法。將長(zhǎng)度為6的環(huán)的存在條件與歐式幾何結(jié)合,在避免歐式幾何中出現(xiàn)三個(gè)點(diǎn)兩兩相連的基礎(chǔ)上,給出兩種圍長(zhǎng)至少為8的EG-LDPC碼,(6,9,2,3)碼與(8,12,2,4)碼。隨后將一種長(zhǎng)度為8的環(huán)的不存在條件與歐式幾何結(jié)合,在歐式幾何中避免出現(xiàn)四個(gè)點(diǎn)首尾相連且固定行重與列重小于4,給出一種圍長(zhǎng)至少為10的EG-LDPC碼,(8,12,2,3)碼。最后經(jīng)循環(huán)置換矩陣擴(kuò)展,得到對(duì)應(yīng)碼長(zhǎng)的QC-LDPC碼。同目前對(duì)EG-LDPC已有研究相比,此類(lèi)方法為構(gòu)造高圍長(zhǎng)校驗(yàn)矩陣提供一種簡(jiǎn)單有效的方法。最后用比特翻轉(zhuǎn)算法對(duì)第一類(lèi)逐步最小值算法構(gòu)造的QC-LDPC碼和第二類(lèi)圍長(zhǎng)至少為8的QC-LDPC碼進(jìn)行仿真分析。仿真結(jié)果表明,兩類(lèi)QC-LDPC碼均具有良好的譯碼性能。
[Abstract]:With the rapid development of information technology, the demand for information transmission is becoming higher and higher, which promotes the research of modern coding theory. As a class of excellent codes with approximation to the limit of Shannon, low density parity check (LDPC) code has been a hot spot in the research of channel coding for nearly twenty years, and plays an irreplaceable role in many fields,.L DPC code is a special class of linear block codes. The check matrix has sparsity, so it has excellent decoding performance. The research direction includes the construction of the check matrix, the optimization of the coding and decoding algorithm and the performance analysis. The quasi cyclic low density parity check (QC-LDPC) code is a class of heavy required LDPC codes, and the check matrix is quasi cyclic and does not need to be used. Taking up a large amount of storage space and low compiling and coding complexity, it is of great significance to study the channel coding. This paper mainly gives the construction methods of the check matrix of two kinds of QC-LDPC codes. The first class is derived from the Van Redmond matrix, based on a given sequence, the corresponding matrix is constructed first, and then the construction of the matrix is constructed by cyclic substitution matrix. The QC-LDPC code is obtained with the minimum circumference of 6. Then the matrix element is reduced to a more flexible and convenient checksum matrix, and a ring with a length of 6 is removed. Finally, a gradual minimum value algorithm is given under the condition that the order of the expansion matrix is small, and the calculation results are given in 2004. The construction is compared. With the row number 2 and the row, and the row number is 3, the order of the expansion matrix is smaller. The number of rows is 3, the number of columns is 7 or 8. In the case of the smaller mother matrix, the order of the expansion matrix obtained by the algorithm proposed by us is close to the limit value of the Fossorier calculation machine. The second classes are based on the limit value. Previous studies on Euclidean geometry (EG) LDPC code provide a novel method for improving the length of check matrix. Combining the existence condition of the ring with the length of 6 and the Euclidean geometry, on the basis of avoiding the appearance of three points and 22 connections in the Euclidean geometry, two kinds of EG-LDPC codes, (6,9,2,3) codes and (8,12,2,4) codes are given, and then the (6,9,2,3) code and (8,12,2,4) codes are given. The non existence condition of a ring with a length of 8 is combined with the Euclidean geometry. In the Euclidean geometry, four points are avoided and the fixed row weight and the column weight are less than 4. A EG-LDPC code, (8,12,2,3) code with a peri length of at least 10, is given. Finally, the QC-LDPC code of the corresponding code length is obtained by the extension of the cyclic permutation matrix. In comparison, this method provides a simple and effective method for constructing the high peri length parity check matrix. Finally, the bit flipping algorithm is used to simulate the QC-LDPC code of the first class step minimum value algorithm and the second class of QC-LDPC codes with a circumference of at least 8. The simulation results show that the two classes of QC-LDPC codes have good decoding performance.

【學(xué)位授予單位】：揚(yáng)州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O157.4
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本文編號(hào)：1825092