本文選題：前向糾刪碼　切入點(diǎn)：可Zigzag解碼　出處：《浙江大學(xué)》2016年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著網(wǎng)絡(luò)技術(shù)的飛速發(fā)展,接入網(wǎng)絡(luò)的用戶越來越多,基于網(wǎng)絡(luò)的多媒體應(yīng)用也越來越豐富多彩。急速增長(zhǎng)的網(wǎng)絡(luò)流量和多樣化的業(yè)務(wù)需求對(duì)通信系統(tǒng)的有效性和可靠性要求越來越高。由于網(wǎng)絡(luò)擁塞、信道衰落等因素影響,網(wǎng)絡(luò)中的數(shù)據(jù)傳輸不可避免地會(huì)遇到數(shù)據(jù)丟包問題。前向糾刪編碼技術(shù)是解決網(wǎng)絡(luò)丟包的有效手段之而一種實(shí)用的前向糾刪編碼方法需在編解碼復(fù)雜度與前向糾刪性能之間權(quán)衡。2013年提出的可Zigzag解碼的前向糾刪碼具有很低的編解碼復(fù)雜度和最大距離可分特性,但其冗余編碼數(shù)據(jù)包比原始數(shù)據(jù)包略長(zhǎng)。本文以可Zigzag解碼的前向糾刪編碼方法展開研究工作。論文提出了一種基于有限域GF(qp)(q為素?cái)?shù),p≥1)上柯西矩陣的編碼系數(shù)矩陣構(gòu)造方法,并證明了根據(jù)這種編碼系數(shù)矩陣構(gòu)造的編碼數(shù)據(jù)包滿足可Zigzag解碼的條件。在所提出編碼系數(shù)矩陣構(gòu)造方法中,先構(gòu)造有限域上的柯西矩陣,然后將矩陣元素用本原元表示法表示,并把本原元符號(hào)看成編碼偏移符號(hào),得到可Zigzag解碼的編碼系數(shù)矩陣�；贕F(qp)上柯西矩陣的構(gòu)造方法巧妙地將高階有限域上面向數(shù)據(jù)包的乘法和加法運(yùn)算轉(zhuǎn)化為數(shù)據(jù)包的移位和異或運(yùn)算,生成的編碼數(shù)據(jù)包不僅具有最大距離可分特性,而且冗余度較小。仿真結(jié)果表明,與現(xiàn)有的編碼系數(shù)矩陣構(gòu)造方法相比,在生成相同數(shù)量的冗余編碼數(shù)據(jù)包時(shí),所提出的基于GF(qp)上柯西矩陣的編碼系數(shù)矩陣構(gòu)造方法生成的冗余編碼數(shù)據(jù)包的冗余度更小。針對(duì)時(shí)變除刪信道環(huán)境,結(jié)合可Zigzag解碼的前向糾刪碼的性質(zhì),論文提出了一種可Zigzag解碼的無速率碼的編碼系數(shù)矩陣構(gòu)造方法。無速率碼編碼時(shí),在一定的范圍內(nèi)隨機(jī)地選取編碼偏移量組成編碼系數(shù)矢量,編碼端根據(jù)編碼系數(shù)矢量將原始數(shù)據(jù)包做異或運(yùn)算可以無限地產(chǎn)生新的編碼數(shù)據(jù)包。仿真結(jié)果表明,當(dāng)編碼偏移量選取范圍的最大值等于254比特(約32字節(jié))時(shí),論文所提出的可Zigzag解碼的無速率碼的編碼數(shù)據(jù)包具有最大距離可分性質(zhì)的概率約為99.6%�？蒢igzag解碼的前向糾刪碼具有達(dá)到前向糾刪編碼性能限和很低的編解碼復(fù)雜度兩大優(yōu)點(diǎn),在網(wǎng)絡(luò)傳輸、分布式存儲(chǔ)等領(lǐng)域有廣泛的應(yīng)用前景。
[Abstract]:With the rapid development of network technology, more and more users are accessing the network. The multimedia applications based on the network are becoming more and more colorful. The rapid growth of network traffic and diversified service requirements are increasingly demanding the efficiency and reliability of the communication system. Due to network congestion, channel fading and other factors, Data transmission in the network will inevitably encounter the problem of data packet loss. Forward erasure coding is an effective method to solve the problem of packet loss in network. A practical forward erasure coding method should be used in coding and decoding complexity and forward correction. The forward erasure code proposed in 2013, which can be decoded by Zigzag, has the characteristics of low complexity and maximum distance separability. However, the redundant encoded data packet is a little longer than the original packet. In this paper, the forward erasure coding method which can be decoded by Zigzag is used. In this paper, a method of constructing the coding coefficient matrix based on Cauchy matrix over finite field GF(qp)(q is proposed. It is proved that the coded data packets constructed according to the encoding coefficient matrix satisfy the Zigzag decoding condition. In the proposed method of constructing the encoding coefficient matrix, the Cauchy matrix over the finite field is constructed first. Then the matrix elements are represented by primitive representation, and the primitive symbols are regarded as coded offset symbols. The construction method of Cauchy matrix based on Zigzag decode is used to subtly convert the multiplication and addition operations for data packets on high order finite fields into the shift and XOR operations of data packets. The generated coded packets not only have the characteristics of maximum distance separability, but also low redundancy. The simulation results show that, compared with the existing coding coefficient matrix construction methods, when generating the same number of redundant coded packets, The redundancy of the redundant coded data packets generated by the method of constructing the coding coefficient matrix of the Cauchy matrix based on GF-QP) is less. For the time-varying divide-delete channel environment, combining with the properties of forward erasure codes that can be decoded by Zigzag, In this paper, a method of constructing the coding coefficient matrix of rate free code with Zigzag decode is proposed. In the coding of rate code, the encoding offset is randomly selected to form the encoding coefficient vector in a certain range. According to the encoding coefficient vector, the encoding end can generate the new coded data packet infinitely by using the XOR operation of the original data packet. The simulation results show that when the maximum value of the encoding offset is equal to 254 bits (about 32 bytes), In this paper, the probability of maximum distance separability of Zigzag decoded data packets without rate codes is about 99.6. The forward erasure codes that can be decoded by Zigzag have the advantages of achieving the performance limit of forward erasure coding and low encoding and decoding complexity. In network transmission, distributed storage and other fields have a wide range of applications.
【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：TN911.2

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