【作者】 王栋；

【导师】 肖嵩；

【作者基本信息】 西安电子科技大学 ， 通信与信息系统， 2013， 硕士

【摘要】 随着互联网技术不断的发展，以及计算机计算能力的不断提高，大数据存储和通信日益频繁，人们对数据存储质量和通信质量要求也越来越高。循环冗余检验（CRC）以其简单的算法和良好的检错性能得到广泛应用,特别是在网络数据传输，数据存储检错，嵌入式等方面。在网络数据传输方面， CRC检错配合了错误重传机制，从而能够对出现错误的数据进行重传以保证其正确性。而CRC纠错能力的发现则有望缩小重传时延，在一定程度上提高CRC的应用效率及改善网络通信质量，减小数据存储误码率。CRC纠错能力是建立在其检错性能基础之上，是对检错性能的一个延伸与强化。单比特纠错现在已经得到了初步应用，本文的工作则是在单比特纠错的基础上，研究CRC多比特纠错，以及纠错性能极限情况。另外，还对其纠错和检错性能的局限性做了阐述。本文做了如下工作：在CCITT的CRC-16单比特纠错算法的基础上，研究CRC-32的单比特及其双比特纠错算法可能性，并验证了算法思想，进一步对CRC-32四比特纠错算法的可能性进行了验证，并完成最终算法的实现。在对多比特错误数据分析的基础上，最后得出多比特纠错与其检错极限之间的一般关系，并验证了多比特纠错理论证明。最终可以将我们的算法思想应用于任何一个知道其检错能力的CRC进行多比特纠错。最终得出结论，在知道任何的一个生成多项式对一定长度信息位最大检错能力的情况下，均可以获得其最大的纠错能力。更多还原

【Abstract】 With the development of the Internet and the evolvement of computation of thecomputer, the big data is frequently used in the people’s life. Then the quality of datagets big concern. In the data transmission on the internet, the CRC(CyclicRedundancy Check) is wildly implemented for its simplicity in algorithm and hardware implementation. Along with its using, the ARQ (Automatic Repeat Quest)method is also used for data retransmitted in case the errors happen. The CRC methodis also used for detection the bit riot in big block data storage. The CRCerror-correction will be promising in improving the quality of the data in the Internettransmission as well as reducing the bit riot in data storage. The single biterror-correction has been adopted in some fields. Multi-bits error-correction as well itslimit will be investigated in this paper.The contribution as following has done in this paper: First, it presents theerror-correction basement and the single bit and double bits of CRC-16and CRC32error-correction algorithm is presented followed by the single bits and double bits errorcorrection algorithm.Third, it presents the CRC-32bits error-correction algorithm andC source code.Finally, after the bits-errors data is analyzed, the relationship betweenthe ability error detection and multiple error correction, as well as its proof. All theerror correction method is based on the fact the bits errors correspond with its CRCand no duplicated ones appear so that we can find the riot bits precisely. Of course ourmethod perhaps has a constraint that the I/O from file perhaps will prolong the delay,especially in Internet use. Also the resolution is offered in the last section.更多还原