【作者】 邓从政；

【导师】 王学理；

【作者基本信息】 广州大学 ， 应用数学， 2007， 硕士

【摘要】 现代数字通信中,评价一个通信系统性能优劣主要从可靠性和有效性来衡量,而信源编码可以提高信号的有效性,信道编码可以提高信号传输的可靠性。由于信号必须在信道中传输,因此必定会产生误码,采用纠错码技术可以保证数据传输的正确性和可靠性。二元BCH码是目前数字通信中常用的纠错码之一,它是一类重要的循环纠错码,能够纠正多个随机错误。具有纠错能力强,构造方便,编码简单,译码比较容易实现等一系列优点,在数字通信中被广泛采用,因此研究二元BCH码的译码算法无论在理论上,还是在实践上都有着重要的意义。二元BCH码是好码,其译码算法的研究一直是编码理论的重要课题之一。随着现代通信和计算机技术的飞速发展,算法容量的不断加大,传统的译码算法已经不能很好地满足高速通信系统的要求了,本文对传统的译码算法加以了两点优化。其一是在BM迭代算法流程中增加一个对迭代次数i的模2逻辑判断模块,以判断i的奇偶性。当i为奇数时, d i= 0,无需计算修正差值d i,直接进入下一次迭代,通过这个模块的优化,整个迭代次数可以减少一半,大大地减少了译码器的计算量,从而加快了整个二元BCH码的译码进程。其二是根据接受码字的伴随式来构造矩阵,根据伴随式矩阵的可逆性来判断接受码字的实际错误个数λ,使得实际中当接受码字有λ(λ≤t)比特出错时,只需迭代2λ次就可以得到错位多项式,这样对于每一个码字可以减少迭代次数2(t ?λ),而对于一段消息来说,大大地减少了迭代次数。通过使用优化的迭代算法,可以使得整个二元BCH码的译码速度得到明显的提高。更多还原

【Abstract】 We evaluate a digital communication whether its performance is excellent or inferior from its dependability and its validity in the process of its transmission.The coding of message sources can improve validity of signals,and the coding of channel can improve dependability of transmission . Since signals must be transmitted in noise channel,it will produce many inaccurate code consequentially. Adoption of error-correcting technique can assure accuracy and reliability of data.Binary BCH codes are a very important kind of linear cyclic error-correcting code which can correct many random errors and have a series of strongpoint such as their powerful correction abilities, simple structure. They are widely used in digital communication, therefore, study of decoding algorithm of binary BCH codes have important meanings no matter in practice or theory.Binary BCH codes are a kind of good code. The study of decoding algorithm is one of very important tasks of coding theory. With fast development of modern communication and computer technology, the traditional BM algorithm can not satisfy the need of high speed communications any more. This text improves the traditional decoding algorithm in two aspects. First, we add a logic judge module of modul 2 to judge the parity of i.To binary BCH codes, we get that d i= 0 when i is an odd number. We don’t calculate d i and do the next iterative directly when i is an odd number.In this way, we reduce the iterative times by half and reduce the times of count of encoder consumedly. Second, we construct matrix according to the syndromes of received codes, and then judge actual error bits in the received codes according to reversibility of the matrix. When there areλ(λ≤t) mistaken bits actually, we can get the error locator polynomial by iterating 2λtimes only. So the iterative times are reduced greatly. By optimized iterative algorithm, the speed of decoding BCH codes gets increased obviously.更多还原