The study of ldpc codes was resurrected in the mid - 1990 ’ s with the work of mackay , luby , and others . ldpc codes are one of the hottest topics in coding theory today . indeed , the performance is almost as close to the shannon limit as that of turbo codes Ldpc码由gallager于1960年首次提出,只是限于当时的技术发展水平难于实现而未能引起足够重视,直到上世纪九十年代中期, mackay , luby等人重新发现ldpc码与turbo码一样也是一种能够逼近香农限的非常好码,从而使ldpc码成为新的研究热点。
However , after decades of years , it is now rediscovered by mackay and neal , along with the enhancement of computer ability and the development of some relative theory such as graph theory , bp algorithm , turbo codes and so on . it is also shown that the performance of ldpc codes is close to the shannon limits when combined with bp decoding algorithm 经数十年的沉寂,随着计算机能力的增强和相关理论(如图论、 bp算法、 turbo码等)的发展, mackay和neal重新发现了它,并证明它在与基于bp迭代译码算法相结合的条件下具有非常逼近shannon限的性能。
This paper discusses the results in ricean channel in addition . the analysis of rayleigh and ricean channel are based on two cases , state information ( si ) , and no state information ( nsi ) . while the code rate approaching to zero , the shannon limit of bsc channel model is 0 . 37db , the result of awgn ’ s is - 1 . 59db , of rayleigh si is - 2 . 31db , of rayleigh nsi is - 1 . 45db , of riceansi is - 2 . 31db , and of ricean nsi is - 1 . 44db 当码率趋近于0时bsc信道下的香农限为0 . 37db , awgn信道下的香农限为- 1 . 59db ,瑞利信道下信道增益已知时的香农限为- 2 . 31db 、信道未知时的香农限为- 1 . 45db ,莱斯信道下信道增益已知时的香农限为- 2 . 31db ,信道增益未知时香农限为- 1 . 44db 。
Low - density parity - check ( ldpc ) codes are a class of capacity approaching error - correcting codes . by using low complexity sum - product algorithm , ldpc codes can get near shannon limit decoding performance with almost all errors detectable . for long code lengths , ldpc codes can even outperform turbo codes 低密度校验码是一种能逼近shannon容量限的渐进好码，在长码时其性能甚至超过了turbo码，其译码采用具有线性复杂度的和积算法，复杂度大大低于turbo码，并且几乎所有错误都是可检的。
As is well know that turbo codes and multiuser detection ( mud ) are among the most important techniques in the third generation ( 3g ) mobile communication , turbo codes are recognized as having the performance closed to the shannon limit and be regarded as the milestone on channel coding theory Turbo码和多用户检测是第三代移动通信的关键技术之一，也是未来通信的重要研究课题。 turbo码具有近shannon限的性能，它的出现被看作是信道编码理论发展史上的一个里程碑。
Different channel has different shannon limits , only the continuous input and output awgn channel has a compact shannon limit description . but the other channels have no brief description for the limit , so the numerical solution for the limit is needed . this paper introduces the calculation method of multi - dimension integral and linear interpolation , and indicates the usage of these numerical solution methods in the shannon limit calculation 不同信道模型有不同的香农限,只有理想的输入输出均连续的awgn信道有较为简洁的香农限计算,对于其它信道模型的香农限计算难有简明的代数解析解,而只能进行积分方程的数值解计算,所以本文对多重积分的数值解以及线性插值法进行了介绍,并详细的指出了应用数值计算方法计算香农限的过程。
In fact , the mobile channel is one of the most unpredictable channels , so people are seeking for advanced techniques like error control coding . for example ; in the proposals of ieee 802 . 11n of next generation wlan the ldpc code is presented . at the present , ldpc code is a hot topic with sparse parity - check matries , the performance is near shannon limit and complexity is low 为此,人们不断地研究和寻找多种先进的通信技术以提高移动通信的性能,纠错编码就是这样一种技术。如在下一代高速wlan的ieee802 . 11n的提案中,都提到了采用低密度校验码( lower - densityparity - checkcode , ldpccode ) 。
