Research on Decoding Algorithm For（n, 1, M） Convolutional Code

This paper takes (2, 1, 5) convolutional codes as example, disscusses the decoding algorithm for (n, 1, m) convolutional codes according to the principle of the reversibility of the modulo 2 operation.We designed the decoder and the syndrome of the (2, 1, 5) convolutional codesbased on its encoder firstly; then studied on the error correction methodused for one or two bits error within a constraint lengthaccording to the corresponding relationships between syndrome and the type of error codes; finally validity of this algorithm is verified through the computer simulation. 1.IntroductionThe noise and attenuation always exist in the channel of digital communication, itwill produce inaccurate code consequentially.Improve the reliability and availability of transmission is the goal of the researchers worked in the field of communication all the time, and error control coding is a method to improve the reliability of communication.The research on this coding method is aimed to realize the reliable data transmission by reducing error rate by coding and decoding under the condition of certain transmission effieciency and make sure the decoder is as simple as possible.Error control coding can be classified as block code and convolutional code according to information processing method.It proved that the performance of the later is better than the former at the same error rate and the same complexity of the devices condition both intheory and in pratical, and the convolutional code gets high coding gain in the Additive White Gaussian Noise channel, and error code rate of 10-5 can be realized).Owing to its superior performance, the convolutional code is widely used insatellite communication, space communication and mobile communication today, it takes an important role in improving reliability of digital communication. Convolutional codesConvolutional code was presented by Elas of MIT in 1955, it is a type of method to deal with burst error codes, and always be marked as 0 0 ( , , ) n k m , in which k information bits consititute n bits, that is the coding efficiency can be denoted by the equation Rc = k/ n, and constraint length is N, that means there are Nk shifting registers, n modular 2 adders, n shifting registers are output, and the structure of the encoder can be illustrated in fig 1 .