Research On Primitive And Non-Primitive Convolutional Code

Since P.Elias firstly put forward convolutional code in 1955, this encoding technology has develop rapidly. Whether theory or practical application has proved that under the same conditions, for example, both the same code-rate and complexity of equipment, the performance of convolutional code outperforms block code. As a kind of important linear error-correction code and with efficient decoding algorithm convolutional code is widely applied in some digital communications systems such as universal mobile telecommunications system, global mobile communications, digital cellular systems, satellite communications. For example, convolutional code for error-correction and block code for error-detection are employed in GSM system as channel coding; and convolutional code with code rate 1/2 and 1/3 is adopted to deal voice information in CDMA system. Along with the development of error-correction code theory recently, the research of convolutional code is being deepened. Because of the correlation between the bits of convolutional code, we lack effective tools to treat it, and coorespondingly, the performance analysis is quite difficult. The study on convolutional code at home and abroad is limited to the improvement of coding and decoding algorithm, rarely refer to the performance of convolution code from code structure.Introducing two concepts, primitive and non-primitive, arising from modern algebra, this paper explores and compares the performance of primitive and non-primitive convolutional code, and especially discusses some factors that influence the performance of non-primitive code. Firstly this paper illustrates channel coding, the description methods, coding and decoding principles on convolutional code; and constructs both primitive and non-primitive convolutional codes with different status numbers using MATLAB simulation software, and then compares and analyzes the performance of primitive and non-primitive convolutional code under the condition of low signal-noise ratio. This paper examines the influence factors of performance arising from code-rate and constraint length of convolutional code as well. On this basis this paper constructs two groups of non-primitive convolutional code with code-rate 1/2 and 1/3 whose function are better than that of convolutional code of 3GPP when the signal-to-noise ratio is low. Finally this paper summarizes and prospects for the full text, puts forward some problems that still exist in research, and makes a clear direction for the future study.