Research On Linear System Theory Of Convolution Code

Convolution code is used widely in satellite communication and mobile communication at present and the research on the technique of encoding and decoding is progressing steadily.Because convolution code is a kind of important linear discrete time-invariable system defined in Galoias field, the algebraic structure of convolution code is analyzed in this dissertation by using some classical ideas of linear discrete time-invariable system theory and some positive results are obtained and summarized as follows:1. The connection of convolution code and linear system is summarized.The model of linear discreet system for convolution code is founded and the matrix description (A,B,C,D) is proposed.At the same time,the concept of encoding complexity and equivalence of convolution code are first proposed from the point of linear system theory.2. The transmission function and state space realization of convolution code are discussed in detail.Also,the properties of linear system description for convolution codes are presented and the parity-check matrix is analyzed.Finally,the controllability and observability of convolution code are studied using classical ideas of linear system theory.3. An efficient algebraic iterative decoding algorithm is presented for general convolutional code based on linear system state variable equation and it is proved that the iterative algorithm has perfect performance with low complexity and delay when the bit error rate (BER) is lower by theoretic analysis and programming experiment.Also,the algorithm can substitute for viterbi algorithm when the encoding complexity is higher.4. A special kind of maximum distance separable (MDS) convolution code which free distance (dfree) achieves the upper bound of generalized singleton bound is introduced.Because of the linear discrete time-invariable system theory is developed perfectly,the ideas of linear systems theory and the description of convolution code based on state space realization can give us new way on exploring convolution code with good performance and studying it's technique of encoding and decoding.