Research On Several Problems In Turbo Codes

Channel coding is the absolutely necessary part in modern digital communication systems. Turbo codes with excellent error-corrected performance is the practical coding method which first breaks through channel cut-off rate and approaches the Shannon limit. Since its naissance Turbo Code has absorbed enough attention to be always the research center of many fields. The supreme contribution of Turbo codes lie in its iterative idea well dealing with the long code decoding which reflects on the developing of encoding of Turbo codes in the shade. So this dissertation focuses most attention on several key problems related to the Turbo encoding.First, based on the theory of finite field and the theory of signal and linear system we state that the recursive systemic convolutional (RSC) encoder can be described by the total response, and the total one is divided into the zero-input response and the zero-state response. The zero-input solution corresponding to the transferring of the states and the total solution gives the code words of the encoder. Several control matrices in the three responses are given to realize a simple encoding method.Two useful algorithms of Turbo decoding namely MAP and SOVA are studied and the results of simulation are given. Based on the MAP algorithm we investigate the correlation among the code bits which has effect on the design of interleaver and the number of iteration.This dissertation discusses the tail-biting problem of Turbo codes grounded on the theory of finite fields and the theory of matrix. Especially when the feedback polynomial of RSC is irreducible, the control matrix correspondence to feedback polynomial of RSC is the companion matrix whose eigenfiinction happens to be the feedback polynomial. Thus we can calculate the period of the companion matrix over finite field. At the same time we give the method to check up whether the length of the information sequence satisfies the condition of tail-biting and the calculation complexity can be reduced.Based on the study of the divisibility of polynomial over finite field, we give a method to find the form of the optimal period interleaver and after expending it with block interleaver and random interleaver for short frame Turbo codes we give the simulation results.