Abstract: For the optimum design problem of punctured convolutional codes based on the distance spectrum, an efficient computing method of the distance spectrum for punctured convolutional codes is proposed. A state transition matrix sequence is constructed with the state graph and punctured pattern, and the product of the matrix sequence is used to compute the transfer function and distance spectrum; furthermore, a state reduction algorithm for computing the transfer function is proposed to avoid the inverting operation of the symbolic matrix. Analyses and simulation results show that this method for computing the distance spectrum can provide efficiency and practicability, and may be used for optimal design or theoretical analysis.

Key words: punctured convolutional codes, distance spectrum, transition matrix, transfer function, state reduction algorithm