Properties of Finite Response Input Sequences of Recursive Convolutional Codes

A recursive convolutional encoder can be regarded as an innite impulse response system over the Galois Field of order 2. First, in this paper, we introduce nite response input sequences for recursive convolutional codes that give nite weight output sequences. In practice, we often need to describe the nite response sequence with a certain Hamming weight. Then, di erent properties of nite response input sequences are presented. It is shown that all nite response input sequences with a certain Hamming weight can be obtained in closed-form expressions from the so-called basic sequences. These basic sequences are presented for important recursive convolutional encoders and some possible applications are given .