Properties of Finite Response Input Sequences of Recursive Convolutional Codes

A recursive convolutional encoder can be regarded as an infinite impulse response system over the Galois Field of order 2. First, in this paper, we introduce finite response input sequences for recursive convolutional codes that give finite weight output sequences. In practice, we often need to describe the finite response sequence with a certain Hamming weight. Then, different properties of finite response input sequences are presented. It is shown that all finite 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.