A Novel Method to Derive Transfer Function and Tight BER Bound of Convolutional Codes

In this paper, a novel method is proposed to first derive an exact closed-form transfer function (TF) for any convolutional code, and then using this exact TF, a tight upper bound for bit error rate (BER) is derived for the code. This method applies submatrices of the code adjacent matrix, and its complexity is in the order of L³(L is the number of states in the state diagram of the code). The derived BER bound is especially important for applications with low signal-to-noise power ratio values, such as in the cases with high interference power, in satellite communications, and in multihop wireless networks.