Construction and Decoding of Convolutional Codes with optimal Column Distances

Abstract: The construction of Maximum Distance Profile (MDP) convolutional codes in general requires the use of very large finite fields. In contrast convolutional codes with optimal column distances maximize the column distances for a given arbitrary finite field. In this paper, we present a construction of such convolutional codes. In addition, we prove that for the considered parameters the codes that we constructed are the only ones achieving optimal column distances. The structure of the presented convolutional codes with optimal column distances is strongly related to first order Reed-Muller block codes and we leverage this fact to develop a reduced complexity version of the Viterbi algorithm for these codes.