From Block to Convolutional Codes using Block Distances

It is well known that convolutional codes can be considered as block codes over a field of rational functions. Being a block code, every convolutional code has "block" distance d_f. The free distance df of a convolutional code is lower bounded by d,B, d_f ges d_B. With this approach, every method of designing or combining block codes immediately gives a method to design or to combine convolutional codes. The block distance d_B of the new convolutional code is known (or can be estimated), this gives a lower bound for the free distance of the new convolutional code. We investigate the properties of block distance and show that block distance of blocked convolutional codes reaches free distance. The proposed method is demonstrated for Reed-Solomon codes, for the direct product codes and for bipartite graph codes. For these examples, bounds of type d_f ges d_B and improved bounds are obtained.