From Block to Convolutional Codes using Block Distances
Vladimir R. Sidorenko, Carlos Medina, Martin Bossert · 2007
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 df. The free distance df of a convolutional code is lower bounded by d,B, dfges dB. 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 dBof 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 dfges dBand improved bounds are obtained.