Multirate structures for arbitrary rate error control coding

We present the most general form for error control coding using finite field multirate filters. This method shows how different types of codes can easily be generated by multirate filters and filter banks. In all previous works, codes and syndromes were generated using prefilters. We present simple multirate structures for encoding and generating syndromes. We show that all kinds of arbitrary rate K/L, circulant linear codes can be generated by these structures. Then we claim that a similar simple structure exists for syndrome generation in all presented cases.