Wheel codes: turbo-like codes on graphs of small order

We investigate a specific class of codes on graphs called wheel codes, where the underlying graph of a wheel code is constructed by the wheel construction. Wheel codes were first introduced by N. Wiberg ("Codes and Decoding on General Graphs", PhD thesis, U. Linkping, Sweden, 1996). They are very similar to turbo codes except that the interleaver has more structure, which allows for a simpler implementation of the encoder and decoder. Wheel codes also allow for no loss of rate due to termination of the involved trellis codes, which is especially beneficial for codes of short lengths. We provide a more thorough discussion of the wheel construction itself and the codes that result. A sliding-window decoder for the wheel codes is also discussed and decoding performance charts are presented.