MAP tailbiting decoders

The output of a MAP decoder is the probability of various data symbols and encoder states, rather than the symbol or state itself. The input is the channel observations and the a priori data distribution. For trellis decoding and Markov data, the MAP decoder becomes the BCJR algorithm. The algorithm as given by Bahl et al. (1974) requires that the starting and ending states of the trellis be known, or at least assigned a priori probabilities. With a tailbiting encoder, these quantities cannot be known. The tailbiting technique, in which the starting state of the encoder is set equal to its eventual ending state, improves the decoder error probability when the code word length is short, without the rate reduction that occurs with encoder termination bits. Until now, the BCJR algorithm and tailbiting have not been compatible techniques. This has meant that methods such as turbo decoding and Hagenauer´s (see IEEE Trans. Communications, vol.COM-43, p.2449-57, 1995) source-controlled decoding could not be combined with tailbiting encoders