Low complexity MAP decoding of tailbiting convolutional codes

Tailbiting is an effective technique to terminate convolutional codes without a rate loss. The latest application of tailbiting codes can be seen in the broadcast channel of the long term evolution (LTE) cellular systems. Due to the high computational complexity of maximum likelihood (ML) decoding of tailbiting codes, suboptimum decoding techniques are often used in practice. In this paper, we propose a low-complexity MAP decoder based on the observation that the MAP decoder can forget the erroneous initial conditions faster in forward calculations than in backward calculations. The proposed decoder uses a head length for forward calculations and a tail length for backward calculations in the well-known BCJR algorithm. This allows the decoder to eliminate the starting and ending transients in the bit error rate that occur due to the uniform initial conditions thereby improving the performance. Using the tailbiting convolutional code proposed for LTE over different channel conditions, it is shown that circular MAP decoding performs close to ML decoding.