SISO MAP decoding of rate-1 recursive convolutional codes: A revisit

In this paper, we revisit the BCJR soft-input soft-output (SISO) maximum a posteriori probability (MAP) decoding process of rate-1 recursive convolutional (RC) codes. From this we establish some interesting duality properties between encoding and decoding of RC codes. We observe that the forward and backward BCJR decoders can be simply represented by their dual SISO channel encoders using shift registers in the complex field. Similarly, the bidirectional MAP decoding can be implemented by linearly combining the outputs of the dual SISO encoders of the respective forward and backward decoders.