Duality of channel encoding and decoding ‐ Part I: rate‐1 binary convolutional codes. Issue 5 (20th January 2016) - Li, Yonghui; You, Qimin; Liew, Soung C.; Vucetic, Branka
Abstract: In this paper, we revisit the forward, backward and bidirectional Bahl–Cocke–Jelinek–Raviv (BCJR) soft‐input soft‐output (SISO) maximum a posteriori probability (MAP) decoding process of rate‐1 binary convolutional codes. From this, we establish some interesting explicit relationships between encoding and decoding of rate‐1 convolutional codes. We observe that the forward and backward BCJR SISO MAP decoders can be simply represented by their dual SISO channel encoders using shift registers in the complex number field. Similarly, the bidirectional MAP decoding can be implemented by linearly combining the shift register contents of the dual SISO encoders of the respective forward and backward decoders. The dual encoder structures for various recursive and non‐recursive rate‐1 convolutional codes are derived. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : We revisit the Bahl‐Cocke‐Jelinek‐Raviv soft‐input soft‐output maximum a posteriori probability decoding process of rate‐1 binary convolutional codes. From this, we establish some interesting explicit relationships between their encoding and decoding. We observe that the Bahl‐Cocke‐Jelinek‐Raviv maximum a posteriori probability decoders can be simply represented by their dual soft‐input soft‐output channel encoders using shift registers in the complex number field. With logarithm of soft symbol estimates of coded symbols as the input, the dual encoder output produces the logarithm of the soft symbol estimates of information symbols.