English

Duality of Channel Encoding and Decoding - Part I: Rate-1 Binary Convolutional Codes

Information Theory 2016-11-14 v2 math.IT

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.

Keywords

Cite

@article{arxiv.1201.2483,
  title  = {Duality of Channel Encoding and Decoding - Part I: Rate-1 Binary Convolutional Codes},
  author = {Yonghui Li and Qimin You and Soung C. Liew and Branka Vucetic},
  journal= {arXiv preprint arXiv:1201.2483},
  year   = {2016}
}

Comments

32 pages, 20 figures, to appear in ETT

R2 v1 2026-06-21T20:03:32.671Z