Polar Coding with Chemical Reaction Networks for Molecular Communications

In this paper, we propose a new polar coding scheme with molecular programming, which is capable of highly parallel implementation at a nano-scale without the need for electrical power sources. We designed chemical reaction networks (CRN) to employ either successive cancellation (SC) or maximum-likelihood (ML) decoding schemes for short polar codes. From differential equation analysis of the proposed CRNs, we demonstrate that SC and ML decoding achieve accurate computations across fully-parallel chemical reactions. In terms of the number of required chemical reactions, we verify the superiority of ML decoding over SC decoding for very short block lengths.