  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 a need of 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 ordinary
differential equation (ODE) analysis of the proposed CRNs, we demonstrate that
SC and ML decoding achieve accurate computations across fully-parallel chemical
reactions. We also make a comparison in terms of the number of required
chemical reactions and species, where the superiority of ML decoder over SC
decoder is observed for very short block lengths.
