Molecular Arithmetic Coding (MoAC) and Optimized Molecular Prefix Coding (MoPC$^{*}$) for Diffusion-Based Molecular Communication

Molecular communication (MC) has emerged as a promising paradigm employing molecules to transfer information at the nano-scale. In a recent paper, prefix source coding was introduced into the field, through an MC-adapted version of the Huffman coding. We first demonstrate that, although MC-adapted Huffman coding improves symbol error rates compared to Huffman coding, it does not always produce an optimal MC-adapted prefix codebook in terms of expected length and power. Accordingly, we utilise a straightforward brute-force algorithm to find an optimal MC-adapted prefix (MoPC$^{*}$) codebook for any given alphabet. In the context of MC source coding, the major finding of this paper is the Molecular Arithmetic Coding (MoAC) whose algorithmic implementation and code-structure is non-arbitrarily different than that of the widely-known classical arithmetic coding (AC). MoAC is designed to mitigate inter-symbol interference (ISI) for alphabets with known symbol probabilities through, in a highly efficient way, avoiding consecutive 1-bits. However, due to bit precision limitations, unique-decodability of MoAC is not guaranteed. Accordingly, a uniquely-decodable new coding scheme named Molecular Arithmetic with Prefix Coding (MoAPC) is introduced. On two exemplary nucleotide alphabets, we show that MoAPC has a better compression performance than MoPC$^{*}$. Simulation results demonstrate the highly superior word error rate (WER) and symbol error rate (SER) values of MoAPC compared to its arithmetic contenders: AC, and the Substitution Arithmetic Coding (SAC), which is introduced for the first time in this paper, and is a simple and trivial adaption of AC to molecular communication. Simulation results show that on the first alphabet, MoAPC surpasses all given methods in WER and asymptotically in SER; while on the second alphabet, MoPC$^{*}$ surpasses all in SER and WER.