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

Molecular communication (MC) enables information transfer through molecules at the nano-scale. This paper presents new and optimized source coding (data compression) methods for MC. In a recent paper, prefix source coding was introduced into the field, through an MC-adapted version of the Huffman coding. We first show that while MC-adapted Huffman coding improves symbol error rate (SER), it does not always produce an optimal prefix codebook in terms of coding length and power. To address this, we propose optimal molecular prefix coding (MoPC\(^*\)). The major finding of this paper is the Molecular Arithmetic Coding (MoAC), which differs significantly from classical arithmetic coding (AC) and is designed to mitigate inter-symbol-interference, a major issue in MC. However, MoAC's unique decodability is limited by bit precision. Accordingly, a uniquely-decodable new coding scheme named Molecular Arithmetic with Prefix Coding (MoAPC) is introduced. On two nucleotide alphabets, we show that MoAPC has a better compression performance than MoPC\(^*\). Simulation results show that MoAPC achieves superior word error rate (WER) and SER compared to AC and SAC (our trivial adaptation of AC for MC). On the first alphabet, MoAPC outperforms all compared methods in WER and asymptotically in SER, while MoPC\(^*\) outperforms all in both SER and WER on the second alphabet.