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.

翻译：分子通信（MC）已成为一种利用分子在纳米尺度传输信息的前沿范式。在近期的一篇论文中，通过一种适用于MC的Huffman编码变体，前缀信源编码被引入该领域。我们首先证明，尽管MC适配的Huffman编码相比传统Huffman编码改善了符号错误率，但就期望长度与功率而言，它并不总能产生最优的MC适配前缀码本。为此，我们采用一种直接的暴力搜索算法，为任意给定字母表寻找最优的MC适配前缀（MoPC$^{*}$）码本。在MC信源编码的背景下，本文的主要贡献是提出了分子算术编码（MoAC），其算法实现与码结构与广为人知的经典算术编码（AC）存在非任意的本质差异。MoAC旨在通过高效避免连续1比特的出现，以缓解已知符号概率字母表的符号间干扰（ISI）。然而，由于比特精度限制，MoAC无法保证唯一可译性。为此，我们引入了一种新的唯一可译编码方案，称为带前缀的分子算术编码（MoAPC）。在两个示例性核苷酸字母表上，我们证明MoAPC具有优于MoPC$^{*}$的压缩性能。仿真结果表明，与算术编码类方案——AC以及本文首次提出的、对AC进行简单直接适配的替代算术编码（SAC）相比，MoAPC在字错误率（WER）和符号错误率（SER）上均表现出显著优势。仿真结果显示，在第一个字母表上，MoAPC在WER及渐近SER上超越所有给定方法；而在第二个字母表上，MoPC$^{*}$在SER和WER上均优于所有其他方案。