# Low-Complexity Channel Codes for Reliable Molecular Communication via Diffusion
## 1 Introduction
One of the main aspects when designing an MC system is the selection of the modulation which has a direct impact on the behavior of the channel and in the implementation complexity. In the case of MC, where molecules are the information carriers, several different schemes have been proposed [6; 13; 17]. These comprise approaches where information can be encoded via the emission of a single molecule type (e.g., with on-off keying (OOK)), changing the concentration (e.g., concentration shift keying (CSK)), type of molecules (e.g., molecule shift keying (MoSK)), ratio (e.g., isomer-based ratio shift keying (IRSK)), release time (e.g., release time shift keying (RTSK)), release order of molecules (e.g., molecular array-based communication (MARC)), as well as the base sequences of nucleotides (e.g., nucleotide shift keying (NSK)). Another aspect that plays a central role in the performance of MC communications is the detection task. Optimal and suboptimal detection methods have been proposed in the literature as addressed in [18], with some recent innovative approaches as in [19]. However, the complexity of many of the approaches can be excessive particularly, when one considers the need for instantaneous channel state information which, in the MC channel can be very challenging due to the fast time varying nature. To cope with this problem, non-coherent detection techniques can be adopted. This is the approach followed in [20], which relied on the comparison of the number of molecules in each interval against an adaptive threshold. While being simple, this detection scheme tends to perform poorly when sequences of consecutive ones occur. Another relevant component for reducing the effect of extreme noise and inter-symbol interference (ISI) that is typical in MC channels corresponds to channel codes. This is achieved by adding redundancy to the emitted message, and by making it possible to correct the errors caused by noise during transmission at the receiver, improving the reliability of the communication link. Some studies have been made, for instance, in [21; 22] where authors demonstrated that Hamming codes are able to improve the performance of MC systems. However it was also shown that there is a Hamming order at which they become self-defeating, making it important to study other codes. Anotherproposed solution relies on the \"ISI-mitigating channel codes\" (ISI-mtg) [14], which is a code that has properties specially adapted to the MC channel environment, namely, the codewords do not contain consecutive '1's, they always start with '0', and they contain at least one bit '1'. This code proved to present a significant improvement in terms of bit error rate (BER). Motivated by the work above, in this paper, we study Tomlinson, Cercas, Hughes (TCH) codes, as a new concept applied to MC systems. These codes possess several properties that make them appealing for various applications, such as error correction, synchronism, spread spectrum systems, and channel estimation [23; 24; 25]. The main goal of adopting these codes for MC is to achieve good coding gains due to a smaller autocorrelation distribution, that is, higher minimum distances, while supporting low implementation complexity based on soft-decision decoding for best performance. The main contributions of this paper can be summarized as follows:  
\(\bullet\) We introduced a new low complexity coding scheme, the TCH codes, targeted to the typically tightly constrained MC applications. \(\bullet\) We propose adequate symbol detection schemes for the MC channel which enable low-complexity hard and soft decision TCH decoding. \(\bullet\) The efficiency of the TCH encoder and decoder is analyzed and compared with other existing alternatives proposed in the literature. A thorough performance assessment of the resulting scheme is accomplished through an end-to-end MC simulator incorporating a diffusion-based channel model. Different pulse types and modulations are considered in this evaluation.