Diffusion based molecular communications system enhancement using high order hamming codes

This work considers a performance enhancement technique that can be applied to diffusion based molecular communications systems. Comparisons are made between an un-coded system and coded system which uses Hamming codes up to an order of 10. The analysis is further advanced to consider the energy expenditure during the coding and decoding process. Results show that compared with un-coded system, down to a BER (Bit Error Rate) of 10^-9, a coding gain can be obtained from using a Hamming code but importantly, the gain is shown to be non-linear such that, when one also considers energy requirements - an optimum code order exists. It is shown that for the scenarios considered here, Hamming (31,26) provides the shortest critical distance whilst Hamming (63,57) provides the largest coding gain. These results should resolve an open issue of how large a Hamming code can be used before it is self-defeating in nano-communications applications.