Encoding of cellular positional information and maximum capacity of parallel coupled channels

Inspired by the parallels between information coding in morphogenesis and information coding in computer communication, we introduce a new model for coupled discrete memoryless channels in which the error probability of one channel depends on the output of the other channel. The model is motivated by a type of cell-cell communication. It is shown that coupling will lead to higher sum capacities with both optimal input distribution and with uniform input distribution under joint coding. Thereby, nature can achieve more than the sum of the individual capacities (synergistic effect). We compare this result with the maximum achievable sum capacity by arbitrary ideal coupling using Majorization theory. Finally, we illustrate the model with applications from wireless communications.