This thesis investigates communication systems constrained by thermal limits, where overheating can lead to data disruption or system failure. Focusing on thermal-aware (TA) channels in the finite domain, we study binary input sequences of fixed length that influence the system’s thermal state.
To start, we determine the number of admissible sequences that keep the system within thermal limits, both isolated and put into cascade. These sequences are represented by sets Ca, where a denotes the starting temperature. Transition matrices derived from the TA-channel model are used to compute size of Ca for varying values of a, aiming to maximize the number of valid sequences.
Extending prior results on monotonicity in ∣Ca∣ for a specific parameter configuration, we analytically prove a new case using an injective mapping technique. Moreover, we propose conjectures for more general settings, supported by numerical evidence. Our findings indicate that the largest admissible sets typically occur when the initial temperature a is approximately half of the system’s maximum allowable temperature. This offers both theoretical insight and a basis for future research on thermal-aware channel capacity.