Robust Multi-Layer Coding in the Presence of Channel Distribution Uncertainty

A block fading point-to-point communication channel is considered, where the channel statistic varies between two possible choices. Assuming the transmitter is unaware of the instantaneous channel gain values and the current channel statistic, a multi-layer coding approach is incorporated where the optimal rate allocation strategy across code layers is devised maximizing the worst case average achievable rate. Moreover, noting that the proposed optimization problem is convex, the problem is tackled from another perspective by employing the notion of strong duality, which leads to introducing a least favorable distribution based on the considered possible distributions. This helps to effectively solve the problem for any arbitrary number of distributions. Finally, the results are compared with those of single- and double-layer coding, in order to get an insight regarding the rate loss due to incorporating finite number of layer(s).