Successive improvement of capacity with power constraints

This paper analyzes the problem of hierarchical channel coding for memoryless channels: given a codebook at a particular power level, if the allowed power level is increased, the expanded codebook is generated by pairwise addition of elements from the existing codebook and an auxiliary codebook. This is the counterpart of the problem of additive successive refinement in source coding. The supported set of rates in the channel coding scenario is fully characterized in this paper. The behavior of hierarchical coding schemes is analyzed for some representative channels. It is shown that for many common channels, hierarchical coding does not entail a loss of capacity at either layer.