Capacity region of a class of deterministic K-receiver broadcast channels with degraded message sets

In this paper, we establish the capacity region of a new class of deterministic K-receiver broadcast channels with degraded message sets, where the output Y_i, i ∈ {1, ..., K}, is a deterministic function of the channel input X and user i requires messages (M₁, ... M_i). In this class of deterministic broadcast channels, the outputs Y₁ → Y₂ → Y₃ ... → Y_K form a Markov chain for a sufficient class of input probability distributions p (x) ∈ P. The main idea of the coding strategy is to allow user i to decode not only its own messages (M₁, ..., M_i), but also part of the messages (M_i+1, ..., M_K) intended for user j ∈ {i + 1, i + 2, ..., K}. We then show that the achievable rate region attains the capacity region of this new class of deterministic K-receiver broadcast channels.