Capacity and Coding for Degraded Broadcast Channels

The capacity region of discrete memoryless degraded broadcast channels with two receivers is defined. A converse to the coding theorem is then proved, which shows that small error probability is not possible for transmission rates outside of this capacity region. An earlier coding theorem of Bergmans [IEEE Trans. Inf. Theory, 1973, vol. 2, no. 19, pp. 197–207] showing that arbitrarily small error probability is achievable within the capacity region is strengthened by obtaining bounds on error probability that are exponential in block length and analogous to the results for single receiver channels.