Coding schemes for discrete memoryless broadcast channels with rate-limited feedback

We propose two coding schemes for discrete memoryless broadcast channels (DMBCs) with rate-limited feedback. In our first scheme, the encoder does not process the feedback information that it receives, but simply relays it to the other receiver. This first scheme shows that arbitrary small, but positive, feedback rate suffices to improve over the nofeedback capacity for many DMBCs such as: any binary erasure BC (BEBC) with unequal erasure probability at the two receivers, any binary symmetric BC (BSBC) with unequal crossover probability at the receivers, and any binary erasure/binary symmetric BC (BEC/BSC-BC) with nonequal single-user capacity to the receivers. The scheme also improves the entire nofeedback capacity region for any strictly essentially less-noisy BC-a new class of BCs introduced in this paper-that is not physically degraded.