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. In our second scheme, the encoder decodes all the feedback information and processes it with some local information before sending the result to the receivers. For some setups, this second scheme performs better than our first scheme. In the limit, as the available feedback-rates tend to infinity, our second scheme coincides with a special case of the Shayevitz and Wigger (SW) scheme for DMBCs with generalized feedback. The mentioned special case of the SW-scheme includes several other schemes as further special cases, e.g, the schemes by Dueck and by MaddahAli and Tse which achieve capacity or the degrees of freedom on the respectively studied channels. All our results hold also with noisy feedback when the receivers can code over the feedback links.