Fourier analysis of MAC polarization

Abstract

One problem with MAC polar codes that are based on MAC polarization is that they may not achieve the entire capacity region. The reason behind this problem is that MAC polarization sometimes induces a loss in the capacity region. This paper provides a single letter necessary and sufficient condition which characterizes all the MACs that do not lose any part of their capacity region by polarization.

Polar Codes for Arbitrary Classical-Quantum Channels and Arbitrary cq-MACs

“…We have shown that cq-MAC polarization can induce a loss in the symmetric capacity region. A necessary and sufficient condition for J pol (W ) = J (W ) in the case of classical MACs was given in [19].…”

“…Generalizing the results of [19] to cq-MACs is an open problem. We note that the condition in [19] was given in terms of the Fourier transform of the probability distribution of one input conditioned on the output and on the other input.…”

“…Generalizing the results of [19] to cq-MACs is an open problem. We note that the condition in [19] was given in terms of the Fourier transform of the probability distribution of one input conditioned on the output and on the other input. Since this conditional probability does not have an analogue in the case of cq-MACs, generalizing the results of [19] to cq-MACs might be challenging and a completely different approach might be needed.…”