Fourier Analysis of MAC Polarization
Rajai Nasser, Emre Telatar
TL;DR
This paper characterizes the conditions under which MAC polarization preserves the entire capacity region, addressing a key limitation in MAC polar codes.
Contribution
It provides a single-letter necessary and sufficient condition for MACs to avoid capacity loss during polarization.
Findings
Identifies conditions for capacity-preserving MAC polarization
Characterizes all MACs that do not lose capacity region
Provides theoretical foundation for improved MAC polar codes
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.
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