|| On the extremal configurations of MAC polarization over erasure channels
||Min Ye, Tsinghua Shenzhen International Graduate School, China|
||D5-S2-T2: Polar Codes III
||Friday, 16 July, 22:20 - 22:40
||Friday, 16 July, 22:40 - 23:00
Consider an $m$-user multiple access channel (MAC) $(X_1,X_2,\dots,X_m) \to Y$, where all the $X_i$'s are Bernoulli-$1/2$ random variables. It is well known that applying the Arikan transform individually to each user leads to MAC polarization. In general, MAC polarization may include many intermediate extremal configurations, in addition to the ``almost perfect" and ``completely noisy" configurations, and a major open problem in MAC polarization is to identify the proportion of all the extremal configurations. In this paper, we consider two classes of Multiple Access Erasure Channels (MAEC). For the more general class, we identify a necessary and sufficient condition of two-level polarization in the two-user case. This proves a conjecture in [Nasser-Telatar, IEEE Transactions on Information Theory, 2016]. For the other class, we are able to calculate the proportion of the extremal configurations for the $m$-user case.