IRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES Achieving Marton’s Region for Broadcast Channels Using Polar Codes

This paper presents polar coding schemes for the 2-user discrete memoryless broadcast channel (DM-BC) which achieve Marton’s region with both common and private messages. This is the best achievable rate region up to date, and it is tight for all classes of 2-user DM-BCs whose capacity regions are known. To accomplish this task, first we construct polar codes for the superposition and binning strategies. Then, by a combination of these two schemes, we obtain Marton’s region with private messages only. Finally, we add also common information. The proposed coding schemes possess the usual advantages of polar codes, i.e., low encoding and decoding complexity and sub-exponential scaling of the error probability. We follow the lead of the recent work by Goela, Abbe, and Gastpar, who introduce polar codes emulating the superposition and the binning schemes. In order to align the polar indices, in both the superposition and the binning scenario their solution involves some degradedness constraints that are assumed to hold between the auxiliary random variables and the channel outputs. To remove these constraints, we consider the transmission of k blocks and employ chaining constructions that guarantee the proper alignment of polarized indices. The techniques described in this work are quite general, and they can be adopted in many other multi-terminal scenarios whenever there is the need for the aligning of polar indices.