Polar codes for compress-and-forward in binary relay channels

We construct polar codes for binary relay channels with orthogonal receiver components. We show that polar codes achieve the cut-set bound when the channels are symmetric and the relay-destination link supports compress-and-forward relaying based on Slepian-Wolf coding. More generally, we show that a particular version of the compress-and-forward rate is achievable using polar codes for Wyner-Ziv coding. In both cases the block error probability can be bounded as O(2
^-(Nβ)
) for 0 <; β <; 1/2 and sufficiently large block length N.