Polar codes are optimal for lossy source coding

We consider lossy source compression of a binary symmetric source with Hamming distortion function. We show that polar codes combined with a low-complexity successive cancellation encoding algorithm achieve the rate-distortion bound. The complexity of both the encoding and the decoding algorithm is O(N log(N)), where N is the blocklength of the code. Our result mirrors Ar¿kan´s capacity achieving polar code construction for channel coding.