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 Arikan's capacity achieving polar code construction for channel coding.