Polar codes for sources with finite reconstruction alphabets

Polar codes are a new class of codes introduced by Arikan capable of achieving the symmetric capacity of discrete memoryless channels. It was later shown that polar codes can achieve the symmetric rate-distortion bound for the lossy source coding problem when the size of the reconstruction alphabet is a prime. In this paper, we show that polar codes achieve the symmetric rate-distortion bound for finite-alphabet sources regardless of the size of the reconstruction alphabet.