  We consider lossy source compression of a binary symmetric source using polar
codes and the low-complexity successive encoding algorithm. It was recently
shown by Arikan that polar codes achieve the capacity of arbitrary symmetric
binary-input discrete memoryless channels under a successive decoding strategy.
We show the equivalent result for lossy source compression, i.e., we show that
this combination achieves the rate-distortion bound for a binary symmetric
source. We further show the optimality of polar codes for various problems
including the binary Wyner-Ziv and the binary Gelfand-Pinsker problem
