Despite remarkable advances in the algebraic and iterative codes used in modern communication systems, finding codes that operate at rates close to capacity; have low computational complexity; and have provable reliability guarantees was an elusive goal until recently. Polar Codes have all of these desirable properties. The design philosophy of polar codes is fundamentally different from those of both algebraic codes and iterative codes. The technique underlying polar codes is channel polarization': creating extremal channels those that are either noiseless or useless from mediocre ones....