How do polar codes work and why were they selected for 5G control channels?

Polar codes provably achieve channel capacity through channel polarization: recursively combining channels creates extremes of reliable and unreliable bit channels. Information bits use reliable channels; frozen bits (known values) use unreliable ones. Encoding is simple (multiplication by generator matrix, O(N log N)). Decoding: Successive cancellation (SC, O(N log N)), SC-List (near-ML performance), or belief propagation. 5G selection rationale: excellent performance at short block lengths (control channels), low complexity, proven capacity-achieving, and efficient encoding. Polar codes are first provably capacity-achieving codes with practical complexity.