Polar codes with a stepped boundary
Ilya I. Dumer · 2017
We design polar codes of blocklength n→∞ and code rate R →1 that achieve the vanishing output error rates on the binary symmetric channels with transition error probability p → 0. These codes have a substantially smaller redundancy order (1 - R)n than do other known high-rate codes, such as Reed-Muller (RM) or BCH codes. The construction is explicit and has complexity of order nlog n. We also design asymptotically optimal low-rate codes that achieve the vanishing output error rates if p → 1/2.