Improved Bounds on the Finite Length Scaling of Polar Codes
Dina Goldin, David Burshtein · IEEE Transactions on Information Theory · 2014
Improved upper bounds on the blocklength required to communicate over binary-input channels using polar codes, below some given error probability, are derived. For that purpose, an improved bound on the number of non-polarizing channels is obtained. The main result is that the blocklength required to communicate reliably scales at most as O((I(W ) - R)-5.702), where R is the code rate and I(W ) is the symmetric capacity of the channel W. The results are then extended to polar lossy source coding at rate R of a source with symmetric distortion-rate function D(·). The blocklength required scales at most as O((D0)-5.702), where D0is the maximal allowed gap between the actual average (or typical) distortion and D(R).