by M. Mondelli, S. H. Hassani, R. Urbanke

Abstract:

Consider transmission of a polar code of block length N and rate R over a binary memoryless symmetric channel W with capacity I(W) and Bhattacharyya parameter Z(W) and let $P_e$ be the error probability under successive cancellation decoding. Recall that in the error exponent regime, the channel W and R

Reference:

Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors M. Mondelli, S. H. Hassani, R. UrbankeIn International Symposium on Information Theory (ISIT), 2015Best Student Paper Award

Bibtex Entry:

@inproceedings{hassani15isit1}$. In the scaling exponent regime, the channel W and $P_e$ are fixed, while the gap to capacity I(W)-R scales as $N^{-1/\mu}$, with $3.579 \le \mu \le 5.702$ for any W. We develop a unified framework to characterize the relationship among R, N, $P_e$, and the quality of W. First, we provide the tighter upper bound $\mu \le 4.714$, valid for any W. Furthermore, when W is a binary erasure channel, we obtain an upper bound approaching very closely the value which was previously derived in a heuristic manner. Secondly, we consider a moderate deviations regime and we study how fast both the gap to capacity I(W)-R and the error probability $P_e$ simultaneously go to 0 as N goes large. Thirdly, we prove that polar codes are not affected by error floors. To do so, we fix a polar code of block length N and rate R, we let the channel W vary, and we show that $P_e$ scales roughly as $Z(W)^{\sqrt{N}}$.}, Author = {Marco Mondelli and S. Hamed Hassani and Ruediger Urbanke}, Booktitle = {International Symposium on Information Theory (ISIT)}, Title = {Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors}, Year = {2015}}