TY - GEN
T1 - Fast Polarization for Processes with Memory
AU - Shuval, Boaz
AU - Tal, Ido
N1 - Publisher Copyright: © 2018 IEEE.
PY - 2018/8/15
Y1 - 2018/8/15
N2 - Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. We consider polar codes for processes with memory that are characterized by an underlying aperiodic and irreducible finite state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both to the high and to the low-entropy sets. Thus, polar codes achieve the Markov capacity in many information-theoretic applications.
AB - Fast polarization is crucial for the performance guarantees of polar codes. In the memoryless setting, the rate of polarization is known to be exponential in the square root of the block length. A complete characterization of the rate of polarization for models with memory has been missing. We consider polar codes for processes with memory that are characterized by an underlying aperiodic and irreducible finite state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both to the high and to the low-entropy sets. Thus, polar codes achieve the Markov capacity in many information-theoretic applications.
UR - http://www.scopus.com/inward/record.url?scp=85052466091&partnerID=8YFLogxK
U2 - https://doi.org/10.1109/ISIT.2018.8437742
DO - https://doi.org/10.1109/ISIT.2018.8437742
M3 - منشور من مؤتمر
SN - 9781538647806
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 851
EP - 855
BT - 2018 IEEE International Symposium on Information Theory, ISIT 2018
T2 - 2018 IEEE International Symposium on Information Theory, ISIT 2018
Y2 - 17 June 2018 through 22 June 2018
ER -