Fast Polarization for Processes with Memory

2017/10/08 by Boaz Shuval, Shuval, Boaz, Ido Tal +1 · 2 citations
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Algorithms and Data Compression #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.1710.02849

openalex publication_date 2017/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. Namely, previous works have not addressed fast polarization of the high entropy set under memory. We consider polar codes for processes with memory that are characterized by an underlying ergodic finite-state Markov chain. We show that the rate of polarization for these processes is the same as in the memoryless setting, both for the high and for the low entropy sets.

Citations

• Polar codes with a stepped boundary
• Polarization for arbitrary discrete memoryless channels

Cited by

• Polar Codes for Erasure and Unital Classical-Quantum Markovian Channels
• A Lower Bound on the Probability of Error of Polar Codes over BMS Channels
• Polarization Decomposition and Its Applications

Related

• Polar Coding for Processes with Memory
• Universal Polarization for Processes with Memory
• Polar Codes: Speed of polarization and polynomial gap to capacity
• Constant Weight Polar Codes through Periodic Markov Processes
• Channel Polarization under Channel Noise with Memory