Sub-4.7 Scaling Exponent of Polar Codes

Polar codes approach channel capacity provably and empirically are thereby a constituent code of the 5G standard. Compared to low-density parity-check codes, however, performance short-length polar have rooms for improvement that could hinder its adoption by wider class applications. As part program addresses issue at short length, it is crucial understand how fast binary memoryless symmetric channels polarize. A number, called scaling exponent, was defined measure speed polarization several estimates exponent were given in literature. 2022, tightest overestimate 4.714 made Mondelli, Hassani, Urbanke 2015. We lower 4.63. The idea behind this that, instead describing relation between W children ◻ ⊛, we describe grandchildren ◻◻, ◻⊛, ⊛◻, ⊛⊛. By doing so, evolution becomes “less Markovian” hence more tighter inequalities can be obtained.