Polarization Improves $E_{0}$
Mine Alsan, Emre Telatar · IEEE Transactions on Information Theory · 2014
We prove that channel combining and splitting via Arikan's polarization transformation improves Gallager's reliability function E0for binary input channels. In this sense, polarization creates E0. This observation gives yet another justification as to why the polar transform yields capacity achieving and low complexity codes: the improvement in E0translates to an improvement in complexity-error-probability trade-off. In analyzing polar codes, one examines auxiliary random processes that follow the evolution of information measures as an underlying communication channel undergoes a sequence of transformations. The conclusion of this paper shows that the E0process associated to such an analysis is a submartingale.