Polarization Improves E-0

We prove that channel combining and splitting via Arikan's polarization transformation improves Gallager's reliability function E-0 for binary input channels. In this sense, polarization creates E-0. This observation gives yet another justification as to why the polar transform yields capacity achieving and low complexity codes: the improvement in E-0 translates 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 E-0 process associated to such an analysis is a submartingale.


Published in:
Ieee Transactions On Information Theory, 60, 5, 2714-2719
Year:
2014
Publisher:
Piscataway, Ieee-Inst Electrical Electronics Engineers Inc
ISSN:
0018-9448
Keywords:
Laboratories:




 Record created 2014-06-16, last modified 2018-03-17


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