In this paper, we consider the problem of polar coding for block fading channels, with emphasis on those with instantaneous channel state information (CSI) at neither the transmitter nor the receiver. Our approach is to decompose a block fading channel of Tc symbols per coherent interval into Tc binary-input sub-channels in a capacity-preserving way, and design a polar code for each of them. Fo...

THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. In this paper, an algebraic binning based coding scheme and its associated achievable rate for key generation using physically unclonable functions (PUFs) is determined. This achievable rate is shown to be optimal under the generated-secret (GS) model for PUFs. Furthermore, a polar code based polynomial-time encoding and decoding scheme that a...

In this note, the following basic question is explored: in a cyclic group, how are the Shannon entropies of the sum and difference of i.i.d. random variables related to each other? For the integer group, we show that they can differ by any real number additively, but not too much multiplicatively; on the other hand, for Z/3Z, the entropy of the difference is always at least as large as that of ...

Thanks to the property of provably capacityachieving, the recently-discovered polar codes are being taken many attentions. The Successive Cancellation (SC) is the first and widely known decoding for polar codes. In the paper, we study the decoding beginning with its recursive formula. Compared with previous works, our study is more strict and many fresh results are presented which would be help...

Polar codes under successive cancellation decoding proposed by Ar{\i}kan provably achieve the symmetric capacity of any given binary-input discrete memoryless channel. The successive cancellation list decoder for polar codes was described by Tal and Vardy as a generalization of the successive cancellation decoder of Ar{\i}kan. The performance of the successive cancellation list decoder is encou...

In this note, the following basic question is explored: in a cyclic group, how are the Shannon entropies of the sum and difference of i.i.d. random variables related to each other? For the integer group, we show that they can differ by any real number additively, but not too much multiplicatively; on the other hand, for Z/3Z, the entropy of the difference is always at least as large as that of ...

It is shown that nested polar codes achieve the Shannon capacity of arbitrary discrete memoryless sources and the Shannon capacity of arbitrary discrete memory less channels.

In this paper, we propose a new class of lattices constructed from polar codes, namely polar lattices, to achieve the capacity 1 2 log(1+ SNR) of the additive white Gaussian-noise (AWGN) channel for any signal-to-noise ratio (SNR). Our construction follows the multilevel approach of Forney et al., where on each level we construct a capacityachieving polar code. The component polar codes are nat...

A low-complexity systematic encoding algorithm for polar codes with Reed-Solomon kernel is presented. The proposed method relies on fast Fourier transform based ReedSolomon encoding techniques. Application of polar codes in storage systems is considered.