Related papers: On the Correlation Between Polarized BECs
The polar transformation of a binary erasure channel (BEC) can be exactly approximated by other BECs. Ar{\i}kan proposed that polar codes for a BEC can be efficiently constructed by using its useful property. This study proposes a new class…
We study the application of polar codes in deletion channels by analyzing the cascade of a binary erasure channel (BEC) and a deletion channel. We show how polar codes can be used effectively on a BEC with a single deletion, and propose a…
This study proposes \emph{modular arithmetic erasure channels} (MAECs), a novel class of erasure-like channels with an input alphabet that need not be binary. This class contains the binary erasure channel (BEC) and some other known…
Ar{\i}kan's polar coding technique is based on the idea of synthesizing $n$ channels from the $n$ instances of the physical channel by a simple linear encoding transformation. Each synthesized channel corresponds to a particular input to…
Polarization is an unprecedented coding technique in that it not only achieves channel capacity, but also does so at a faster speed of convergence than any other coding technique. This speed is measured by the ``scaling exponent'' and its…
Polar codes are constructed for arbitrary channels by imposing an arbitrary quasigroup structure on the input alphabet. Just as with "usual" polar codes, the block error probability under successive cancellation decoding is…
Polar codes were introduced in 2009 and proven to achieve the symmetric capacity of any binary-input discrete memoryless channel under low-complexity successive cancellation decoding. In this thesis, we construct cyclic polar codes based on…
The polar codes introduced by Arikan in 2009 achieve the capacity of binary-input discrete memoryless channels (BIDMCs) with low complexity encoding and decoding. Identifying the unreliable synthetic channels, generated by Arikan…
A pruned variant of polar coding is reinvented for all binary erasure channels. For small $\varepsilon>0$, we construct codes with block length $\varepsilon^{-5}$, code rate $\text{Capacity}-\varepsilon$, error probability $\varepsilon$,…
We analyze the practical performance of quantum polar codes, by computing rigorous bounds on block error probability and by numerically simulating them. We evaluate our bounds for quantum erasure channels with coding block lengths between…
We study polar coding for stochastic processes with memory. For example, a process may be defined by the joint distribution of the input and output of a channel. The memory may be present in the channel, the input, or both. We show that…
Channel polarization is a method of constructing capacity achieving codes for symmetric binary-input discrete memoryless channels (B-DMCs) [1]. In the original paper, the construction complexity is exponential in the blocklength. In this…
Arikan's recursive code construction is designed to polarize a collection of memoryless channels into a set of good and a set of bad channels, and it can be efficiently decoded using successive cancellation. It was recently shown that the…
Arikan's Polar codes attracted much attention as the first efficiently decodable and capacity achieving codes. Furthermore, Polar codes exhibit an exponentially decreasing block error probability with an asymptotic error exponent upper…
Recently, Ar{\i}kan introduced the method of channel polarization on which one can construct efficient capacity-achieving codes, called polar codes, for any binary discrete memoryless channel. In the thesis, we show that decoding algorithm…
The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that…
Polar codes are a family of capacity-achieving codes that have explicit and low-complexity construction, encoding, and decoding algorithms. Decoding of polar codes is based on the successive-cancellation decoder, which decodes in a bit-…
Polar codes introduced by Arikan in 2009 are the first code family achieving the capacity of binary-input discrete memoryless channels (BIDMCs) with low-complexity encoding and decoding. Identifying unreliable synthetic channels in polar…
We study polarization for nonbinary channels with input alphabet of size q=2^r,r=2,3,... Using Arikan's polarizing kernel H_2, we prove that the virtual channels that arise in the process of polarization converge to q-ary channels with…
We study faulty successive cancellation decoding of polar codes for the binary erasure channel. To this end, we introduce a simple erasure-based fault model and we show that, under this model, polarization does not happen, meaning that…