Related papers: Vard{\o}hus Codes: Polar Codes Based on Castle Cur…
A concatenated coding scheme over binary memoryless symmetric (BMS) channels using a polarization transformation followed by outer sub-codes is analyzed. Achievable error exponents and upper bounds on the error rate are derived. The first…
Polar codes are a new class of error correcting linear block codes, whose generator matrix is specified by the knowledge of transmission channel parameters, code length and code dimension. Moreover, regarding computational security, it is…
In this paper we consider the problem of transmitting a continuous alphabet discrete-time source over an AWGN channel. The design of good curves for this purpose relies on geometrical properties of spherical codes and projections of…
This paper presents a polar coding scheme to achieve secrecy in block fading binary symmetric wiretap channels without the knowledge of instantaneous channel state information (CSI) at the transmitter. For this model, a coding scheme that…
We consider polar subcodes (PSCs), which are polar codes (PCs) with dynamically-frozen symbols, to increase the minimum distance as compared to corresponding PCs. A randomized nested PSC construction with a low-rate PSC and a high-rate PC,…
We develop a low-complexity polar coding scheme for the discrete memoryless broadcast channel with confidential messages under strong secrecy and randomness constraints. Our scheme extends previous work by using an optimal rate of uniform…
Polar codes have been shown to approach capacity of symmetric binary erasure channels and also have low encoding and decoding complexity. Wireless channels are bursty in nature and a method to apply polar codes over wireless channels is…
We present an introduction to the theory of algebraic geometry codes. Starting from evaluation codes and codes from order and weight functions, special attention is given to one-point codes and, in particular, to the family of Castle codes.
The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have…
Information-theoretic work for wiretap channels is mostly based on random coding schemes. Designing practical coding schemes to achieve information-theoretic security is an important problem. By applying the two recently developed…
A generalization of Ar\i kan's polar code construction using transformations of the form $G^{\otimes n}$ where $G$ is an $\ell \times \ell$ matrix is considered. Necessary and sufficient conditions are given for these transformations to…
We study the use of polar codes for both discrete and continuous variables Quantum Key Distribution (QKD). Although very large blocks must be used to obtain the efficiency required by quantum key distribution, and especially continuous…
Polar codes were introduced in 2009 by Arikan as the first efficient encoding and decoding scheme that is capacity achieving for symmetric binary-input memoryless channels. Recently, this code family was extended by replacing the…
Speech recognition is a challenging problem. Due to the acoustic limitations, using visual information is essential for improving the recognition accuracy in real-life unconstraint situations. One common approach is to model the visual…
We construct a new secret-key assisted polar coding scheme for private classical communication over a quantum or classical wiretap channel. The security of our scheme rests on an entropic uncertainty relation, in addition to the channel…
In this paper, we design polar codes and polar lattices for i.i.d. fading channels when the channel state information is only available to the receiver. For the binary input case, we propose a new design of polar codes through single-stage…
A kernel of a directed graph is a subset of vertices that is both independent and absorbing (every vertex not in the kernel has an out-neighbour in the kernel). Not all directed graphs contain kernels, and computing a kernel or deciding…
Polar coding is a method for communication over noisy classical channels which is provably capacity-achieving and has an efficient encoding and decoding. Recently, this method has been generalized to the realm of quantum information…
Kernel-based learning algorithms are widely used in machine learning for problems that make use of the similarity between object pairs. Such algorithms first embed all data points into an alternative space, where the inner product between…
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…