Related papers: Multi-Kernel Polar Codes: Proof of Polarization an…
In the present paper, the models of structural analysis and evaluation of efficiency indicators (reliability, fault tolerance, viability, and flexibility) of a multi core processor with variable structure, equipped with multi functional…
Polar codes based on $2\times2$ non-binary kernels are discussed in this work. The kernel over $\text{GF}(q)$ is selected by maximizing the polarization effect and using Monte-Carlo simulation. Belief propagation (BP) and successive…
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…
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…
The so-called {\it Modern Theory of Polarization}, which rigorously defines the spontaneous polarization of a period solid and provides a route for its computation in electronic structure codes through the Berry phase, is introduced in a…
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…
The structure of polar codes inherently requires block lengths to be powers of two. In this paper, we investigate how different block lengths can be realized by coupling of several short-length polar codes. For this, we first analyze "code…
We show that polar codes can be used to achieve the rate-distortion functions in the problem of hierarchical source coding also known as the successive refinement problem. We also analyze the distributed version of this problem,…
Polar codes that approach capacity at a near-optimal speed, namely with scaling exponents close to $2$, have been shown possible for $q$-ary erasure channels (Pfister and Urbanke), the BEC (Fazeli, Hassani, Mondelli, and Vardy), all BMS…
In this paper, polar codes for the $m$-user multiple access channel (MAC) with binary inputs are constructed. It is shown that Ar{\i}kan's polarization technique applied individually to each user transforms independent uses of a $m$-user…
Polar codes provably achieve the symmetric capacity of a memoryless channel while having an explicit construction. This work aims to increase the throughput of polar decoder hardware by an order of magnitude relative to the state of the art…
Holevo, Schumacher, and Westmoreland's coding theorem guarantees the existence of codes that are capacity-achieving for the task of sending classical data over a channel with classical inputs and quantum outputs. Although they demonstrated…
In this paper, we design explicit codes for strong coordination in two-node networks. Specifically, we consider a two-node network in which the action imposed by nature is binary and uniform, and the action to coordinate is obtained via a…
We introduce a new class of circuits for constructing efficiently decodable error-correction codes, based on a recently discovered contractible tensor network. We perform an in-depth study of a particular example that can be thought of as…
Polar codes are introduced for discrete memoryless broadcast channels. For $m$-user deterministic broadcast channels, polarization is applied to map uniformly random message bits from $m$ independent messages to one codeword while…
Understanding how 5G networks correct errors is no trivial matter. At the heart of the process lie two sophisticated families of codes: LDPC and polar codes. This paper opens the black box, not only by explaining how these codes are…
We prove two results on the universality of polar codes for source coding and channel communication. First, we show that for any polar code built for a source $P_{X,Z}$ there exists a slightly modified polar code - having the same rate, the…
The Modern Theory of Polarization, which rigorously defines the spontaneous electric polarization of a periodic solid and provides a recipe for its computation in electronic structure codes, transformed our understanding of ferroelectricity…
Over the past decade, polar codes have received significant traction and have been selected as the coding method for the control channel in fifth-generation (5G) wireless communication systems. However, conventional polar codes are reliant…
Multi-kernel polar codes have recently been proposed to construct polar codes of lengths different from powers of two. Decoder implementations for multi-kernel polar codes need to account for this feature, that becomes critical in memory…