Related papers: On Puncturing Strategies for Polar Codes
Binary linear [n,k] codes that are proper for error detection are known for many combinations of n and k. For the remaining combinations, existence of proper codes is conjectured. In this paper, a particular class of [n,k] codes is studied…
This paper proposes the architecture of partial sum generator for constituent codes based polar code decoder. Constituent codes based polar code decoder has the advantage of low latency. However, no purposefully designed partial sum…
An implementation-efficient finite alphabet decoder for polar codes relying on coarsely quantized messages and low-complexity operations is proposed. Typically, finite alphabet decoding performs concatenated compression operations on the…
This paper deals with two main issues regarding the short polar codes: the potential of FEC-assisted decoding and optimal code concatenation strategies under various design scenarios. Code concatenation and FEC-assisted decoding are…
For a given symmetric tensor, we aim at finding a new one whose symmetric rank is small and that is close to the given one. There exist linear relations among the entries of low rank symmetric tensors. Such linear relations can be expressed…
From the perspective of tree, we design a length-flexible coding scheme. For an arbitrary code length, we first construct a balanced binary tree (BBT) where the root node represents a transmitted codeword, the leaf nodes represent either…
Symmetric and sparse tensors arise naturally in many domains including linear algebra, statistics, physics, chemistry, and graph theory. Symmetric tensors are equal to their transposes, so in the $n$-dimensional case we can save up to a…
In this paper, we investigate a novel family of polar codes based on multi-kernel constructions, proving that this construction actually polarizes. To this end, we derive a new and more general proof of polarization, which gives sufficient…
Sparse tensor networks are commonly used to represent contractions over sparse tensors. Tensor contractions are higher-order analogs of matrix multiplication. Tensor networks arise commonly in many domains of scientific computing and data…
Structured sparsity is an important modeling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design. In this paper we investigate the…
This paper presents the first proof of polarization for the deletion channel with a constant deletion rate and a regular hidden-Markov input distribution. A key part of this work involves representing the deletion channel using a trellis…
Polar codes are constructed based on the reliability of sub-channels resulting from the polarization effect. However, this information-theoretic construction approach leads to a poor weight distribution. To address this issue,…
A successive cancellation list (SCL) decoder with limited list size for polar codes can not be analyzed as a successive cancellation (SC) decoder, nor as a maximum likelihood (ML) decoder, due to the complicated decoding errors caused by…
In this paper, we first propose a new iterative algorithm, called the K-sets+ algorithm for clustering data points in a semi-metric space, where the distance measure does not necessarily satisfy the triangular inequality. We show that the…
Random linear network coding (RLNC) in theory achieves the max-flow capacity of multicast networks, at the cost of high decoding complexity. To improve the performance-complexity tradeoff, we consider the design of sparse network codes. A…
Purpose: Magnetic polarizability tensors (MPTs) provide an economical characterisation of conducting magnetic metallic objects and their spectral signature can aid in the solution of metal detection inverse problems, such as scrap metal…
This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…
This work deals with the generation of theoretical correlation matrices with specific sparsity patterns, associated to graph structures. We present a novel approach based on convex optimization, offering greater flexibility compared to…
Achieving security against adversaries with unlimited computational power is of great interest in a communication scenario. Since polar codes are capacity achieving codes with low encoding-decoding complexity and they can approach perfect…
Deep metric learning aims to learn embeddings that contain semantic similarity information among data points. To learn better embeddings, methods to generate synthetic hard samples have been proposed. Existing methods of synthetic hard…