Related papers: On the Uniqueness of Group Sparse Coding
We introduce new yet easily accessible codes for elements of $GL_r(A)$ with $A$ the adelic ring of a (dimension one) function field over a finite field. They are linear codes, and coincide with classical algebraic geometry codes when $r=1$.…
Soft-decision decoding is NP-hard problem of great interest to developers of communication system. We present an efficient soft-decision decoding of linear block codes based on compact genetic algorithm (cGA) and compare its performance…
In this paper, we consider compressed sensing (CS) of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An efficient algorithm, called zero-point attracting projection (ZAP) algorithm, is…
The problem of blind identification of channel codes at a receiver involves identifying a code chosen by a transmitter from a known code-family, by observing the transmitted codewords through the channel. Most existing approaches for…
Convolutional sparse coding (CSC) is an important building block of many computer vision applications ranging from image and video compression to deep learning. We present two contributions to the state of the art in CSC. First, we…
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…
The Convolutional Sparse Coding (CSC) model has recently gained considerable traction in the signal and image processing communities. By providing a global, yet tractable, model that operates on the whole image, the CSC was shown to…
We introduce a notion of code sparsification that generalizes the notion of cut sparsification in graphs. For a (linear) code $\mathcal{C} \subseteq \mathbb{F}_q^n$ of dimension $k$ a $(1 \pm \epsilon)$-sparsification of size $s$ is given…
Noiseless coding theorem for finite stationary memoryless information sources is proved by using induction on the number of source symbols and the inequality of geometric and harmonic means.
In this paper, we propose a new coding scheme and establish new bounds on the capacity region for the multi-sender unicast index-coding problem. We revisit existing partitioned Distributed Composite Coding (DCC) proposed by Sadeghi et al.…
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…
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…
This paper presents a method to calculate the exact average block error probability of some random code ensembles under maximum-likelihood decoding. The proposed method is applicable to various channels and ensembles. The focus is on both…
A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs, e.g., Steiner systems, balanced incomplete block designs and t-designs. The…
Recently, the sparse vector code (SVC) is emerging as a promising solution for short-packet transmission in massive machine type communication (mMTC) as well as ultra-reliable and low-latency communication (URLLC). In the SVC process, the…
We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…
The notion of $S$-labeling of graphs, where $S$ is a subset of a symmetric group, was introduced in 2019 by Jin, Wong, and Zhu. This notion provides the framework for a common generalization of various well studied notions of graph…
The aim of this paper is to prove the achievability of fixed-rate universal coding problems by using our previously introduced notion of hash property. These problems are the fixed-rate lossless universal source coding problem and the…
Several types of AL-FEC (Application-Level FEC) codes for the Packet Erasure Channel exist. Random Linear Codes (RLC), where redundancy packets consist of random linear combinations of source packets over a certain finite field, are a…
In this paper will be presented new approach to entropy coding: family of generalizations of standard numeral systems which are optimal for encoding sequence of equiprobable symbols, into asymmetric numeral systems - optimal for freely…