Related papers: Convolutional Codes with Maximum Column Sum Rank f…
Histograms, i.e., piece-wise constant approximations, are a popular tool used to represent data distributions. Traditionally, the difference between the histogram and the underlying distribution (i.e., the approximation error) is measured…
Rank-metric codes are subspaces of matrices over finite fields endowed with the rank metric and admit a natural tensorial representation. The tensor rank provides a measure of the minimal size of a decomposition of a code into rank-one…
One pervasive challenge in providing a high quality-of-service for live communication is to recover lost packets in real-time. Streaming codes are a class of erasure codes that are designed for such strict, low-latency streaming…
The movement of large quantities of data during the training of a Deep Neural Network presents immense challenges for machine learning workloads. To minimize this overhead, especially on the movement and calculation of gradient information,…
A systematic convolutional encoder of rate $(n-1)/n$ and maximum degree $D$ generates a code of free distance at most ${\cal D} = D+2$ and, at best, a column distance profile (CDP) of $[2,3,\ldots,{\cal D}]$. A code is \emph{Maximum…
We study the problem of reducing the communication overhead from a noisy wire-tap channel or storage system where data is encoded as a matrix, when more columns (or their linear combinations) are available. We present its applications to…
Convolutional sparse coding (CSC) improves sparse coding by learning a shift-invariant dictionary from the data. However, existing CSC algorithms operate in the batch mode and are expensive, in terms of both space and time, on large…
Algebraic methods for the design of series of maximum distance separable (MDS) linear block and convolutional codes to required specifications and types are presented. Algorithms are given to design codes to required rate and required…
A widely-used tool for binary classification is the Support Vector Machine (SVM), a supervised learning technique that finds the "maximum margin" linear separator between the two classes. While SVMs have been well studied in the batch…
This paper investigates adaptive streaming codes over a three-node relayed network. In this setting, a source node transmits a sequence of message packets to a destination through a relay. The source-to-relay and relay-to-destination links…
The convolution neural nets (conv nets) have achieved a state-of-the-art performance in many applications of image and video processing. The most recent studies illustrate that the conv nets are fragile in terms of recognition accuracy to…
In this paper, we first introduce the concept of elementary linear subspace, which has similar properties to those of a set of coordinates. We then use elementary linear subspaces to derive properties of maximum rank distance (MRD) codes…
Streaming is a model where an input graph is provided one edge at a time, instead of being able to inspect it at will. In this work, we take a parameterized approach by assuming a vertex cover of the graph is given, building on work of…
A directed acyclic network is considered where all the terminals need to recover the sum of the symbols generated at all the sources. We call such a network a sum-network. It is shown that there exists a solvably (and linear solvably)…
The problem of error correction in both coherent and noncoherent network coding is considered under an adversarial model. For coherent network coding, where knowledge of the network topology and network code is assumed at the source and…
Inspired by the recent advances of image super-resolution using convolutional neural network (CNN), we propose a CNN-based block up-sampling scheme for intra frame coding. A block can be down-sampled before being compressed by normal intra…
It has been shown that maximum distance profile (MDP) convolutional codes have optimal recovery rate for windows of a certain length, when transmitting over an erasure channel. In addition, the subclass of complete MDP convolutional codes…
We consider decoding of vertically homogeneous interleaved sum-rank-metric codes with high interleaving order $s$, that are constructed by stacking $s$ codewords of a single constituent code. We propose a Metzner--Kapturowski-like decoding…
Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…
Synthesis of DNA molecules offers unprecedented advances in storage technology. Yet, the microscopic world in which these molecules reside induces error patterns that are fundamentally different from their digital counterparts. Hence, to…