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We present a low-complexity and low-latency decoding algorithm for a class of Reed-Muller (RM) subcodes that are defined based on the product of smaller RM codes. More specifically, the input sequence is shaped as a multi-dimensional array,…
We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an…
The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders (ISD). However, recently…
The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…
Erasure coding techniques are getting integrated in networked distributed storage systems as a way to provide fault-tolerance at the cost of less storage overhead than traditional replication. Redundancy is maintained over time through…
This paper considers a network where a node wishes to transmit a source message to a legitimate receiver in the presence of an eavesdropper. The transmitter secures its transmissions employing a sparse implementation of Random Linear…
We consider the problem of encoding information in a system of N=K+R processors that operate in a decentralized manner, i.e., without a central processor which orchestrates the operation. The system involves K source processors, each…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
This article introduces a novel concatenated coding scheme called sparse regression LDPC (SR-LDPC) codes. An SR-LDPC code consists of an outer non-binary LDPC code and an inner sparse regression code (SPARC) whose respective field size and…
A new coding scheme for image transmission over noisy channel is proposed. Similar to standard image compression, the scheme includes a linear transform followed by successive refinement scalar quantization. Unlike conventional schemes, in…
Quantum error-correcting codes (QECCs) can eliminate the negative effects of quantum noise, the major obstacle to the execution of quantum algorithms. However, realizing practical quantum error correction (QEC) requires resolving many…
The capacity of symmetric, neighboring and consecutive side-information single unicast index coding problems (SNC-SUICP) with number of messages equal to the number of receivers was given by Maleki, Cadambe and Jafar. For these index coding…
Peer-to-peer distributed storage systems provide reliable access to data through redundancy spread over nodes across the Internet. A key goal is to minimize the amount of bandwidth used to maintain that redundancy. Storing a file using an…
Anomalies in time-series provide insights of critical scenarios across a range of industries, from banking and aerospace to information technology, security, and medicine. However, identifying anomalies in time-series data is particularly…
The concepts of pseudocodeword and pseudoweight play a fundamental role in the finite-length analysis of LDPC codes. The pseudoredundancy of a binary linear code is defined as the minimum number of rows in a parity-check matrix such that…
This paper establishes information-theoretic limits in estimating a finite field low-rank matrix given random linear measurements of it. These linear measurements are obtained by taking inner products of the low-rank matrix with random…
The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network…
While every network node only relays messages in a traditional communication system, the recent network coding (NC) paradigm proposes to implement simple in-network processing with packet combinations in the nodes. NC extends the concept of…
This paper addresses the issue of design of low-rate sparse-graph codes with linear minimum distance in the blocklength. First, we define a necessary condition which needs to be satisfied when the linear minimum distance is to be ensured.…
Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate…