Related papers: Multishot Codes for Network Coding using Rank-Metr…
The projective space of order $n$ over a finite field $\F_q$ is a set of all subspaces of the vector space $\F_q^{n}$. In this work, we consider error-correcting codes in the projective space, focusing mainly on constant dimension codes. We…
Link and node failures are common two fundamental problems that affect operational networks. Hence, protection of communication networks is essential to increase their reliability, performance, and operations. Much research work has been…
This paper describes a novel approach for combining Luby Transform (LT) codes and Network Coding (NC) in the context of PowerLine Communications (PLC) smart grid networks. Multihop transmissions of LT-encoded data on PLC networks are…
A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making…
Sum-rank metric codes have recently attracted the attention of many researchers, due to their relevance in several applications. Mathematically, the sum-rank metric is a natural generalization of both the Hamming metric and the rank metric.…
We consider the problem of error control in a coded, multicast network, focusing on the scenario where the errors can occur only on a proper subset of the network edges. We model this problem via an adversarial noise, presenting a formal…
Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical…
Exponentially growing subpacketization is known to be a major issue for practical implementation of coded caching, specially in networks with multi-antenna communication setups. We provide a new coded caching scheme for such networks, which…
We present a multi-scale predictive coding model for future video frames prediction. Drawing inspiration on the ``Predictive Coding" theories in cognitive science, it is updated by a combination of bottom-up and top-down information flows,…
Future communication scenarios for NASA spacecraft may involve multiple communication links and relay nodes, so that there is essentially a network in which there may be multiple paths from a sender to a destination. The availability of…
While feasibility and obtaining a solution of a given network coding problem are well studied, the decoding procedure and complexity have not garnered much attention. We consider the decoding problem in a network wherein the sources…
In the present paper we initiate the study of the product higher rank numerical range. The latter, being a variant of the higher rank numerical range [M.--D. Choi {\it et al.}, Rep. Math. Phys. {\bf 58}, 77 (2006); Lin. Alg. Appl. {\bf…
This paper extends the well-known source coding problem of multiple descriptions, in its general and basic setting, to analog source-channel coding scenarios. Encoding-decoding functions that optimally map between the (possibly continuous…
Non-adaptive joint source network coding of correlated sources is discussed in this paper. By studying the information flow in the network, we propose quantized network coding as an alternative for packet forwarding. This technique has both…
In visual recognition tasks, few-shot learning requires the ability to learn object categories with few support examples. Its re-popularity in light of the deep learning development is mainly in image classification. This work focuses on…
We propose a simple yet effective wireless network coding and decoding technique. It utilizes spatial diversity through cooperation between nodes which carry out distributed encoding operations dictated by generator matrices of linear block…
This paper considers insertion and deletion channels with the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. No segment markers are available…
We present a new application of multi-orbit cyclic subspace codes to construct large optical orthogonal codes, with the aid of the multiplicative structure of finite fields extensions. This approach is different from earlier approaches…
This paper proposes a practical successive decoding scheme with finite levels for the finite-state Markov channels where there is no a priori state information at the transmitter or the receiver. The design employs either a random…
In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that generally consist of duplicate entries. We first introduce a class of binary matrices called…