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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…
While there are continuous efforts to introduce new communication systems and standards, it is legitimate to ask the question: how can one send additional bits by minimally changing the systems that are already operating? This is of a…
We investigate robust linear consensus over networks under capacity-constrained communication. The capacity of each edge is encoded as an upper bound on the number of state variables that can be communicated instantaneously. When the edge…
Predictive coding is a message-passing framework initially developed to model information processing in the brain, and now also topic of research in machine learning due to some interesting properties. One of such properties is the natural…
This paper investigates the first- and second-order maximum achievable rates of codes with/without cost constraints for mixed {channels} whose channel law is characterized by a general mixture of (at most) uncountably many stationary and…
We consider a network multicast example that relates the solvability of the multicast problem with the existence of an entropy function. As a result, we provide an alternative approach to the proving of the insufficiency of linear (and…
In networks, there are often more than one source of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity and…
While network coding can be an efficient means of information dissemination in networks, it is highly susceptible to "pollution attacks," as the injection of even a single erroneous packet has the potential to corrupt each and every packet…
This paper is concerned with a class of low density generator matrix codes (LDGM), called repetition and superposition (RaS) codes, which have been proved to be capacity-achieving over binary-input output-symmetric (BIOS) channels in terms…
We consider the problem of broadcast with common messages, and focus on the case that the common message rate $R_{\mathcal{A}}$, i.e., the rate of the message intended for all the receivers in the set $\mathcal{A}$, is the same for all the…
We establish a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric…
Though network coding is traditionally performed over finite fields, recent work on nested-lattice-based network coding suggests that, by allowing network coding over certain finite rings, more efficient physical-layer network coding…
This paper presents an analysis of spinal codes, a class of rateless codes proposed recently. We prove that spinal codes achieve Shannon capacity for the binary symmetric channel (BSC) and the additive white Gaussian noise (AWGN) channel…
Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing…
In this paper, the problem of designing network codes that are both communicationally and computationally efficient over packet line networks with worst-case schedules is considered. In this context, random linear network codes (dense…
We examine the issue of separation and code design for networks that operate over finite fields. We demonstrate that source-channel (or source-network) separation holds for several canonical network examples like the noisy multiple access…
Anytime reliable communication systems are needed in contexts where the property of vanishing error probability with time is critical. This is the case of unstable real time systems that are to be controlled through the transmission and…
The capacity of a class of multi-way relay channels, where L users communicate via a relay (at possibly different rates), is derived for the case where the channel outputs are modular sums of the channel inputs and the receiver noise. The…
Coded caching is able to exploit accumulated cache size and hence superior to uncoded caching by distributing different fractions of a file in different nodes. This work investigates coded caching in a large-scale small-cell network (SCN)…
In this paper, we study the redundancy of linear codes with graph constraints. First we consider linear parity check codes based on bipartite graphs with diversity and with generalized graph constraints. We describe sufficient conditions on…