Related papers: Structural Properties of Index Coding Capacity Usi…
A distributed quantum storage code maps a quantum message to N storage nodes, of arbitrary specified sizes, such that the stored message is robust to an arbitrary specified set of erasure patterns. The sizes of the storage nodes, and…
Positional encoding has become a standard component in graph learning, especially for graph Transformers and other models that must distinguish structurally similar nodes, yet its fundamental identifiability remains poorly understood. In…
We consider transmission over a general memoryless channel, with bounded decoding complexity per bit under message passing decoding. We show that the achievable rate is bounded below capacity if there is a finite success in the decoding in…
We introduce load-balanced fractional repetition (LBFR) codes, which are a strengthening of fractional repetition (FR) codes. LBFR codes have the additional property that multiple node failures can be sequentially repaired by downloading no…
Consider a coloring of a graph such that each vertex is assigned a fraction of each color, with the total amount of colors at each vertex summing to $1$. We define the fractional defect of a vertex $v$ to be the sum of the overlaps with…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
We describe a rational approach to reduce the computational and communication complexities of lossless point-to-point compression for computation with side information. The traditional method relies on building a characteristic graph with…
It is shown that polar coding schemes achieve the known achievable rate regions for several multi-terminal communications problems including lossy distributed source coding, multiple access channels and multiple descriptions coding. The…
The index coding problem is studied from an interference alignment perspective, providing new results as well as new insights into, and generalizations of, previously known results. An equivalence is established between multiple unicast…
In this paper we consider the identification (ID) via multiple access channels (MACs). In the general MAC the ID capacity region includes the ordinary transmission (TR) capacity region. In this paper we discuss the converse coding theorem.…
We consider the problem of computing the capacity of a coded, multicast network over a small alphabet. We introduce a novel approach to this problem based on mixed integer programming. As an application of our approach, we recover, extend…
The randomized fixe-composition with optimal decoding error exponents are studied \cite{Raul_ISIT,Raul_journal} for the finite alphabet interference channel (IFC) with two transmitter-receiver pairs. In this paper we investigate the…
A single-letter characterization is provided for the capacity region of finite-state multiple-access channels, when the channel state process is an independent and identically distributed sequence, the transmitters have access to partial…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
In contrast to the network coding problem wherein the sinks in a network demand subsets of the source messages, in a network computation problem the sinks demand functions of the source messages. Similarly, in the functional index coding…
Computational feasibility is a widespread concern that guides the framing and modeling of biological and artificial intelligence. The specification of cognitive system capacities is often shaped by unexamined intuitive assumptions about the…
The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most…
In this work, we study the problem of index coding from graph homomorphism perspective. We show that the minimum broadcast rate of an index coding problem for different variations of the problem such as non-linear, scalar, and vector index…
Nowadays computer networks use different kind of memory whose speeds and capacities vary widely. There exist methods of a so-called caching which are intended to use the different kinds of memory in such a way that the frequently used data…
A sum-network is an instance of a network coding problem over a directed acyclic network in which each terminal node wants to compute the sum over a finite field of the information observed at all the source nodes. Many characteristics of…