Related papers: Generalized Lexicographic Products and the Index C…
In this paper, we propose a new coding scheme and establish new bounds on the capacity region for the multi-sender unicast index-coding problem. We revisit existing partitioned Distributed Composite Coding (DCC) proposed by Sadeghi et al.…
This paper studies a variant of the Pliable Index CODing (PICOD) problem, i.e., an index coding problem where a user can be satisfied by decoding any message that is not in its side information set, where communication is decentralized,…
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…
A variant of the index coding problem (ICP), the embedded index coding problem (EICP) was introduced in [A. Porter and M. Wootters, "Embedded index coding," ITW, Sweden, 2019] which was motivated by its application in distributed computing…
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…
The performance of codes defined from graphs depends on the expansion property of the underlying graph in a crucial way. Graph products, such as the zig-zag product and replacement product provide new infinite families of constant degree…
This paper investigates the problem of single-source multicasting over a communication network in the presence of restricted adversaries. When the adversary is constrained to operate only on a prescribed subset of edges, classical cut-set…
In this paper, we present a general formula for the capacity region of a general interference channel with two pairs of users. The formula shows that the capacity region is the union of a family of rectangles, where each rectangle is…
We consider the \emph{functional index coding problem} over an error-free broadcast network in which a source generates a set of messages and there are multiple receivers, each holding a set of functions of source messages in its cache,…
The identification capacity region of the compound broadcast channel is determined under an average error criterion, where the sender has no channel state information. We give single-letter identification capacity formulas for discrete…
To tackle the expected enormous increase in mobile video traffic in cellular networks, an architecture involving a base station along with caching femto stations (referred to as helpers), storing popular files near users, has been proposed…
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…
An index coding problem arises when there is a single source with a number of messages and multiple receivers each wanting a subset of messages and knowing a different set of messages a priori. The noiseless Index Coding Problem is to…
In this paper, we explore the mystery of synchronous CDMA as applied to wireless and optical communication systems under very general settings for the user symbols and the signature matrix entries. The channel is modeled with real/complex…
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 question of under what condition some side information for index coding can be removed without affecting the capacity region is studied, which was originally posed by Tahmasbi, Shahrasbi, and Gohari. To answer this question, the notion…
The Pliable Index CODing (PICOD) problem is a variant of the Index Coding (IC) problem, where the desired messages by the users, who are equipped with message side information, is part of the optimization. This paper studies the PICOD…
The index coding problem involves a sender with K messages to be transmitted across a broadcast channel, and a set of receivers each of which demands a subset of the K messages while having prior knowledge of a different subset as side…
The hypergraph product (HGP) is a famous code construction technique with an equally famous canonical visualisation. This visual perspective provides much more than simply a way to build intuition: HGP codes can be defined graphically,…
We study the parameterized complexity of the problems of finding a maximum common (induced) subgraph of two given graphs. Since these problems generalize several NP-complete problems, they are intractable even when parameterized by strongly…