Related papers: On Linear Operator Channels over Finite Fields
The problem of error-control in random linear network coding is considered. A ``noncoherent'' or ``channel oblivious'' model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer…
We construct linear network codes utilizing algebraic curves over finite fields and certain associated Riemann-Roch spaces and present methods to obtain their parameters. In particular we treat the Hermitian curve and the curves associated…
In this paper, throughput achieved in cognitive radio channels with finite blocklength codes under buffer limitations is studied. Cognitive users first determine the activity of the primary users' through channel sensing and then initiate…
We introduce a formal framework to study the multiple unicast problem for a coded network in which the network code is linear over a finite field and fixed. We show that the problem corresponds to an interference alignment problem over a…
As the mobile application landscape expands, wireless networks are tasked with supporting different connection profiles, including real-time traffic and delay-sensitive communications. Among many ensuing engineering challenges is the need…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
Channel coding alone is not sufficient to reliably transmit a message of finite length $K$ from a source to one or more destinations as in, e.g., file transfer. To ensure that no data is lost, it must be combined with rateless erasure…
Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern,…
This paper investigates the maximal secret communication rate over a wiretap channel subject to reliability and secrecy constraints at a given blocklength. New achievability and converse bounds are derived, which are uniformly tighter than…
We study finite-length bounds for source coding with side information for Markov sources and channel coding for channels with conditional Markovian additive noise. For this purpose, we propose two criteria for finite-length bounds. One is…
Optimal transport has numerous applications, particularly in machine learning tasks involving generative models. In practice, the transportation process often encounters an information bottleneck, typically arising from the conversion of a…
The multiplicative-additive finite-field matrix channel arises as an adequate model for linear network coding systems when links are subject to errors and erasures, and both the network topology and the network code are unknown. In a…
The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, the upper bound on the achievable rate of a class of codes, called batched codes, is studied for line networks. Batched…
This paper proposes a method to optimize communication code rates via the application of neural polar decoders (NPDs). Employing this approach enables simultaneous optimization of code rates over input distributions while providing a…
Vector linear network coding (LNC) is a generalization of the conventional scalar LNC, such that the data unit transmitted on every edge is an $L$-dimensional vector of data symbols over a base field GF($q$). Vector LNC enriches the choices…
This paper investigates low-latency streaming codes for a three-node relay network. The source transmits a sequence of messages (streaming messages) to the destination through the relay between them, where the first-hop channel from the…
We present nonasymptotic bounds on the maximum coding rate achievable over a Rician block-fading channel for a fixed packet size and a fixed packet error probability. Our bounds, which apply to the scenario where no a priori channel state…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
This work investigates the fundamental limits of communication over a noisy discrete memoryless channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless…
Random linear network coding (RLNC) provides a powerful framework for non-coherent communication, where reliable transmission requires correcting errors and erasures induced by network mixing and motivates the use of subspace codes. In this…