Related papers: An Outer Bound for the Multi-Terminal Rate-Distort…
Transformers achieve superior performance on many tasks, but impose heavy compute and memory requirements during inference. This inference can be made more efficient by partitioning the process across multiple devices, which, in turn,…
The rate-distortion curve captures the fundamental tradeoff between compression length and resolution in lossy data compression. However, it conceals the underlying dynamics of optimal source encodings or test channels. We argue that these…
This paper studies the last-column-block-augmented northwest-corner truncation (LC-block-augmented truncation, for short) of discrete-time block-monotone Markov chains under subgeometric drift conditions. The main result of this paper is to…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
We consider Markov chains on general state spaces in stationary random environment which are defined by a random mapping that is contractive up to a bounded perturbation. We prove their convergence to a limiting law, providing convergence…
Consider the two-way rate-distortion problem in which a helper sends a common limited-rate message to both users based on side information at its disposal. We characterize the region of achievable rates and distortions where a Markov form…
We find upper bounds for the probability of underestimation and overestimation errors in penalized likelihood context tree estimation. The bounds are explicit and applies to processes of not necessarily finite memory. We allow for general…
A new approach is developed for evaluating the convergence rate for nonlinear Markov chains (MC) based on the recently developed spectral radius technique of markovian coupling for linear MC and the idea of small nonlinear perturbations of…
We propose an achievable rate-region for the two-way multiple-relay channel using decode-and-forward block Markovian coding. We identify a conflict between the information flow in both directions. This conflict leads to an intractable…
Channel symmetry properties that imply the tightness of Shannon's random coding inner bound have recently been used to determine the capacity region of discrete-memoryless two-way channels (DM-TWCs). For channels without such symmetry…
We present a new outer bound for the sum capacity of general multi-unicast deterministic networks. Intuitively, this bound can be understood as applying the cut-set bound to concatenated copies of the original network with a special…
A new single-letter achievable rate region is proposed for the two-user discrete memoryless multiple-access channel(MAC) with noiseless feedback. The proposed region includes the Cover-Leung rate region [1], and it is shown that the…
We propose a new construction for low-density source codes with multiple parameters that can be tuned to optimize the performance of the code. In addition, we introduce a set of analysis techniques for deriving upper bounds for the expected…
A unified framework to obtain all known lower bounds (random coding, typical random coding and expurgated bound) on the reliability function of a point-to-point discrete memoryless channel (DMC) is presented. By using a similar idea for a…
From a recent geometric generalization of Thermodynamic Uncertainty Relations (TURs) we derive novel upper bounds on the nonlinear response of an observable of an arbitrary system undergoing a change of probabilistic state. Various…
We consider a remote source coding problem subject to a {distortion function}. Contrary to the use of the classical separable distortion criterion, herein we consider the more general, $f$-separable distortion measure and study its…
Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how…
Given a graph where vertices are partitioned into $k$ terminals and non-terminals, the goal is to compress the graph (i.e., reduce the number of non-terminals) using minor operations while preserving terminal distances approximately.The…
We give new bounds on the reliability function of a typewriter channel with 5 inputs and crossover probability $1/2$. The lower bound is more of theoretical than practical importance; it improves very marginally the expurgated bound,…
Understanding generalization in modern machine learning settings has been one of the major challenges in statistical learning theory. In this context, recent years have witnessed the development of various generalization bounds suggesting…