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A Single-Letter Upper Bound on the Feedback Capacity of Unifilar Finite-State Channels [article]

Oron Sabag, Haim H. Permuter, Henry D. Pfister
2016 arXiv   pre-print
An upper bound on the feedback capacity of unifilar finite-state channels (FSCs) is derived.  ...  This upper bound indicates that a single-letter expression might exist for the capacity of finite-state channels with or without feedback based on a construction of auxiliary random variable with specified  ...  CONCLUSIONS An upper bound on the feedback capacity of unifilar state channels was derived.  ... 
arXiv:1604.01878v1 fatcat:gj6cau7vlzd5zedamgcthxs6aa

Capacity of Finite State Channels with Feedback: Algorithmic and Optimization Theoretic Properties [article]

Andrea Grigorescu, Holger Boche, Rafael F. Schaefer, H. Vincent Poor
2022 arXiv   pre-print
The capacity of finite state channels (FSCs) with feedback has been shown to be a limit of a sequence of multi-letter expressions.  ...  Furthermore, it is shown that the feedback capacity cannot be characterized as the maximization of a finite-letter formula of entropic quantities.  ...  For |S| = 1, the channel is a DMC and the capacity is given by Shannon's single-letter formula. The capacity of a DMC is Turing computable.  ... 
arXiv:2201.11639v2 fatcat:wjhawnjkcjh5zg7fyavsp4t53q

Computing the Feedback Capacity of Finite State Channels using Reinforcement Learning [article]

Ziv Aharoni, Oron Sabag, Haim Henry Permuter
2020 arXiv   pre-print
Hence, RL can be used to estimate numerically the feedback capacity of unifilar finite state channels (FSCs) with large alphabet size.  ...  These insights can be converted into analytic, single-letter capacity expressions by solving corresponding lower and upper bounds.  ...  Specifically, we use the graphical structure in Fig. 5 to compute a tight upper bound, and analyze the rate of the proposed coding scheme. 1) Bounds on the feedback capacity: The Q-graph method, introduced  ... 
arXiv:2001.09685v1 fatcat:m2uhhgty2bbnbjtkfuwvc2s44e

Reinforcement Learning Evaluation and Solution for the Feedback Capacity of the Ising Channel with Large Alphabet [article]

Ziv Aharoni, Oron Sabag, Haim Henri Permuter
2020 arXiv   pre-print
We propose a new method to compute the feedback capacity of unifilar finite state channels (FSCs) with memory using reinforcement learning (RL).  ...  The outcome of the RL algorithm is a numerical lower bound on the feedback capacity, which is used to reveal the structure of the optimal solution.  ...  Feedback Capacity of Unifilar Finite State Channels The feedback capacity of a unifilar FSC is presented in the following theorem.  ... 
arXiv:2008.07983v1 fatcat:6wk7fadeovcnvi34v3xza3m4sa

Computable Upper Bounds on the Capacity of Finite-State Channels

Bashar Huleihel, Oron Sabag, Haim H. Permuter, Navin Kashyap, Shamai (Shitz), Shlomo
2021 Zenodo  
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 67, NO. 9, SEPTEMBER 2021  ...  ACKNOWLEDGMENT The authors would like to thank the Associate Editor and the anonymous reviewers for their valuable and constructive comments, which helped to improve this paper.  ...  Nevertheless, in this section we present single-letter upper bounds on the capacity of several channels that were derived by solving a DP problem with a continuous DP state space while using the insights  ... 
doi:10.5281/zenodo.5335953 fatcat:4jmbqnxmwbfg5ibce5bs4jkvey

Computable Upper Bounds on the Capacity of Finite-State Channels [article]

Bashar Huleihel, Oron Sabag, Haim H. Permuter, Navin Kashyap, Shlomo Shamai
2021 arXiv   pre-print
We consider the use of the well-known dual capacity bounding technique for deriving upper bounds on the capacity of indecomposable finite-state channels (FSCs) with finite input and output alphabets.  ...  In this technique, capacity upper bounds are obtained by choosing suitable test distributions on the sequence of channel outputs.  ...  ACKNOWLEDGMENT The authors would like to thank the Associate Editor and the anonymous reviewers for their valuable and constructive comments, which helped to improve this paper.  ... 
arXiv:1911.02113v3 fatcat:hb274we3qrhghpkqzivarlpfli

A sequential transmission scheme for unifilar finite-state channels with feedback based on posterior matching

Achilleas Anastasopoulos
2012 2012 IEEE International Symposium on Information Theory Proceedings  
The capacity of unifilar finite-state channels with feedback has been recently derived in the form of a single-letter expression and it has been evaluated analytically for a number of channels of interest  ...  , such as the trapdoor channel and the Ising channel with feedback.  ...  One of the first results on the capacity of channels with memory and feedback was by Viswanathan [2] , who studied the capacity of a finite-state channel (FSC) with receiver channel-state information  ... 
doi:10.1109/isit.2012.6284059 dblp:conf/isit/Anastasopoulos12 fatcat:gqyfwers2vg4dngcy7iike7dgq

Variable-length codes for channels with memory and feedback: error-exponent lower bounds [article]

Achilleas Anastasopoulos, Jui Wu
2017 arXiv   pre-print
In unifilar channels the channel state evolves in a deterministic fashion based on the previous state, input, and output, and is known to the transmitter but is unknown to the receiver.  ...  Simulation results confirm that the bounds are tight compared to the upper bounds derived in a companion paper.  ...  For channels with ergodic behavior, the capacity has a single-letter expression C = sup P X|SB I(X t , S t ; Y t |B t−1 ), (3) where B t−1 ∈ P(S) is the posterior belief on the current state S t given  ... 
arXiv:1701.06681v5 fatcat:ry2vsoulonf6tfo4phqgp46gbu

Upper Bounds on the Capacities of Noncontrollable Finite-State Channels With/Without Feedback

Xiujie Huang, Aleksandar Kavcic, Xiao Ma
2012 IEEE Transactions on Information Theory  
With this technique, we derive a series of upper bounds on the capacities of noncontrollable FSCs with/without feedback.  ...  Since single-letter formulae for the channel capacities are rarely available for general noncontrollable FSCs, computable bounds are usually utilized to numerically bound the capacities.  ...  ACKNOWLEDGMENT The authors would like to thank Dr. S. Yang for his helpful advice at the beginning of this work, and Prof. X. Guo for providing helpful references on Markov decision processes.  ... 
doi:10.1109/tit.2012.2201341 fatcat:qhlhfz3awbbkne35jeuch5gkfi

The Feedback Capacity of Noisy Output is the STate (NOST) Channels [article]

Eli Shemuel, Oron Sabag, Haim Permuter
2022 arXiv   pre-print
We consider finite-state channels (FSCs) where the channel state is stochastically dependent on the previous channel output. We refer to these as Noisy Output is the STate (NOST) channels.  ...  We derive the feedback capacity of NOST channels in two scenarios: with and without causal state information (CSI) available at the encoder.  ...  For a sub-family of unifilar FSCs where the channel state is a deterministic function of the channel output, a single-letter feedback capacity expression was derived and formulated as a DP optimization  ... 
arXiv:2107.07164v2 fatcat:2yoxjdwaybabbpewyre7euvoge

On Separation in the Presence of Feedback

Haim Permuter, Tsachy Weissman
2007 2007 IEEE Information Theory Workshop  
We present a framework for characterizing the fundamental limit of communication with feedback for various point-to-point and multi-terminal finite-state channels.  ...  For example, we will characterize a large class of finite-state multiple access channels for which separation holds with, without, or with partial feedback.  ...  ACKNOWLEDGMENT The authors would like to thank Amos Lapidoth and Andrea Goldsmith for helpful discussions.  ... 
doi:10.1109/itw.2007.4313085 fatcat:5ysugusw45e5dbjlatokauykha

Hidden Markov processes

Y. Ephraim, N. Merhav
2002 IEEE Transactions on Information Theory  
In recent years, the work of Baum and Petrie on finite-state finite-alphabet HMPs was expanded to HMPs with finite as well as continuous state spaces and a general alphabet.  ...  An HMP is a discrete-time finite-state homogeneous Markov chain observed through a discrete-time memoryless invariant channel.  ...  They also thank Randal Douc, Catherine Matias, Éric Moulines, and Tobias Rydén for making available preprints of their most recent work.  ... 
doi:10.1109/tit.2002.1003838 fatcat:6r7stou5ijgi7kjs6tifsyghfm

The Feedback Capacity of the (1,∞)-RLL Input-Constrained Erasure Channel [article]

Oron Sabag, Haim H. Permuter, Navin Kashyap
2015 arXiv   pre-print
The derived capacity expression also serves as the only non-trivial upper bound known on the capacity of the input-constrained erasure channel without feedback, a problem that is still open.  ...  Moreover, we prove that a-priori knowledge of the erasure at the encoder does not increase the feedback capacity.  ...  ACKNOWLEDGMENT The authors would like to thank Yonglong Li and Guangyue Han for providing us the data for the lower bound in plotted in Fig. 3 .  ... 
arXiv:1503.03359v1 fatcat:ozlag5idbjeytpatruoil3jy7u

The method of types [information theory]

I. Csiszar
1998 IEEE Transactions on Information Theory  
The method of types is one of the key technical tools in Shannon Theory, and this tool is valuable also in other fields.  ...  These range from hypothesis testing and large deviations theory through error exponents for discrete memoryless channels and capacity of arbitrarily varying channels to multiuser problems.  ...  Finite-State Types A sequence of -valued RV's is called a unifilar finite-state source if there exists a (finite) set of "states," an initial state , and a mapping that specifies the next state as a function  ... 
doi:10.1109/18.720546 fatcat:rmitj3v4lfbdjjl63aibbqxcce

Neural Estimation and Optimization of Directed Information over Continuous Spaces [article]

Dor Tsur, Ziv Aharoni, Ziv Goldfeld, Haim Permuter
2022 arXiv   pre-print
Applications for channel capacity estimation of continuous channels with memory are explored, and empirical results demonstrating the scalability and accuracy of our method are provided.  ...  When the channel is memoryless, we investigate the mapping learned by the optimized input generator.  ...  Tools from dynamic programming were used in [34, 35] to estimate the feedback capacities of a class of binary finite state channels (FSCs).  ... 
arXiv:2203.14743v1 fatcat:irj45fufdjdhxnarqzkoluxz3a
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