HKU Scholars Hubhttp://hub.hku.hkThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 27 Jul 2021 03:35:35 GMT2021-07-27T03:35:35Z50751- Asymptotics of entropy rate in special families of hidden Markov chainshttp://hdl.handle.net/10722/156252Title: Asymptotics of entropy rate in special families of hidden Markov chains
Authors: Han, G; Marcus, BH
Abstract: We derive an asymptotic formula for entropy rate of a hidden Markov chain under certain parameterizations. We also discuss applications of the asymptotic formula to the asymptotic behaviors of entropy rate of hidden Markov chains as outputs of certain channels, such as binary symmetric channel, binary erasure channel, and some special Gilbert-Elliot channel. © 2006 IEEE.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1562522010-01-01T00:00:00Z
- Generalized PSK in space-time codinghttp://hdl.handle.net/10722/156131Title: Generalized PSK in space-time coding
Authors: Han, G
Abstract: A wireless communication system using multiple antennas promises reliable transmission under Rayleigh flat fading assumptions. Design criteria and practical schemes have been presented for both coherent and noncoherent communication channels. In this paper, we generalize one-dimensional (l-D) phase-shift keying (PSK) signals and introduce space-time constellations from generalized PSK (GPSK) signals based on the complex and real orthogonal designs. The resulting space-time constellations reallocate the energy for each transmitting antenna and feature good diversity products; consequently, their performances are better than some of the existing comparable codes. Moreover, since the maximum-likelihood (ML) decoding of our proposed codes can be decomposed to 1-D PSK signal demodulation, the ML decoding of our codes can be implemented in a very efficient way. © 2005 IEEE.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/1561312005-01-01T00:00:00Z
- One-Dimensional Markov Random Fields, Markov Chains and Topological Markov Fieldshttp://hdl.handle.net/10722/202986Title: One-Dimensional Markov Random Fields, Markov Chains and Topological Markov Fields
Authors: Chandgotia, N; Han, G; Marcus, B; Meyerovitch, T; Pavlov, R
Abstract: A topological Markov chain is the support of an ordinary first-order Markov chain. We develop the concept of topological Markov field (TMF), which is the support of a Markov random field. Using this, we show that any one-dimensional (discrete-time, finite-alphabet) stationary Markov random field must be a stationary Markov chain, and we give a version of this result for continuous-time processes. We also give a general finite procedure for deciding if a given shift space is a TMF.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2029862014-01-01T00:00:00Z
- Geometrical and numerical design of structured unitary space-time constellationshttp://hdl.handle.net/10722/156167Title: Geometrical and numerical design of structured unitary space-time constellations
Authors: Han, G; Rosenthal, J
Abstract: There exist two important design criteria for unitary space time codes. In the situation where the signal-to-noise ratio (SNR) is large the diversity product (DP) of a constellation should be as large as possible. It is less known that the diversity sum (DS) is a very important design criterion for codes working in a low SNR environment. So far, no general method to design good-performing constellations with large diversity for any number of transmit antennas and any transmission rate exists. In this correspondence, we propose constellations with suitable structures, which allow one to construct codes with excellent diversity using geometrical symmetry and numerical methods. The presented design methods work for any dimensional constellation and for any transmission rate. © 2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/1561672006-01-01T00:00:00Z
- Recent Results on Input-Constrained Erasure Channels: A Case Study for Markov Approximationhttp://hdl.handle.net/10722/252564Title: Recent Results on Input-Constrained Erasure Channels: A Case Study for Markov Approximation
Authors: Li, Y; Han, G
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10722/2525642017-01-01T00:00:00Z
- A numerical approach for designing unitary space time codes with large diversity product and diversity sumhttp://hdl.handle.net/10722/158858Title: A numerical approach for designing unitary space time codes with large diversity product and diversity sum
Authors: Han, G; Rosenthal, J
Abstract: We define the diversity function and analyze its limiting behavior which results in two important design criteria: the diversity product and the diversity sum. Numerical methods are derived which allows one to construct codes with excellent diversity function and excellent diversity product and sum.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10722/1588582003-01-01T00:00:00Z
- Analyticity of entropy rate in families of hidden Markov chainshttp://hdl.handle.net/10722/158862Title: Analyticity of entropy rate in families of hidden Markov chains
Authors: Han, G; Marcus, B
Abstract: We prove that under mild assumptions a hidden Markov chain varies analytically, in a strong sense, as a function of the underlying Markov chain parameters. In particular, we show that, under these assumptions, the entropy rate of a hidden Markov chain is an analytic function of the parameters. We give examples to show how this can fail in some cases. And we study two natural special classes of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol and binary Markov chains corrupted by binary symmetric noise.
Sat, 01 Jan 2005 00:00:00 GMThttp://hdl.handle.net/10722/1588622005-01-01T00:00:00Z
- Analyticity of entropy rate in families of hidden Markov chains (II)http://hdl.handle.net/10722/158865Title: Analyticity of entropy rate in families of hidden Markov chains (II)
Authors: Han, G; Marcus, B
Abstract: We give relaxed sufficient conditions (compared to [2]) for analyticky of the entropy rate of a hidden Markov chain. Several special cases of the relaxed conditions are discussed. A general principle to calculate the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. Finally, we prove a "stabilizing" property of "Black Hole" case, which suggests that one can explicitly compute the derivatives and obtain an explicit Taylor series in certain cases, generalizing the results in [13], [12]. © 2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/1588652006-01-01T00:00:00Z
- Upper bound analysis of diversity for unitary space time constellationshttp://hdl.handle.net/10722/158867Title: Upper bound analysis of diversity for unitary space time constellations
Authors: Han, G; Rosenthal, J
Abstract: Diversity product and diversity sum are two important parameters for unitary space time constellation design. An interesting observation in this paper is that full diversity can be easily achieved by Haar distributed random constellations. Using the packing techniques on the compact Lie group U(n), we derive an upper bound for the diversity product and the diversity sum.
Thu, 01 Jan 2004 00:00:00 GMThttp://hdl.handle.net/10722/1588672004-01-01T00:00:00Z
- Asymptotics of noisy constrained channel capacityhttp://hdl.handle.net/10722/158868Title: Asymptotics of noisy constrained channel capacity
Authors: Han, G; Marcus, B
Abstract: In this paper, we generalize a result in [18] and derive an asymptotic formula for the entropy rate of a hidden Markov chain, observed when a Markov chain passes through a binary symmetric channel. And we prove an asymptotic formula for the capacity of a binary symmetric channel with input process supported on an irreducible finite type constraint. ©2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/1588682007-01-01T00:00:00Z
- Asymptotics of entropy rate of hidden Markov chains at weak Black Holeshttp://hdl.handle.net/10722/124816Title: Asymptotics of entropy rate of hidden Markov chains at weak Black Holes
Authors: Han, G; Marcus, B
Abstract: We generalize a result in [8] and derive an asymptotic formula for entropy rate of a hidden Markov chain around a "weak Black Hole". We also discuss applications of the asymptotic formula to certain channels. © 2008 IEEE.
Tue, 01 Jan 2008 00:00:00 GMThttp://hdl.handle.net/10722/1248162008-01-01T00:00:00Z
- A tree-based wall-building algorithm for solving container loading problem with multi-drop constraintshttp://hdl.handle.net/10722/158871Title: A tree-based wall-building algorithm for solving container loading problem with multi-drop constraints
Authors: Pan, L; Chu, SCK; Han, G; Huang, JZ
Abstract: This paper presents a container loading algorithm for generating a container truck loading plan for a set of goods to be distributed to different retail outlets in one trip. This is a problem of container loading with multi-drop constraints. According to the destinations and travel plan of the truck, the set of goods items is divided into groups, one for each destination, and the groups are ordered according to the unloading order at the destinations. A general container loading algorithm is revised by replacing the layer loading strategy with a wall-building loading strategy in order to deal with the order of unloading destinations in the travel plan. The numerical analysis results have shown that the algorithm achieved satisfactory loading results in utilization of container space in comparison with the space utilization by human loading. ©2009 IEEE.
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1588712009-01-01T00:00:00Z
- A Randomized Algorithm for the Capacity of Finite-state Channelshttp://hdl.handle.net/10722/236605Title: A Randomized Algorithm for the Capacity of Finite-state Channels
Authors: Han, G
Abstract: Inspired by ideas from the field of stochastic approximation, we propose a randomized algorithm to compute the capacity of a finite-state channel with a Markovian input. When the mutual information rate of the channel is concave with respect to the chosen parameterization, the proposed algorithm proves to be convergent to the capacity of the channel almost surely with the derived convergence rate. We also discuss the convergence behavior of the algorithm without the concavity assumption.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2366052016-01-01T00:00:00Z
- Coding advantage in communications among peershttp://hdl.handle.net/10722/232366Title: Coding advantage in communications among peers
Authors: Cai, K; Han, G
Abstract: We consider the problem of network coding advantage in a communication scenario where information exchange is bi-directional and peers communicate via multiple unicast sessions. In such a setting, we study the overall performance of all multiple unicast sessions and propose a version of the multiple unicast conjecture. One of our main results is a weaker version of the proposed conjecture: Consider all the multiple unicast sessions associated with a number of terminals in an undirected network. Then, the common transmission rate of all these multiple unicast sessions achieved by network coding in the sense of Langberg and Médard [13] can also be achieved by fractional routing. © 2016 IEEE.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2323662016-01-01T00:00:00Z
- On Connections between Stochastic Calculus and Information Theoryhttp://hdl.handle.net/10722/228526Title: On Connections between Stochastic Calculus and Information Theory
Authors: Liu, X; Han, G
Abstract: In this talk, making use of interesting connections between stochastic differential equations and information theory, we derive the capacity regions of several classes of continuous-time Gaussian channels. The 'complete' results obtained in this work stand in stark contrast to the status quo of network information theory in discrete-time, where the capacity regions of the all the above-mentioned channels are known only for a handful of special scenarios.
Description: MS-Th-E-10: Stochastic Dynamics with Applications - paper no. MS-Th-E-10-1
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2285262015-01-01T00:00:00Z
- Derivatives of entropy rate in special families of hidden Markov chainshttp://hdl.handle.net/10722/135158Title: Derivatives of entropy rate in special families of hidden Markov chains
Authors: Han, G; Marcus, B
Abstract: Consider a hidden Markov chain obtained as the observation process of an ordinary Markov chain corrupted by noise. Recently Zuk etal showed how, in principle, one can explicitly compute the derivatives of the entropy rate of at extreme values of the noise. Namely, they showed that the derivatives of standard upper approximations to the entropy rate actually stabilize at an explicit finite time. We generalize this result to a natural class of hidden Markov chains called "Black Holes."We also discuss in depth special cases of binary Markov chains observed in binary-symmetric noise, and give an abstract formula for the first derivative in terms of a measure on the simplex due to Blackwell. © 2007 IEEE.
Mon, 01 Jan 2007 00:00:00 GMThttp://hdl.handle.net/10722/1351582007-01-01T00:00:00Z
- Analyticity of entropy rate of hidden Markov chainshttp://hdl.handle.net/10722/156183Title: Analyticity of entropy rate of hidden Markov chains
Authors: Han, G; Marcus, B
Abstract: We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. We then show that the positivity assumptions can be relaxed, and examples are given for the relaxed conditions. We study a special class of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol, and we give necessary and sufficient conditions for analyticity of the entropy rate for this case. Finally, we show that under the positivity assumptions, the hidden Markov chain itself varies analytically, in a strong sense, as a function of the underlying Markov chain parameters. © 2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/1561832006-01-01T00:00:00Z
- Unitary space-time constellation analysis: An upper bound for the diversityhttp://hdl.handle.net/10722/156182Title: Unitary space-time constellation analysis: An upper bound for the diversity
Authors: Han, G; Rosenthal, J
Abstract: The diversity product and the diversity sum are two very important parameters for a good-performing unitary space-time constellation. A basic question is what the maximal diversity product (or sum) is. In this correspondence, we are going to derive general upper bounds on the diversity sum and the diversity product for unitary constellations of any dimension n and any size m using packing techniques on the compact Lie group U(n). © 2006 IEEE.
Sun, 01 Jan 2006 00:00:00 GMThttp://hdl.handle.net/10722/1561822006-01-01T00:00:00Z
- Network encoding complexity: exact values, bounds and inequalitieshttp://hdl.handle.net/10722/247477Title: Network encoding complexity: exact values, bounds and inequalities
Authors: Xu, L; Shang, W; Han, G
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10722/2474772017-01-01T00:00:00Z
- Multi-criteria Student Project Allocation: A Case Study of Goal Programming Formulation with DSS Implementationhttp://hdl.handle.net/10722/100362Title: Multi-criteria Student Project Allocation: A Case Study of Goal Programming Formulation with DSS Implementation
Authors: Pan, L; Chu, SCK; Han, G; Huang, JZ
Abstract: This paper concerns a typical Student Project Allocation (SPA) problem involving distributing a set of projects to students of an undergraduate 'Directed Studies in Mathematics' course at the Department of Mathematics of the University of Hong Kong. Among a set of projects, each student indicates a preference list over their eligible projects, while the Department wants to make the most allocations, with its preferences over the individual students according to their GPA’s. We apply pre-emptive goal programming to a multi-criteria SPA model for allocating these projects to students with a DSS implementation. The numerical results illustrate the clear effectiveness and efficiency of this approach.
Description: The conference is organized by Asia-Pacific Operations Research Center (APORC) under APORS and the Chinese Academy of Sciences (CAS),
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/1003622009-01-01T00:00:00Z
- On Sampling Theoremshttp://hdl.handle.net/10722/252562Title: On Sampling Theorems
Authors: Han, G
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2525622016-01-01T00:00:00Z
- ARMA(1) Gaussian feedback capacity revisitedhttp://hdl.handle.net/10722/234164Title: ARMA(1) Gaussian feedback capacity revisited
Authors: Liu, T; Han, G
Abstract: Recently, the capacity of the first-order autoregressive moving average Gaussian feedback channel has been explicitly computed using a variational formulation of the corresponding optimization problem. In this paper, we recover this result using a different approach, which may also help enhance our understanding of general Gaussian feedback channels at large.
Description: Session - Mo-A-2: Channel Coding with Feedback
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2341642016-01-01T00:00:00Z
- On Network Hubshttp://hdl.handle.net/10722/242726Title: On Network Hubs
Authors: Han, G
Abstract: Consider a network G = (V, E), where V denotes the set of vertices in G, and E denotes the set of edges in G. A vertex in G is said to be a source if it is only incident with outgoing edges, and a sink if it is only incident with incoming edges. Often, a source or sink is referred to as a terminal vertex. A non-terminal vertex is said to be a hub if its degree is greater than or equal to 3. In this paper, we are primarily concerned with the minimum number of hubs needed when certain constraints on the flow demand between multiple pairs of sources and sinks are imposed. The flow demand constraints considered in this paper will be in terms of the vertex-cuts between pairs of sources and sinks. This can be justified by a vertex version of the max-flow min-cut theorem [1], which states that for a network with infinite edge-capacity and unit vertex-capacity, the maximum flow between one source and one sink is equal to the minimum vertex-cut between them. Here, we remark that with appropriately modified setup, our results can be stated in terms of edge-cuts as well.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2427262014-01-01T00:00:00Z
- On network coding advantage for multiple unicast networkshttp://hdl.handle.net/10722/218964Title: On network coding advantage for multiple unicast networks
Authors: Cai, K; Han, G
Abstract: In this paper, by studying the feasible fractional routing solution under the so-called full reachability condition, we give bounds on the network coding advantage for undirected multiple unicast networks. More precisely, we prove that, for certain class of fully reachable networks, the network coding advantage is upper bounded by 9/8, improving the previous bound 3 by M. Langberg and M. Médard.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2189642015-01-01T00:00:00Z
- On the capacity of multilevel NAND flash memory channelshttp://hdl.handle.net/10722/233953Title: On the capacity of multilevel NAND flash memory channels
Authors: Li, Y; Kavcic, A; Han, G
Abstract: In this paper, we initiate a first information-theoretic study on multilevel NAND flash memory channels [2] with intercell interference. More specifically, for a multilevel NAND flash memory channel under mild assumptions, we first prove that such a channel is indecomposable and it features asymptotic equipartition property; we then further prove that stationary processes achieve its information capacity, and consequently, as its order tends to infinity, its Markov capacity converges to its information capacity; eventually, we establish that its operational capacity is equal to its information capacity. Our results suggest that it is highly plausible to apply the ideas and techniques in the computation of the capacity of finite-state channels, which are relatively better explored, to that of the capacity of multilevel NAND flash memory channels. © 2016 IEEE.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2339532016-01-01T00:00:00Z
- Anote on a complex Hilbert metric with application to domain of analyticity for entropy rate of hidden Markov processeshttp://hdl.handle.net/10722/207440Title: Anote on a complex Hilbert metric with application to domain of analyticity for entropy rate of hidden Markov processes
Authors: Han, G; Marcus, B; Peres, Y
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/2074402011-01-01T00:00:00Z
- Prime Factorization Theory of Networkshttp://hdl.handle.net/10722/209262Title: Prime Factorization Theory of Networks
Authors: Li, SYR; Han, G; Yang, Y
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/2092622011-01-01T00:00:00Z
- Concavity of mutual information rate for input-restricted finite-state memoryless channels at high SNRhttp://hdl.handle.net/10722/62185Title: Concavity of mutual information rate for input-restricted finite-state memoryless channels at high SNR
Authors: Han, G; Marcus, B
Abstract: We consider a finite-state memoryless channel with i.i.d. channel state and the input Markov process supported on a mixing finite-type constraint. We discuss the asymptotic behavior of entropy rate of the output hidden Markov chain and deduce that the mutual information rate of such a channel is concave with respect to the parameters of the input Markov processes at high signal-to-noise ratio. In principle, the concavity result enables good numerical approximation of the maximum mutual information rate and capacity of such a channel. © 2009 IEEE.
Description: 2009 IEEE International Symposium on Information Theory
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/621852009-01-01T00:00:00Z
- The ARMA(k) Gaussian feedback capacityhttp://hdl.handle.net/10722/247844Title: The ARMA(k) Gaussian feedback capacity
Authors: Liu, T; Han, G
Abstract: Using Kim's variational formulation [1] (with a slight yet important modification), we derive the ARMA(fc) Gaussian feedback capacity, i.e., the feedback capacity of an additive channel where the noise is a k-th order autoregressive moving average Gaussian process. More specifically, the ARMA(fc) Gaussian feedback capacity is expressed as a simple function evaluated at a solution to a system of polynomial equations, which proves to have only finitely many solutions for the cases k = 1,2 and possibly beyond.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10722/2478442017-01-01T00:00:00Z
- A heuristic algorithm for the inner-city multi-drop container loading problemhttp://hdl.handle.net/10722/135157Title: A heuristic algorithm for the inner-city multi-drop container loading problem
Authors: Pan, L; Chu, SCK; Han, G; Huang, JZ
Abstract: Economic globalization, increasing fuel cost, and environmental problems provide a strong stimulation for inner-city container carriers to utilize container space more efficiently in transporting goods for multiple clients during a single round trip. A wall-building heuristic algorithm based on the binary tree data structure is proposed to solve the container loading problem with multi-drop constraints. A dynamic space decomposition approach, together with a repacking and space amalgamation strategy, permits an efficient and effective loading plan to pack containers, illustrated by numerical experiments.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1351572011-01-01T00:00:00Z
- Sampling theorems for continuous-time Gaussian channels http://hdl.handle.net/10722/236608Title: Sampling theorems for continuous-time Gaussian channels
Authors: Han, G
Abstract: We prove sampling theorems for continuous-time Gaussian channels with possible feedback. More specifically, we show that the mutual information of the discrete-time versions of a class of continuous-time Gaussian channels, obtained through sampling in time, will converges to the mutual information of the original Gaussian channel, as the step-sizes of the samplings tend to zero.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2366082015-01-01T00:00:00Z
- On Renyi entropy rate of hidden Markov processeshttp://hdl.handle.net/10722/236607Title: On Renyi entropy rate of hidden Markov processes
Authors: Han, G
Abstract: We prove that under mild assumptions, the Renyi entropy rate of hidden Markov processes exists with a tight convergence rate. Possible applications of this result and some related open problems will be discussed as well.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2366072016-01-01T00:00:00Z
- The ARMK(k) Gaussian feedback capacityhttp://hdl.handle.net/10722/252556Title: The ARMK(k) Gaussian feedback capacity
Authors: Han, G
Abstract: Using Kim's variational formulation (with a slight yet important modification), we derive the ARMA(k) Gaussian feedback capacity, i.e., the feedback capacity of an additive channel where the noise is a k-th order autoregressive moving average Gaussian process. More specifically, the ARMA(k) Gaussian feedback capacity is expressed as a simple function evaluated at a solution to a system of polynomial equations, which proves to have only finitely many solutions for some small k and possibly beyond.
Description: Feedback capacity
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10722/2525562017-01-01T00:00:00Z
- Capacity of multilevel NAND flash memory channelshttp://hdl.handle.net/10722/247476Title: Capacity of multilevel NAND flash memory channels
Authors: Li, Y; Kavcic, A; Han, G
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10722/2474762017-01-01T00:00:00Z
- Entropy rate of continuous-state hidden Markov chainshttp://hdl.handle.net/10722/126236Title: Entropy rate of continuous-state hidden Markov chains
Authors: Han, G; Marcus, B
Abstract: We prove that under mild positivity assumptions, the entropy rate of a continuous-state hidden Markov chain, observed when passing a finite-state Markov chain through a discrete-time continuous-output channel, is analytic as a function of the transition probabilities of the underlying Markov chain. We further prove that the entropy rate of a continuous-state hidden Markov chain, observed when passing a mixing finite-type constrained Markov chain through a discrete-time Gaussian channel, is smooth as a function of the transition probabilities of the underlying Markov chain. © 2010 IEEE.
Fri, 01 Jan 2010 00:00:00 GMThttp://hdl.handle.net/10722/1262362010-01-01T00:00:00Z
- On the criteria for designing complex orthogonal space-time block codeshttp://hdl.handle.net/10722/247475Title: On the criteria for designing complex orthogonal space-time block codes
Authors: Kan, H; Liu, X; Han, G
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10722/2474752016-01-01T00:00:00Z
- Menger's paths with minimum mergingshttp://hdl.handle.net/10722/62186Title: Menger's paths with minimum mergings
Authors: Han, G
Abstract: For an acyclic directed graph with multiple sources and multiple sinks, we prove that one can choose the Menger's paths between the sources and the sinks such that the number of mergings between these paths is upper bounded by a constant depending only on the min-cuts between the sources and the sinks, regardless of the size and topology of the graph. We also give bounds on the minimum number of mergings between these paths, and discuss how it depends on the min-cuts. © 2009 IEEE.
Description: 2009 IEEE Information Theory Workshop on Networking and Information Theory
Thu, 01 Jan 2009 00:00:00 GMThttp://hdl.handle.net/10722/621862009-01-01T00:00:00Z
- Rényi entropy rate of hidden Markov processeshttp://hdl.handle.net/10722/247843Title: Rényi entropy rate of hidden Markov processes
Authors: Wu, C; Xu, L; Han, G
Abstract: In this paper, we focus our attention on the Rényi entropy rate of hidden Markov processes under certain positivity assumptions. The existence of the Rényi entropy rate for such processes is established. Furthermore, we show that, with some extra “fast-forgetting” assumptions, the Rényi entropy rate of the approximating Markov processes exponentially converges to that of the original hidden Markov process, as the Markov order goes to infinity.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10722/2478432017-01-01T00:00:00Z
- Information-Theoretic Extensions of the Shannon-Nyquist Sampling Theoremhttp://hdl.handle.net/10722/269902Title: Information-Theoretic Extensions of the Shannon-Nyquist Sampling Theorem
Authors: Han, G
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10722/2699022018-01-01T00:00:00Z
- A graph theoretical approach to network encoding complexityhttp://hdl.handle.net/10722/160280Title: A graph theoretical approach to network encoding complexity
Authors: Xu, EL; Shang, W; Han, G
Abstract: For an acyclic directed network with multiple pairs of sources and sinks and a group of edge-disjoint paths connecting each pair of source and sink, it is known that the number of mergings among different groups of edge-disjoint paths is closely related to network encoding complexity. Using this connection, we derive exact values of and bounds on two functions relevant to encoding complexity for such networks. © 2012 IEICE Institute of Electronics Informati.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/10722/1602802012-01-01T00:00:00Z
- Analyticity of Entropy Rate of Hidden Markov Chains With Continuous Alphabethttp://hdl.handle.net/10722/218754Title: Analyticity of Entropy Rate of Hidden Markov Chains With Continuous Alphabet
Authors: Han, G; Marcus, B
Abstract: We first prove that under certain mild assumptions, the entropy rate of a hidden Markov chain, observed when passing a finite-state stationary Markov chain through a discrete-time continuous-output channel, is analytic with respect to the input Markov chain parameters. We then further prove, under strengthened assumptions on the chan- nel, that the entropy rate is jointly analytic as a function of both the input Markov chain parameters and the channel parameters. In particular, the main theorems estab- lish the analyticity of the entropy rate for two representative channels: Cauchy and Gaussian.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2187542015-01-01T00:00:00Z
- A Randomized Algorithm for the Capacity of Finite-State Channelshttp://hdl.handle.net/10722/217072Title: A Randomized Algorithm for the Capacity of Finite-State Channels
Authors: Han, G
Abstract: Inspired by ideas from the field of stochastic approximation, we propose a ran- domized algorithm to compute the capacity of a finite-state channel with a Markovian input. When the mutual information rate of the channel is concave with respect to the chosen parameterization, the proposed algorithm proves to be convergent to the ca- pacity of the channel almost surely with the derived convergence rate. We also discuss the convergence behavior of the algorithm without the concavity assumption.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10722/2170722015-01-01T00:00:00Z
- Concavity of mutual information rate of finite-state channelshttp://hdl.handle.net/10722/189946Title: Concavity of mutual information rate of finite-state channels
Authors: Li, Y; Han, G
Abstract: The computation of the capacity of a finite-state channel (FSC) is a fundamental and long-standing open problem in information theory. The capacity of a memoryless channel can be effectively computed via the classical Blahut-Arimoto algorithm (BAA), which, however, does not apply to a general FSC. Recently Vontobel et al. [1] generalized the BAA to compute the capacity of a finite-state machine channel with a Markovian input. Their proof of the convergence of this algorithm, however, depends on the concavity conjecture posed in their paper. In this paper, we confirm the concavity conjecture for some special FSCs. On the other hand, we give examples to show that the conjecture is not true in general.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1899462013-01-01T00:00:00Z
- A randomized approach to the capacity of finite-state channelshttp://hdl.handle.net/10722/189947Title: A randomized approach to the capacity of finite-state channels
Authors: Han, G
Abstract: Inspired by the ideas from the field of stochastic approximation, we propose a randomized algorithm to compute the capacity of a finite-state channel with a Markovian input. When the mutual information rate of the channel is concave with respect to the chosen parameterization, we show that, at least for some practical channels, the proposed algorithm will converge to the capacity almost surely.
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1899472013-01-01T00:00:00Z
- Bounds and exact values in network encoding complexity with two sinkshttp://hdl.handle.net/10722/158882Title: Bounds and exact values in network encoding complexity with two sinks
Authors: Xu, L; Han, G
Abstract: For an acyclic directed network with multiple pairs of sources and sinks and a set of Menger's paths connecting each pair of source and sink, it is well known that the number of mergings among these Menger's paths is closely related to network encoding complexity. In this paper, we focus on networks with two distinct sinks and we derive bounds on and exact values of two functions relevant to encoding complexity for such networks. © 2011 IEEE.
Sat, 01 Jan 2011 00:00:00 GMThttp://hdl.handle.net/10722/1588822011-01-01T00:00:00Z
- Input-Constrained Erasure Channels: Mutual Information and Capacityhttp://hdl.handle.net/10722/204178Title: Input-Constrained Erasure Channels: Mutual Information and Capacity
Authors: Li, Y; Han, G
Abstract: In this paper, we derive an explicit formula for the entropy rate of a hidden Markov chain, observed when the Markov chain passes through a memoryless erasure channel. This result naturally leads to an explicit formula for the mutual information rate of memoryless erasure channels with Markovian inputs. Moreover, if the input Markov chain is of first-order and supported on the (1,∞)-run length limited (RLL) constraint, we show that the mutual information rate is strictly concave with respect to a chosen parameter. Then we apply a recent algorithm [1] to approximately compute the first-order noisy constrained channel capacity and the corresponding capacity-achieving distribution.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2041782014-01-01T00:00:00Z
- Extensions of the I-MMSE Relationhttp://hdl.handle.net/10722/204177Title: Extensions of the I-MMSE Relation
Authors: Han, G; Song, J
Abstract: Unveiling a fundamental link between information theory and estimation theory, the I-MMSE relation by Guo, Shamai and Verdú [4] has great theoretical significance and numerous practical applications. On the other hand, its influences to date have been restricted to channels without feedback or memory, due to the lack of extensions of the I-MMSE relation to such channels. In this paper, we propose extensions of the I-MMSE relation for discrete and continuous-time Gaussian channels with feedback or memory. Our approach is based on a very simple observation, which can be applied to other scenarios, such as a simple and direct proof of the classical de Bruijn's identity.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2041772014-01-01T00:00:00Z
- On the Solvability of Three-Pair Networks With Common Bottleneck Linkshttp://hdl.handle.net/10722/204180Title: On the Solvability of Three-Pair Networks With Common Bottleneck Links
Authors: Cai, K; Han, G
Abstract: We consider the solvability problem under network coding and derive a sufficient and necessary condition for 3-pair networks with common “bottleneck links” being solvable. We show that, for such networks: (1) the solvability can be determined in polynomial time; (2) being solvable is equivalent to being linear solvable; (3) finite fields of size 2 or 3 are sufficient to construct linear solutions.
Description: Session We2A: Network Coding II
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2041802014-01-01T00:00:00Z
- Recent Results in Continuous-Time Network Information Theoryhttp://hdl.handle.net/10722/204179Title: Recent Results in Continuous-Time Network Information Theory
Authors: Liu, X; Han, G
Abstract: In this paper, we propose to use Brownian motions to formulate continuous-time multiuser Gaussian networks and derive the capacity regions of a continuous-time white Gaussian multiple access channel with/without feedback, a continuous-time white Gaussian interference channel without feedback and a continuous-time white Gaussian broadcast channel without feedback. These “complete” results stand in stark contrast to the status quo of network information theory in discrete-time, where the capacity regions of the all the above-mentioned channels are known only for a handful of special scenarios. For certain cases, our results echo, from a different perspective, the folklore that “a continuous-time channel is the limit of bandwidth limited discrete-time ones as the bandwidth tends to infinity”.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10722/2041792014-01-01T00:00:00Z
- Limit theorems in hidden Markov modelshttp://hdl.handle.net/10722/189143Title: Limit theorems in hidden Markov models
Authors: Han, G
Tue, 01 Jan 2013 00:00:00 GMThttp://hdl.handle.net/10722/1891432013-01-01T00:00:00Z