2,828 research outputs found
Compositional planning in Markov decision processes: Temporal abstraction meets generalized logic composition
In hierarchical planning for Markov decision processes (MDPs), temporal
abstraction allows planning with macro-actions that take place at different
time scale in form of sequential composition. In this paper, we propose a novel
approach to compositional reasoning and hierarchical planning for MDPs under
temporal logic constraints. In addition to sequential composition, we introduce
a composition of policies based on generalized logic composition: Given
sub-policies for sub-tasks and a new task expressed as logic compositions of
subtasks, a semi-optimal policy, which is optimal in planning with only
sub-policies, can be obtained by simply composing sub-polices. Thus, a
synthesis algorithm is developed to compute optimal policies efficiently by
planning with primitive actions, policies for sub-tasks, and the compositions
of sub-policies, for maximizing the probability of satisfying temporal logic
specifications. We demonstrate the correctness and efficiency of the proposed
method in stochastic planning examples with a single agent and multiple task
specifications.Comment: 8 pages, 4 figures, 2 tables, accepted as a conference paper for
presentation at American Control Conference 201
On Random Linear Network Coding for Butterfly Network
Random linear network coding is a feasible encoding tool for network coding,
specially for the non-coherent network, and its performance is important in
theory and application. In this letter, we study the performance of random
linear network coding for the well-known butterfly network by analyzing the
failure probabilities. We determine the failure probabilities of random linear
network coding for the well-known butterfly network and the butterfly network
with channel failure probability p.Comment: This paper was submitted to IEEE Communications Letter
Linear Network Error Correction Multicast/Broadcast/Dispersion/Generic Codes
In the practical network communications, many internal nodes in the network
are required to not only transmit messages but decode source messages. For
different applications, four important classes of linear network codes in
network coding theory, i.e., linear multicast, linear broadcast, linear
dispersion, and generic network codes, have been studied extensively. More
generally, when channels of communication networks are noisy, information
transmission and error correction have to be under consideration
simultaneously, and thus these four classes of linear network codes are
generalized to linear network error correction (LNEC) coding, and we say them
LNEC multicast, broadcast, dispersion, and generic codes, respectively.
Furthermore, in order to characterize their efficiency of information
transmission and error correction, we propose the (weakly, strongly) extended
Singleton bounds for them, and define the corresponding optimal codes, i.e.,
LNEC multicast/broadcast/dispersion/generic MDS codes, which satisfy the
corresponding Singleton bounds with equality. The existences of such MDS codes
are discussed in detail by algebraic methods and the constructive algorithms
are also proposed.Comment: Single column, 38 pages. Submitted for possible publicatio
Distributed Storage Schemes over Unidirectional Ring Networks
In this paper, we study distributed storage problems over unidirectional ring
networks. A lower bound on the reconstructing bandwidth to recover total
original data for each user is proposed, and it is achievable for arbitrary
parameters. If a distributed storage scheme can achieve this lower bound with
equality for each user, we say it an optimal reconstructing distributed storage
scheme (ORDSS). Furthermore, the repair problem for a failed storage node in
ORDSSes is under consideration and a tight lower bound on the repair bandwidth
for each storage node is obtained. Particularly, we indicate the fact that for
any ORDSS, every storage node can be repaired with repair bandwidth achieving
the lower bound with equality. In addition, we present an efficient approach to
construct ORDSSes for arbitrary parameters by using the concept of Euclidean
division. Finally, we take an example to characterize the above approach.Comment: two columns, 5 pages, 8 figures, and submitted to the ISIT 201
Variable-Rate Linear Network Error Correction MDS Codes
In network communication, the source often transmits messages at several
different information rates within a session. How to deal with information
transmission and network error correction simultaneously under different rates
is introduced in this paper as a variable-rate network error correction
problem. Apparently, linear network error correction MDS codes are expected to
be used for these different rates. For this purpose, designing a linear network
error correction MDS code based on the existing results for each information
rate is an efficient solution. In order to solve the problem more efficiently,
we present the concept of variable-rate linear network error correction MDS
codes, that is, these linear network error correction MDS codes of different
rates have the same local encoding kernel at each internal node. Further, we
propose an approach to construct such a family of variable-rate network MDS
codes and give an algorithm for efficient implementation. This approach saves
the storage space for each internal node, and resources and time for the
transmission on networks. Moreover, the performance of our proposed algorithm
is analyzed, including the field size, the time complexity, the encoding
complexity at the source node, and the decoding methods. Finally, a random
method is introduced for constructing variable-rate network MDS codes and we
obtain a lower bound on the success probability of this random method, which
shows that this probability will approach to one as the base field size goes to
infinity.Comment: Single column, 34 pages, submitted for publication. arXiv admin note:
text overlap with arXiv:1311.7466, arXiv:1011.137
Repairable Threshold Secret Sharing Schemes
In this paper, we propose a class of threshold secret sharing schemes with
repairing function between shares without the help of the dealer, that we
called repairable threshold secret sharing schemes. Specifically, if a share
fails, such as broken or lost, it will be repaired just by some other shares. A
construction of such repairable threshold secret sharing schemes is designed by
applying linearized polynomials and regenerating codes in distributed storage
systems. In addition, a new repairing rate is introduced to characterize the
performance and efficiency of the repairing function. Then an achievable upper
bound on the repairing rate is derived, which implies the optimality of the
repair and describes the security between different shares. Under this
optimality of the repair, we further discuss traditional information rate and
also indicate its optimality, that can describe the efficiency of secret
sharing schemes in the aspect of storage. Finally, by applying the minimum
bandwidth regenerating (MBR) codes, our construction designs repairable
threshold secret sharing schemes achieving both optimal repairing and
information rates simultaneously.Comment: One column and 17 pages, submitted for publicatio
On the Optimality of Secure Network Coding
In network communications, information transmission often encounters
wiretapping attacks. Secure network coding is introduced to prevent information
from being leaked to adversaries. The investigation of performance bounds on
the numbers of source symbols and random symbols are two fundamental research
problems. For an important case that each wiretap-set with cardinality not
larger than , Cai and Yeung proposed a coding scheme, which is optimal in
the senses of maximizing the number of source symbols and at the same time
minimizing the number of random symbols. In this letter, we further study
achievable lower bound on the number of random key and show that it just
depends on the security constraint, and particularly, is independent to the
information amount for transmission. This implies that when the number of
transmitted source message changes, we can't reduce the number of random key to
keep the same security level. We further give an intuitive interpretation on
our result. In addition, a similar construction of secure linear network codes
is proposed, which achieves this lower bound on the number of random key no
matter how much information is transmitted. At last, we also extend our result
to imperfect security case.Comment: Accepted for publication in the IEEE Communications Letters. One
column,10 page
Small Field Size for Secure Network Coding
In network coding, information transmission often encounters wiretapping
attacks. Secure network coding is introduced to prevent information from being
leaked to adversaries. For secure linear network codes (SLNCs), the required
field size is a very important index, because it largely determines the
computational and space complexities of a SLNC, and it is also very important
for the process of secure network coding from theoretical research to practical
application. In this letter, we further discuss the required field size of
SLNCs, and obtain a new lower bound. This bound shows that the field size of
SLNCs can be reduced further, and much smaller than the known results for
almost all cases.Comment: Accepted for publication in the IEEE Communications Letters. One
column,10 page
Construction of Network Error Correction Codes in Packet Networks
Recently, network error correction coding (NEC) has been studied extensively.
Several bounds in classical coding theory have been extended to network error
correction coding, especially the Singleton bound. In this paper, following the
research line using the extended global encoding kernels proposed in
\cite{zhang-correction}, the refined Singleton bound of NEC can be proved more
explicitly. Moreover, we give a constructive proof of the attainability of this
bound and indicate that the required field size for the existence of network
maximum distance separable (MDS) codes can become smaller further. By this
proof, an algorithm is proposed to construct general linear network error
correction codes including the linear network error correction MDS codes.
Finally, we study the error correction capability of random linear network
error correction coding. Motivated partly by the performance analysis of random
linear network coding \cite{Ho-etc-random}, we evaluate the different failure
probabilities defined in this paper in order to analyze the performance of
random linear network error correction coding. Several upper bounds on these
probabilities are obtained and they show that these probabilities will approach
to zero as the size of the base field goes to infinity. Using these upper
bounds, we slightly improve on the probability mass function of the minimum
distance of random linear network error correction codes in
\cite{zhang-random}, as well as the upper bound on the field size required for
the existence of linear network error correction codes with degradation at most
.Comment: 14 pages, submitted in 4 Nov. 201
Maximal function characterizations for Hardy spaces on spaces of homogeneous type with finite measure and applications
We prove nontangential and radial maximal function characterizations for
Hardy spaces associated to a non-negative self-adjoint operator satisfying
Gaussian estimates on a space of homogeneous type with finite measure. This not
only addresses an open point in the literature, but also gives a complete
answer to the question posed by Coifman and Weiss in the case of finite
measure. We then apply our results to give maximal function characterizations
for Hardy spaces associated to second order elliptic operators with Neumann and
Dirichlet boundary conditions, Schr\"odinger operators with Dirichlet boundary
conditions, and Fourier--Bessel operators.Comment: 36 page
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