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48
Data Compression Using Adaptive Coding and Partial String Matching
 IEEE Transactions on Communications
, 1984
"... The recently developed technique of arithmetic coding, in conjunction with a Markov model of the source, is a powerful method of data compression in situations where a linear treatment is inappropriate. Adaptive coding allows the model to be constructed dynamically by both encoder and decoder during ..."
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Cited by 331 (20 self)
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The recently developed technique of arithmetic coding, in conjunction with a Markov model of the source, is a powerful method of data compression in situations where a linear treatment is inappropriate. Adaptive coding allows the model to be constructed dynamically by both encoder and decoder during the course of the transmission, and has been shown to incur a smaller coding overhead than explicit transmission of the model's statistics. But there is a basic conflict between the desire to use highorder Markov models and the need to have them formed quickly as the initial part of the message is sent. This paper describes how the conflict can be resolved with partial string matching, and reports experimental results which show that mixedcase English text can be coded in as little as 2.2 bits/ character with no prior knowledge of the source.
The ContextTree Weighting Method: Basic Properties
 IEEE Trans. Inform. Theory
, 1995
"... We describe a sequential universal data compression procedure for binary tree sources that performs the "double mixture." Using a context tree, this method weights in an efficient recursive way the coding distributions corresponding to all bounded memory tree sources, and achieves a desirable coding ..."
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Cited by 159 (12 self)
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We describe a sequential universal data compression procedure for binary tree sources that performs the "double mixture." Using a context tree, this method weights in an efficient recursive way the coding distributions corresponding to all bounded memory tree sources, and achieves a desirable coding distribution for tree sources with an unknown model and unknown parameters. Computational and storage complexity of the proposed procedure are both linear in the source sequence length. We derive a natural upper bound on the cumulative redundancy of our method for individual sequences. The three terms in this bound can be identified as coding, parameter, and model redundancy. The bound holds for all source sequence lengths, not only for asymptotically large lengths. The analysis that leads to this bound is based on standard techniques and turns out to be extremely simple. Our upper bound on the redundancy shows that the proposed contexttree weighting procedure is optimal in the sense that it achieves the Rissanen (1984) lower bound.
The Context Tree Weighting Method: Basic Properties
 IEEE Transactions on Information Theory
, 1995
"... We describe a sequential universal data compression procedure for binary tree sources that performs the "double mixture". Using a context tree, this method weights in an efficient recursive way the coding distributions corresponding to all bounded memory tree sources, and achieves a desirable coding ..."
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Cited by 79 (1 self)
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We describe a sequential universal data compression procedure for binary tree sources that performs the "double mixture". Using a context tree, this method weights in an efficient recursive way the coding distributions corresponding to all bounded memory tree sources, and achieves a desirable coding distribution for tree sources with an unknown model and unknown parameters. Computational and storage complexity of the proposed procedure are both linear in the source sequence length. We derive a natural upper bound on the cumulative redundancy of our method for individual sequences. The three terms in this bound can be identified as coding, parameter and model redundancy. The bound holds for all source sequence lengths, not only for asymptotically large lengths. The analysis that leads to this bound is based on standard techniques and turns out to be extremely simple. Our upper bound on the redundancy shows that the proposed context tree weighting procedure is optimal in the sense that i...
K.: Practical EntropyCompressed Rank/Select Dictionary
 Proceedings of ALENEX’07, ACM
, 2007
"... Rank/Select dictionaries are data structures for an ordered set S ⊂ {0, 1,..., n − 1} to compute rank(x, S) (the number of elements in S which are no greater than x), and select(i, S) (the ith smallest element in S), which are the fundamental components of succinct data structures of strings, trees ..."
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Cited by 51 (1 self)
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Rank/Select dictionaries are data structures for an ordered set S ⊂ {0, 1,..., n − 1} to compute rank(x, S) (the number of elements in S which are no greater than x), and select(i, S) (the ith smallest element in S), which are the fundamental components of succinct data structures of strings, trees, graphs, etc. In those data structures, however, only asymptotic behavior has been considered and their performance for real data is not satisfactory. In this paper, we propose novel four Rank/Select dictionaries, esp, recrank, vcode and sdarray, each of which is small if the number of elements in S is small, and indeed close to nH0(S) (H0(S) ≤ 1 is the zeroth order empirical entropy of S) in practice, and its query time is superior to the previous ones. Experimental results reveal the characteristics of our data structures and also show that these data structures are superior to existing implementations in both size and query time. 1
A Knapsack Type Public Key Cryptosystem Based On Arithmetic in Finite Fields
 IEEE Trans. Inform. Theory
, 1988
"... { A new knapsack type public key cryptosystem is introduced. The system is based on a novel application of arithmetic in nite elds, following a construction by Bose and Chowla. By appropriately choosing the parameters, one can control the density of the resulting knapsack, which is the ratio between ..."
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Cited by 35 (2 self)
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{ A new knapsack type public key cryptosystem is introduced. The system is based on a novel application of arithmetic in nite elds, following a construction by Bose and Chowla. By appropriately choosing the parameters, one can control the density of the resulting knapsack, which is the ratio between the number of elements in the knapsack and their size in bits. In particular, the density can be made high enough to foil \low density" attacks against our system. At the moment, no attacks capable of \breaking" this system in a reasonable amount of time are known. Research supported by NSF grant MCS{8006938. Part of this research was done while the rst author was visiting Bell Laboratories, Murray Hill, NJ. A preliminary version of this work was presented in Crypto 84 and has appeared in [8]. 1 1.
Capacity of a class of deterministic relay channels
 in Proc. IEEE Int. Symp. Information Theory
, 2007
"... The capacity of a class of deterministic relay channels with the transmitter input X, the receiver output Y, the relay output Y1 = f(X, Y), and a separate communication link from the relay to the receiver with capacity R0, is shown to be C(R0) = max p(x) min{I(X; Y) + R0, I(X; Y, Y1)}. Thus every b ..."
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Cited by 32 (2 self)
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The capacity of a class of deterministic relay channels with the transmitter input X, the receiver output Y, the relay output Y1 = f(X, Y), and a separate communication link from the relay to the receiver with capacity R0, is shown to be C(R0) = max p(x) min{I(X; Y) + R0, I(X; Y, Y1)}. Thus every bit from the relay is worth exactly one bit to the receiver. Two alternative coding schemes are presented that achieve this capacity. The first scheme, “hashandforward”, is based on a simple yet novel use of random binning on the space of relay outputs, while the second scheme uses the usual “compressandforward”. In fact, these two schemes can be combined together to give a class of optimal coding schemes. As a corollary, this relay capacity result confirms a conjecture by Ahlswede and Han on the capacity of a channel with ratelimited state information at the decoder in the special
ConstantRound Oblivious Transfer in the Bounded Storage Model
, 2004
"... We present a constant round protocol for Oblivious Transfer in Maurer's bounded storage model. In this model, a long random string R is initially transmitted and each of the parties interacts based on a small portion of R. Even though the portions stored by the honest parties are small, security ..."
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Cited by 31 (5 self)
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We present a constant round protocol for Oblivious Transfer in Maurer's bounded storage model. In this model, a long random string R is initially transmitted and each of the parties interacts based on a small portion of R. Even though the portions stored by the honest parties are small, security is guaranteed against any malicious party that remembers almost all of the string R.
Quantum publickey cryptosystems
 in Proc. of CRYPT0 2000
, 2000
"... Abstract. This paper presents a new paradigm of cryptography, quantum publickey cryptosystems. In quantum publickey cryptosystems, all parties including senders, receivers and adversaries are modeled as quantum (probabilistic) polytime Turing (QPT) machines and only classical channels (i.e., no q ..."
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Cited by 28 (2 self)
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Abstract. This paper presents a new paradigm of cryptography, quantum publickey cryptosystems. In quantum publickey cryptosystems, all parties including senders, receivers and adversaries are modeled as quantum (probabilistic) polytime Turing (QPT) machines and only classical channels (i.e., no quantum channels) are employed. A quantum trapdoor oneway function, f, plays an essential role in our system, in which a QPT machine can compute f with high probability, any QPT machine can invert f with negligible probability, and a QPT machine with trapdoor data can invert f. This paper proposes a concrete scheme for quantum publickey cryptosystems: a quantum publickey encryption scheme or quantum trapdoor oneway function. The security of our schemes is based on the computational assumption (over QPT machines) that a class of subsetsum problems is intractable against any QPT machine. Our scheme is very efficient and practical if Shor’s discrete logarithm algorithm is efficiently realized on a quantum machine.
On universal types
 PROC. ISIT 2004
, 2004
"... We define the universal type class of a sequence x n, in analogy to the notion used in the classical method of types. Two sequences of the same length are said to be of the same universal (LZ) type if and only if they yield the same set of phrases in the incremental parsing of Ziv and Lempel (1978 ..."
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Cited by 22 (6 self)
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We define the universal type class of a sequence x n, in analogy to the notion used in the classical method of types. Two sequences of the same length are said to be of the same universal (LZ) type if and only if they yield the same set of phrases in the incremental parsing of Ziv and Lempel (1978). We show that the empirical probability distributions of any finite order of two sequences of the same universal type converge, in the variational sense, as the sequence length increases. Consequently, the normalized logarithms of the probabilities assigned by any kth order probability assignment to two sequences of the same universal type, as well as the kth order empirical entropies of the sequences, converge for all k. We study the size of a universal type class, and show that its asymptotic behavior parallels that of the conventional counterpart, with the LZ78 code length playing the role of the empirical entropy. We also estimate the number of universal types for sequences of length n, and show that it is of the form exp((1+o(1))γ n/log n) for a well characterized constant γ. We describe algorithms for enumerating the sequences in a universal type class, and for drawing a sequence from the class with uniform probability. As an application, we consider the problem of universal simulation of individual sequences. A sequence drawn with uniform probability from the universal type class of x n is an optimal simulation of x n in a well defined mathematical sense.
Efficient Universal Lossless Data Compression Algorithms Based on a Greedy Sequential Grammar Transform  Part One: Without Context Models
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2000
"... A grammar transform is a transformation that converts any data sequence to be compressed into a grammar from which the original data sequence can be fully reconstructed. In a grammarbased code, a data sequence is first converted into a grammar by a grammar transform and then losslessly encoded. In ..."
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Cited by 21 (4 self)
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A grammar transform is a transformation that converts any data sequence to be compressed into a grammar from which the original data sequence can be fully reconstructed. In a grammarbased code, a data sequence is first converted into a grammar by a grammar transform and then losslessly encoded. In this paper, a greedy grammar transform is first presented; this grammar transform constructs sequentially a sequence of irreducible grammars from which the original data sequence can be recovered incrementally. Based on this grammar transform, three universal lossless data compression algorithms, a sequential algorithm, an improved sequential algorithm, and a hierarchical algorithm, are then developed. These algorithms combine the power of arithmetic coding with that of string matching. It is shown that these algorithms are all universal in the sense that they can achieve asymptotically the entropy rate of any stationary, ergodic source. Moreover, it is proved that their worst case redundancies among all individual sequences of length are upperbounded by �� � �� � �� � , where is a constant. Simulation results show that the proposed algorithms outperform the Unix Compress and Gzip algorithms, which are based on LZ78 and LZ77, respectively.