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A Game of Prediction with Expert Advice
 Journal of Computer and System Sciences
, 1997
"... We consider the following problem. At each point of discrete time the learner must make a prediction; he is given the predictions made by a pool of experts. Each prediction and the outcome, which is disclosed after the learner has made his prediction, determine the incurred loss. It is known that, u ..."
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Cited by 106 (7 self)
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We consider the following problem. At each point of discrete time the learner must make a prediction; he is given the predictions made by a pool of experts. Each prediction and the outcome, which is disclosed after the learner has made his prediction, determine the incurred loss. It is known that, under weak regularity, the learner can ensure that his cumulative loss never exceeds cL+ a ln n, where c and a are some constants, n is the size of the pool, and L is the cumulative loss incurred by the best expert in the pool. We find the set of those pairs (c; a) for which this is true.
Dense quantum coding and a lower bound for 1way quantum automata
 Proceedings of the ThirtyFirst Annual ACM Symposium on the Theory of Computing
, 1999
"... We consider the possibility of encoding m classical bits into much fewer n quantum bits so that an arbitrary bit from the original m bits can be recovered with a good probability, and we show that nontrivial quantum encodings exist that have no classical counterparts. On the other hand, we show that ..."
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Cited by 31 (5 self)
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We consider the possibility of encoding m classical bits into much fewer n quantum bits so that an arbitrary bit from the original m bits can be recovered with a good probability, and we show that nontrivial quantum encodings exist that have no classical counterparts. On the other hand, we show that quantum encodings cannot be much more succint as compared to classical encodings, and we provide a lower bound on such quantum encodings. Finally, using this lower bound, we prove an exponential lower bound on the size of 1way quantum finite automata for a family of languages accepted by linear sized deterministic finite automata. 1
Further results on the covering radius of codes
 IEEE Trans. Information Theory
, 1986
"... AbstractA number of upper and lower bounds are obtained for K ( n, R), the minimal number of codewords in any binary code of length n and covering radius R. Several new constructions are used to derive the upper bounds, including an amalgamated direct sum construction for nonlinear codes. This cons ..."
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Cited by 29 (2 self)
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AbstractA number of upper and lower bounds are obtained for K ( n, R), the minimal number of codewords in any binary code of length n and covering radius R. Several new constructions are used to derive the upper bounds, including an amalgamated direct sum construction for nonlinear codes. This construction works best when applied to normal codes, and we give some new and stronger conditions which imply that a linear code is normal. An upper bound is given for the density of a covering code over any alphabet, and it is shown that K(n + 2,R + 1) 5 K(n, R) holds for sufficiently large n. T I.
Distributed Source Coding using Abelian Group Codes: Extracting Performance from Structure
"... In this work, we consider a distributed source coding problem with a joint distortion criterion depending on the sources and the reconstruction. This includes as a special case the problem of computing a function of the sources to within some distortion and also the classic SlepianWolf problem [12 ..."
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Cited by 9 (1 self)
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In this work, we consider a distributed source coding problem with a joint distortion criterion depending on the sources and the reconstruction. This includes as a special case the problem of computing a function of the sources to within some distortion and also the classic SlepianWolf problem [12], BergerTung problem [5], WynerZiv problem [4], YeungBerger problem [6] and the AhlswedeKornerWyner problem [3], [13]. While the prevalent trend in information theory has been to prove achievability results using Shannon’s random coding arguments, using structured random codes offer rate gains over unstructured random codes for many problems. Motivated by this, we present a new achievable ratedistortion region (an inner bound to the performance limit) for this problem for discrete memoryless sources based on “good” structured random nested codes built over abelian groups. We demonstrate rate gains for this problem over traditional coding schemes using random unstructured codes. For certain sources and distortion functions, the new rate region is strictly bigger than the BergerTung rate region, which has been the best known achievable rate region for this problem till now. Further, there is no known unstructured random coding scheme that achieves these rate gains. Achievable performance limits for singleuser source coding using abelian group codes are also obtained as parts of the proof of the main coding theorem. As a corollary, we also prove that nested linear codes achieve the Shannon ratedistortion bound in the singleuser setting. Note that while group codes retain some structure, they are more general than linear codes which can only be built over finite fields which are known to exist only for certain sizes.
Steganographic strategies for a square distortion function
 In: Security, Forensics, Steganography and Watermarking of Multimedia Contents X. In: Proc. SPIE
, 2008
"... Recent results on the information theory of steganography suggest, and under some conditions prove, that the detectability of payload is proportional to the square of the number of changes caused by the embedding. Assuming that result in general, this paper examines the implications for an embedder ..."
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Cited by 7 (7 self)
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Recent results on the information theory of steganography suggest, and under some conditions prove, that the detectability of payload is proportional to the square of the number of changes caused by the embedding. Assuming that result in general, this paper examines the implications for an embedder when a payload is to be spread amongst multiple cover objects. A number of variants are considered: embedding with and without adaptive source coding, in uniform and nonuniform covers, and embedding in both a fixed number of covers (socalled batch steganography) as well as establishing a covert channel in an infinite stream (sequential steganography, studied here for the first time). The results show that steganographic capacity is sublinear, and strictly asymptotically greater in the case of a fixed batch than an infinite stream. In the former it is possible to describe optimal embedding strategies; in the latter the situation is much more complex, with a continuum of strategies which approach the unachievable asymptotic optimum.
Optimally Pebbling Hypercubes and Powers
 Discrete Math
, 1998
"... We point out that the optimal pebbling number of the ncube is ( 4 3 ) n+O(log n) , and explain how to approximate the optimal pebbling number of the nth cartesian power of any graph in a similar way. ..."
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Cited by 5 (0 self)
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We point out that the optimal pebbling number of the ncube is ( 4 3 ) n+O(log n) , and explain how to approximate the optimal pebbling number of the nth cartesian power of any graph in a similar way.
Thin lattice coverings
"... Let ^ be a compact body of positive volume in W, starshaped with respect to an interior point, taken to be the origin. For subsets Q of R n, the functional sup lattices A represents the minimum density with which Q. can be covered by a lattice A of translates of < S. We obtain an upper bound on «9L ..."
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Cited by 1 (1 self)
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Let ^ be a compact body of positive volume in W, starshaped with respect to an interior point, taken to be the origin. For subsets Q of R n, the functional sup lattices A represents the minimum density with which Q. can be covered by a lattice A of translates of < S. We obtain an upper bound on «9L(#, Z n). If the attributes of # are supplemented with convexity, write 3fC instead. We also bound above the classical minimum la nicecovering density of Jtf. No symmetry conditions are imposed on # and Jf. 1.
1 TimeSpace Constrained Codes for PhaseChange Memories
, 1207
"... Abstract—Phasechange memory (PCM) is a promising nonvolatile solidstate memory technology. A PCM cell stores data by using its amorphous and crystalline states. The cell changes between these two states using high temperature. However, since the cells are sensitive to high temperature, it is impor ..."
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Abstract—Phasechange memory (PCM) is a promising nonvolatile solidstate memory technology. A PCM cell stores data by using its amorphous and crystalline states. The cell changes between these two states using high temperature. However, since the cells are sensitive to high temperature, it is important, when programming cells, to balance the heat both in time and space. In this paper, we study the timespace constraint for PCM, which was originally proposed by Jiang et al. A code is called an (α,β,p)constrained code if for any α consecutive rewrites and for any segment of β contiguous cells, the total rewrite cost of the β cells over those α rewrites is at most p. Here, the cells are binary and the rewrite cost is defined to be the Hamming distance between the current and next memory states. First, we show a general upper bound on the achievable rate of these codes which extends the results of Jiang et al. Then, we generalize their construction for (α � 1,β = 1,p = 1)constrained codes and show another construction for (α = 1,β � 1,p � 1)constrained codes. Finally, we show that these two constructions can be used to construct codes for all values of α, β, and p. I.