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Spacetime codes for high data rate wireless communication: Performance criterion and code construction
 IEEE TRANS. INFORM. THEORY
, 1998
"... We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit ant ..."
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Cited by 1782 (28 self)
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We consider the design of channel codes for improving the data rate and/or the reliability of communications over fading channels using multiple transmit antennas. Data is encoded by a channel code and the encoded data is split into n streams that are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. We derive performance criteria for designing such codes under the assumption that the fading is slow and frequency nonselective. Performance is shown to be determined by matrices constructed from pairs of distinct code sequences. The minimum rank among these matrices quantifies the diversity gain, while the minimum determinant of these matrices quantifies the coding gain. The results are then extended to fast fading channels. The design criteria are used to design trellis codes for high data rate wireless communication. The encoding/decoding complexity of these codes is comparable to trellis codes employed in practice over Gaussian channels. The codes constructed here provide the best tradeoff between data rate, diversity advantage, and trellis complexity. Simulation results are provided for 4 and 8 PSK signal sets with data rates of 2 and 3 bits/symbol, demonstrating excellent performance that is within 2–3 dB of the outage capacity for these channels using only 64 state encoders.
Robust face recognition via sparse representation
 IEEE TRANS. PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2008
"... We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sparse signa ..."
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Cited by 936 (40 self)
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We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models, and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed by ℓ 1minimization, we propose a general classification algorithm for (imagebased) object recognition. This new framework provides new insights into two crucial issues in face recognition: feature extraction and robustness to occlusion. For feature extraction, we show that if sparsity in the recognition problem is properly harnessed, the choice of features is no longer critical. What is critical, however, is whether the number of features is sufficiently large and whether the sparse representation is correctly computed. Unconventional features such as downsampled images and random projections perform just as well as conventional features such as Eigenfaces and Laplacianfaces, as long as the dimension of the feature space surpasses certain threshold, predicted by the theory of sparse representation. This framework can handle errors due to occlusion and corruption uniformly, by exploiting the fact that these errors are often sparse w.r.t. to the standard (pixel) basis. The theory of sparse representation helps predict how much occlusion the recognition algorithm can handle and how to choose the training images to maximize robustness to occlusion. We conduct extensive experiments on publicly available databases to verify the efficacy of the proposed algorithm, and corroborate the above claims.
Proof verification and hardness of approximation problems
 IN PROC. 33RD ANN. IEEE SYMP. ON FOUND. OF COMP. SCI
, 1992
"... We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probabilit ..."
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Cited by 797 (39 self)
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We show that every language in NP has a probablistic verifier that checks membership proofs for it using logarithmic number of random bits and by examining a constant number of bits in the proof. If a string is in the language, then there exists a proof such that the verifier accepts with probability 1 (i.e., for every choice of its random string). For strings not in the language, the verifier rejects every provided “proof " with probability at least 1/2. Our result builds upon and improves a recent result of Arora and Safra [6] whose verifiers examine a nonconstant number of bits in the proof (though this number is a very slowly growing function of the input length). As a consequence we prove that no MAX SNPhard problem has a polynomial time approximation scheme, unless NP=P. The class MAX SNP was defined by Papadimitriou and Yannakakis [82] and hard problems for this class include vertex cover, maximum satisfiability, maximum cut, metric TSP, Steiner trees and shortest superstring. We also improve upon the clique hardness results of Feige, Goldwasser, Lovász, Safra and Szegedy [42], and Arora and Safra [6] and shows that there exists a positive ɛ such that approximating the maximum clique size in an Nvertex graph to within a factor of N ɛ is NPhard.
Good ErrorCorrecting Codes based on Very Sparse Matrices
, 1999
"... We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The ..."
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Cited by 750 (23 self)
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We study two families of errorcorrecting codes defined in terms of very sparse matrices. "MN" (MacKayNeal) codes are recently invented, and "Gallager codes" were first investigated in 1962, but appear to have been largely forgotten, in spite of their excellent properties. The decoding of both codes can be tackled with a practical sumproduct algorithm. We prove that these codes are "very good," in that sequences of codes exist which, when optimally decoded, achieve information rates up to the Shannon limit. This result holds not only for the binarysymmetric channel but also for any channel with symmetric stationary ergodic noise. We give experimental results for binarysymmetric channels and Gaussian channels demonstrating that practical performance substantially better than that of standard convolutional and concatenated codes can be achieved; indeed, the performance of Gallager codes is almost as close to the Shannon limit as that of turbo codes.
LT Codes
, 2002
"... We introduce LT codes, the first rateless erasure codes that are very efficient as the data length grows. ..."
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Cited by 568 (2 self)
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We introduce LT codes, the first rateless erasure codes that are very efficient as the data length grows.
A Pairwise Key PreDistribution Scheme for Wireless Sensor Networks
, 2003
"... this paper, we provide a framework in which to study the security of key predistribution schemes, propose a new key predistribution scheme which substantially improves the resilience of the network compared to previous schemes, and give an indepth analysis of our scheme in terms of network resili ..."
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Cited by 552 (18 self)
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this paper, we provide a framework in which to study the security of key predistribution schemes, propose a new key predistribution scheme which substantially improves the resilience of the network compared to previous schemes, and give an indepth analysis of our scheme in terms of network resilience and associated overhead. Our scheme exhibits a nice threshold property: when the number of compromised nodes is less than the threshold, the probability that communications between any additional nodes are compromised is close to zero. This desirable property lowers the initial payoff of smallerscale network breaches to an adversary, and makes it necessary for the adversary to attack a large fraction of the network before it can achieve any significant gain
Distributed Source Coding Using Syndromes (DISCUS): Design and Construction
 IEEE TRANS. INFORM. THEORY
, 1999
"... We address the problem of distributed source coding, i.e. compression of correlated sources that are not colocated and/or cannot communicate with each other to minimize their joint description cost. In this work we tackle the related problem of compressing a source that is correlated with anothe ..."
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Cited by 407 (9 self)
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We address the problem of distributed source coding, i.e. compression of correlated sources that are not colocated and/or cannot communicate with each other to minimize their joint description cost. In this work we tackle the related problem of compressing a source that is correlated with another source which is however available only at the decoder. In contrast to prior informationtheoretic approaches, we introduce a new constructive and practical framework for tackling the problem based on the judicious incorporation of channel coding principles into this source coding problem. We dub our approach as DIstributed Source Coding Using Syndromes (DISCUS). We focus in this paper on trellisstructured consructions of the framework to illustrate its utility. Simulation results confirm the power of DISCUS, opening up a new and exciting constructive playingground for the distributed source coding problem. For the distributed coding of correlated i.i.d. Gaussian sources that are ...
Efficient erasure correcting codes
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2001
"... We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discretetime random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both si ..."
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Cited by 360 (26 self)
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We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discretetime random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability. By carefully designing these graphs we can construct for any given rate and any given real number a family of linear codes of rate which can be encoded in time proportional to ��@I A times their block length. Furthermore, a codeword can be recovered with high probability from a portion of its entries of length @IC A or more. The recovery algorithm also runs in time proportional to ��@I A. Our algorithms have been implemented and work well in practice; various implementation issues are discussed.
A Fuzzy Commitment Scheme
 ACM CCS'99
, 1999
"... We combine wellknown techniques from the areas of errorcorrecting codes and cryptography to achieve a new type of cryptographic primitive that we refer to as a fuzzy commitment scheme. Like a conventional cryptographic commitment scheme, our fuzzy commitment scheme is both concealing and binding: i ..."
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Cited by 344 (1 self)
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We combine wellknown techniques from the areas of errorcorrecting codes and cryptography to achieve a new type of cryptographic primitive that we refer to as a fuzzy commitment scheme. Like a conventional cryptographic commitment scheme, our fuzzy commitment scheme is both concealing and binding: it is infeasible for an attacker to learn the committed value, and also for the committer to decommit a value in more than one way. In a conventional scheme, a commitment must be opened using a unique witness, which acts, essentially, as a decryption key. By contrast, our scheme is fuzzy in the sense that it accepts a witness that is close to the original encrypting witness in a suitable metric, but not necessarily identical. This characteristic of our fuzzy commitment scheme makes it useful for applications such as biometric authentication systems, in which data is subject to random noise. Because the scheme is tolerant of error, it is capable of protecting biometric data just as conventional cryptographic techniques, like hash functions, are used to protect alphanumeric passwords. This addresses a major outstanding problem in the theory of biometric authentication. We prove the security characteristics of our fuzzy commitment scheme relative to the properties of an underlying cryptographic hash function.