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146
Effective Erasure Codes for Reliable Computer Communication Protocols
, 1997
"... Reliable communication protocols require that all the intended recipients of a message receive the message intact. Automatic Repeat reQuest (ARQ) techniques are used in unicast protocols, but they do not scale well to multicast protocols with large groups of receivers, since segment losses tend to b ..."
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Cited by 420 (14 self)
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Reliable communication protocols require that all the intended recipients of a message receive the message intact. Automatic Repeat reQuest (ARQ) techniques are used in unicast protocols, but they do not scale well to multicast protocols with large groups of receivers, since segment losses tend to become uncorrelated thus greatly reducing the effectiveness of retransmissions. In such cases, Forward Error Correction (FEC) techniques can be used, consisting in the transmission of redundant packets (based on error correcting codes) to allow the receivers to recover from independent packet losses. Despite the widespread use of error correcting codes in many fields of information processing, and a general consensus on the usefulness of FEC techniques within some of the Internet protocols, very few actual implementations exist of the latter. This probably derives from the different types of applications, and from concerns related to the complexity of implementing such codes in software. To f...
On the Capacity of Secure Network Coding
"... We consider the problem of using a multicast network code to transmit information securely in the presence of a "wiretap " adversary who can eavesdrop on a bounded number of network edges. Cai & Yeung (ISIT, 2002) gave a method to alter any given linear network code into a ne ..."
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Cited by 32 (2 self)
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We consider the problem of using a multicast network code to transmit information securely in the presence of a &quot;wiretap &quot; adversary who can eavesdrop on a bounded number of network edges. Cai & Yeung (ISIT, 2002) gave a method to alter any given linear network code into a new code that is secure. However, their construction is in general inefficient, and requires a very large field size; in many cases this is much greater than the field size required by standard network code construction algorithms to achieve the mincut capacity (without a security guarantee). In this paper we generalize and simplify the method of Cai & Yeung, and show that the problem of making a linear network code secure is equivalent to the problem of finding a linear code with certain generalized distance properties. We show that if we give up a small amount of overall capacity, then a random code achieves these properties using a much smaller field size in some cases a field of constant size suffices than the construction of Cai & Yeung. We add further support to this approach by showing that if we are not willing to give up any capacity, then a large field size may sometimes be required to achieve security.
Testing monotone highdimensional distributions
 In STOC
, 2005
"... A monotone distribution P over a (partially) ordered domain assigns higher probability to y than to x if y ≥ x in the order. We study several natural problems concerning testing properties of monotone distributions over the ndimensional Boolean cube, given access to random draws from the distributi ..."
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Cited by 22 (7 self)
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A monotone distribution P over a (partially) ordered domain assigns higher probability to y than to x if y ≥ x in the order. We study several natural problems concerning testing properties of monotone distributions over the ndimensional Boolean cube, given access to random draws from the distribution being tested. We give a poly(n)time algorithm for testing whether a monotone distribution is equivalent to or ɛfar (in the L1 norm) from the uniform distribution. A key ingredient of the algorithm is a generalization of a known isoperimetric inequality for the Boolean cube. We also introduce a method for proving lower bounds on various problems of testing monotone distributions over the ndimensional Boolean cube, based on a new decomposition technique for monotone distributions. We use this method to show that our uniformity testing algorithm is optimal up to polylog(n) factors, and also to give exponential lower bounds on the complexity of several other problems, including testing whether a monotone distribution is identical to or ɛfar from a fixed known monotone product distribution and approximating the entropy of an unknown monotone distribution. 1
Codes for Asymmetric LimitedMagnitude Errors with Application to MultiLevel Flash Memories
"... Several physical effects that limit the reliability and performance of Multilevel Flash Memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limitedmagnitude errors over qary channels. We propose code constructions and bounds ..."
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Cited by 15 (7 self)
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Several physical effects that limit the reliability and performance of Multilevel Flash Memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limitedmagnitude errors over qary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by ℓ. The constructions utilize known codes for symmetric errors, over small alphabets, to protect largealphabet symbols from asymmetric limitedmagnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown to exceed the sizes of known codes (for related error models), and asymptotic rateoptimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation.
Representations of finite groups on RiemannRoch spaces,” preprint
, 2003
"... Abstract. If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X stabilized by G, then under the assumption that D is nonspecial, we compute a simplified formula for the trace of the natural representation of G on RiemannRoch space L(D). 1. ..."
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Cited by 10 (8 self)
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Abstract. If G is a finite subgroup of the automorphism group of a projective curve X and D is a divisor on X stabilized by G, then under the assumption that D is nonspecial, we compute a simplified formula for the trace of the natural representation of G on RiemannRoch space L(D). 1.
Nonbinary quantum ReedMuller codes
 In Proc. 2005 IEEE International Symposium on Information Theory
, 2005
"... ..."
Network protection codes against link failures using network coding
 In Proc. IEEE GlobelComm 08
"... Abstract—Protecting against link failures in communication networks is essential to increase robustness, accessibility, and reliability of data transmission. Recently, network coding has been proposed as a solution to provide agile and cost efficient network protection against link failures, which d ..."
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Cited by 6 (6 self)
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Abstract—Protecting against link failures in communication networks is essential to increase robustness, accessibility, and reliability of data transmission. Recently, network coding has been proposed as a solution to provide agile and cost efficient network protection against link failures, which does not require data rerouting, or packet retransmission. To achieve this, separate paths have to be provisioned to carry encoded packets, hence requiring either the addition of extra links, or reserving some of the resources for this purpose. In this paper, we propose network protection codes against a single link failure using network coding, where a separate path using reserved links is not needed. In this case portions of the link capacities are used to carry the encoded packets. The scheme is extended to protect against multiple link failures and can be implemented at an overlay layer. Although this leads to reducing the network capacity, the network capacity reduction is asymptotically small in most cases of practical interest. We demonstrate that such network protection codes are equivalent to error correcting codes for erasure channels. Finally, we study the encoding and decoding operations of such codes over the binary field. I.
On the Mac Williams identity for convolutional codes
, 2006
"... Abstract: The adjacency matrix associated with a convolutional code collects in a detailed manner information about the weight distribution of the code. A MacWilliams Identity Conjecture, stating that the adjacency matrix of a code fully determines the adjacency matrix of the dual code, will be form ..."
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Cited by 6 (3 self)
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Abstract: The adjacency matrix associated with a convolutional code collects in a detailed manner information about the weight distribution of the code. A MacWilliams Identity Conjecture, stating that the adjacency matrix of a code fully determines the adjacency matrix of the dual code, will be formulated, and an explicit formula for the transformation will be stated. The formula involves the MacWilliams matrix known from complete weight enumerators of block codes. The conjecture will be proven for the class of convolutional codes where either the code itself or its dual does not have Forney indices bigger than one. For the general case the conjecture is backed up by many examples, and a weaker version will be established.
Asymptotically Good Ideal Linear Secret Sharing with Strong Multiplication over Any Finite Field
 Proceeding of 29th Annual IACR CRYPTO
, 2009
"... Abstract. This work deals with “MPCfriendly ” linear secret sharing schemes (LSSS), a mathematical primitive upon which secure multiparty computation (MPC) can be based and which was introduced by Cramer, Damgaard and Maurer (EUROCRYPT 2000). Chen and Cramer proposed a special class of such schem ..."
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Cited by 5 (4 self)
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Abstract. This work deals with “MPCfriendly ” linear secret sharing schemes (LSSS), a mathematical primitive upon which secure multiparty computation (MPC) can be based and which was introduced by Cramer, Damgaard and Maurer (EUROCRYPT 2000). Chen and Cramer proposed a special class of such schemes that is constructed from algebraic geometry and that enables efficient secure multiparty computation over fixed finite fields (CRYPTO 2006). We extend this in four ways. First, we propose an abstract codingtheoretic framework in which this class of schemes and its (asymptotic) properties can be cast and analyzed. Second, we show that for every finite field Fq, there exists an infinite family of LSSS over Fq that is asymptotically good in the following sense: the schemes are “ideal, ” i.e., each share consists of a single Fqelement, and the schemes have tstrong multiplication on n players, where the corruption tolerance 3t n−1 tends to a constant ν(q) with 0 < ν(q) < 1 when n