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573
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 738 (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.
Efficient dispersal of information for security, load balancing, and fault tolerance
 Journal of the ACM
, 1989
"... Abstract. An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = ( F ( into n pieces F,, 1 5 i 5 n, each of length ( F, 1 = L/m, so that every m pieces suffice for reconstructing F. Dispersal and reconstruction are computationally efficient. The sum of the lengths ..."
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Cited by 554 (1 self)
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Abstract. An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = ( F ( into n pieces F,, 1 5 i 5 n, each of length ( F, 1 = L/m, so that every m pieces suffice for reconstructing F. Dispersal and reconstruction are computationally efficient. The sum of the lengths ( F, 1 is (n/m). L. Since n/m can be chosen to be close to I, the IDA is space eflicient. IDA has numerous applications to secure and reliable storage of information in computer networks and even on single disks, to faulttolerant and efficient transmission of information in networks, and to communications between processors in parallel computers. For the latter problem provably timeefftcient and highly faulttolerant routing on the ncube is achieved, using just constant size buffers. Categories and Subject Descriptors: E.4 [Coding and Information Theory]: nonsecret encoding schemes
Priority Encoding Transmission
 IEEE Transactions on Information Theory
, 1994
"... We introduce a new method, called Priority Encoding Transmission, for sending messages over lossy packetbased networks. When a message is to be transmitted, the user specifies a priority value for each part of the message. Based on the priorities, the system encodes the message into packets for tra ..."
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Cited by 310 (11 self)
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We introduce a new method, called Priority Encoding Transmission, for sending messages over lossy packetbased networks. When a message is to be transmitted, the user specifies a priority value for each part of the message. Based on the priorities, the system encodes the message into packets for transmission and sends them to (possibly multiple) receivers. The priority value of each part of the message determines the fraction of encoding packets sufficient to recover that part. Thus, even if some of the encoding packets are lost enroute, each receiver is still able to recover the parts of the message for which a sufficient fraction of the encoding packets are received. International Computer Science Institute, Berkeley, California. Research supported in part by National Science Foundation operating grant NCR941610 y Computer Science Department, Swiss Federal Institute of Technology, Zurich, Switzerland. Research done while a postdoc at the International Computer Science Institute...
A fuzzy vault scheme
 IN INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT
, 2002
"... We describe a simple and novel cryptographic construction that we refer to as a fuzzy vault. A player Alice may place a secret value κ in a fuzzy vault and “lock” it using a set A of elements from some public universe U. If Bob tries to “unlock” the vault using a set B of similar length, he obtain ..."
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Cited by 295 (1 self)
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We describe a simple and novel cryptographic construction that we refer to as a fuzzy vault. A player Alice may place a secret value κ in a fuzzy vault and “lock” it using a set A of elements from some public universe U. If Bob tries to “unlock” the vault using a set B of similar length, he obtains κ only if B is close to A, i.e., only if A and B overlap substantially. In constrast to previous constructions of this flavor, ours possesses the useful feature of order invariance, meaning that the ordering of A and B is immaterial to the functioning of the vault. As we show, our scheme enjoys provable security against a computationally unbounded attacker.
Decoding Reed Solomon Codes beyond the ErrorCorrection Bound
, 1997
"... We present a randomized algorithm which takes as input n distinct points f(xi; yi)g n i=1 from F \Theta F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in a ..."
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Cited by 273 (18 self)
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We present a randomized algorithm which takes as input n distinct points f(xi; yi)g n i=1 from F \Theta F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in at least t places (i.e., yi = f (xi) for at least t values of i), provided t = \Omega (
Applications of ErrorControl Coding
, 1998
"... An overview of the many practical applications of channel coding theory in the past 50 years is presented. The following application areas are included: deep space communication, satellite communication, data transmission, data storage, mobile communication, file transfer, and digital audio/video t ..."
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Cited by 271 (0 self)
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An overview of the many practical applications of channel coding theory in the past 50 years is presented. The following application areas are included: deep space communication, satellite communication, data transmission, data storage, mobile communication, file transfer, and digital audio/video transmission. Examples, both historical and current, are given that typify the different approaches used in each application area. Although no attempt is made to be comprehensive in our coverage, the examples chosen clearly illustrate the richness, variety, and importance of errorcontrol coding methods in modern digital applications.
Coding for errors and erasures in random network coding
, 2007
"... The problem of errorcontrol in random network coding is considered. A “noncoherent” or “channel oblivious ” model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that random network coding is vectorspa ..."
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Cited by 251 (14 self)
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The problem of errorcontrol in random network coding is considered. A “noncoherent” or “channel oblivious ” model is assumed where neither transmitter nor receiver is assumed to have knowledge of the channel transfer characteristic. Motivated by the property that random network coding is vectorspace preserving, information transmission is modelled as the injection into the network of a basis for a vector space V and the collection by the receiver of a basis for a vector space U. We introduce a metric on the space of all subspaces of a fixed vector space, and show that a minimum distance decoder for this metric achieves correct decoding if the dimension of the space V ∩ U is large enough. If the dimension of each codeword is restricted to a fixed integer, the code forms a subset of a finitefield Grassmannian. Spherepacking and spherecovering bounds as well as generalization of the Singleton bound are provided for such codes. Finally, a ReedSolomonlike code construction, related to Gabidulin’s construction of maximum rankdistance codes, is provided.
A tutorial on ReedSolomon coding for faulttolerance in RAIDlike systems
 Software – Practice & Experience
, 1997
"... It is wellknown that ReedSolomon codes may be used to provide error correction for multiple failures in RAIDlike systems. The coding technique itself, however, is not as wellknown. To the coding theorist, this technique is a straightforward extension to a basic coding paradigm and needs no speci ..."
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Cited by 232 (37 self)
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It is wellknown that ReedSolomon codes may be used to provide error correction for multiple failures in RAIDlike systems. The coding technique itself, however, is not as wellknown. To the coding theorist, this technique is a straightforward extension to a basic coding paradigm and needs no special mention. However, to the systems programmer with no training in coding theory, the technique may be a mystery. Currently, there are no references that describe how to perform this coding that do not assume that the reader is already wellversed in algebra and coding theory. This paper is intended for the systems programmer. It presents a complete specification of the coding algorithm plus details on how it may be implemented. This specification assumes no prior knowledge of algebra or coding theory. The goal of this paper is for a systems programmer to be able to implement ReedSolomon coding for reliability in RAIDlike systems without needing to consult any external references. Problem Specification Let there be storage devices, ¡£¢¥¤¦¡¨§©¤�������¤¦¡¨�, each of which holds � bytes. These are called the “Data Devices. ” � Let there be � � more storage devices
An algebraic approach to IP traceback
 ACM Transactions on Information and System Security
, 2002
"... We present a new solution to the problem of determining the path a packet traversed over the Internet (called the traceback problem) during a denial of service attack. This paper reframes the traceback problem as a polynomial reconstruction problem and uses algebraic techniques from coding theory an ..."
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Cited by 223 (0 self)
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We present a new solution to the problem of determining the path a packet traversed over the Internet (called the traceback problem) during a denial of service attack. This paper reframes the traceback problem as a polynomial reconstruction problem and uses algebraic techniques from coding theory and learning theory to provide robust methods of transmission and reconstruction. 1
A Survey of PacketLoss Recovery Techniques for Streaming Audio
 IEEE Network
, 1998
"... We survey a number of packetloss recovery techniques for streaming audio applications operating using IP multicast. We begin with a discussion of the loss and delay characteristics of an IP multicast channel and from this show the need for packet loss recovery. Recovery techniques may be divided in ..."
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Cited by 195 (6 self)
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We survey a number of packetloss recovery techniques for streaming audio applications operating using IP multicast. We begin with a discussion of the loss and delay characteristics of an IP multicast channel and from this show the need for packet loss recovery. Recovery techniques may be divided into two classes: senderand receiverbased. We compare and contrast several senderbased recovery schemes: forward error correction (both media specific and media independent) interleaving and retransmission. In addition a number of error concealment schemes are discussed. We conclude with a series of recommendations for repair schemes to be used, based on application requirements and network conditions. 1 Introduction The development of IP multicast and the Internet multicast backbone has led to be emergence of a new class of scalable audio/video conferencing applications. These are based on the lightweight sessions model [11, 17] and provide efficient multiway communication which scales fr...