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Fingerprinting: Bounding SoftError Detection Latency and Bandwidth
 In Proc. of the Symposium on Architectural Support for Programming Languages and Operating Systems (ASPLOS
, 2004
"... Recent studies have suggested that the softerror rate in microprocessor logic will become a reliability concern by 2010. This paper proposes an e#cient error detection technique, called fingerprinting, that detects di#erences in execution across a dual modular redundant (DMR) processor pair. Finger ..."
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Cited by 53 (7 self)
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Recent studies have suggested that the softerror rate in microprocessor logic will become a reliability concern by 2010. This paper proposes an e#cient error detection technique, called fingerprinting, that detects di#erences in execution across a dual modular redundant (DMR) processor pair. Fingerprinting summarizes a processor's execution history in a hashbased signature; di#erences between two mirrored processors are exposed by comparing their fingerprints. Fingerprinting tightly bounds detection latency and greatly reduces the interprocessor communication bandwidth required for checking. This paper presents a study that evaluates fingerprinting against a range of current approaches to error detection. The result of this study shows that fingerprinting is the only error detection mechanism that simultaneously allows higherror coverage, low error detection bandwidth, and high I/O performance.
New Upper Bounds on Error Exponents
"... We derive new upper bounds on the error exponents for the maximum likelihood decoding and error detecting in the binary symmetric channels. This is an improvement on the straightline bound by ShannonGallagerBerlekamp (1967) and the McElieceOmura (1977) minimum distance bound. For the probability ..."
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Cited by 28 (6 self)
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We derive new upper bounds on the error exponents for the maximum likelihood decoding and error detecting in the binary symmetric channels. This is an improvement on the straightline bound by ShannonGallagerBerlekamp (1967) and the McElieceOmura (1977) minimum distance bound. For the probability of undetected error the new bounds are better than the recent bound by AbdelGhaffar (1997) and the minimum distance and straightline bounds by Levenshtein (1978, 1989). We further extend the range of rates where the undetected error exponent is known to be exact. Keywords: Error exponents, Undetected error, Maximum likelihood decoding, Distance distribution, Krawtchouk polynomials. Submitted to IEEE Transactions on Information Theory 1 Introduction A classical problem of the information theory is to estimate probabilities of undetected and decoding errors when a block code is used for information transmission over a binary symmetric channel (BSC). We will study here exponential bounds ...
Binomial Moments of the Distance Distribution and the Probability of Undetected Error
"... . In [1] K. A. S. AbdelGhaffar derives a lower bound on the probability of undetected error for unrestricted codes. The proof relies implicitly on the binomial moments of the distance distribution of the code. We use the fact that these moments count the size of subcodes of the code to give a very ..."
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Cited by 7 (4 self)
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. In [1] K. A. S. AbdelGhaffar derives a lower bound on the probability of undetected error for unrestricted codes. The proof relies implicitly on the binomial moments of the distance distribution of the code. We use the fact that these moments count the size of subcodes of the code to give a very simple proof of the bound in [1] by showing that it is essentially equivalent to the Singleton bound. This proof reveals connections of the probability of undetected error to the rank generating function of the code and to related polynomials (Whitney function, Tutte polynomial, and higher weight enumerators). We also discuss some improvements of this bound. Finally, we analyze asymptotics. We show that an upper bound on the undetected error exponent that corresponds to the bound of [1] improves known bounds on this function. Keywords: Distance distribution, binomial moments, rank generating function, undetected error 1. Introduction Let C be a code of size M over a qary alphabet F q . Su...
Internet Protocol Small Computer System . . .
, 2002
"... In this memo, we attempt to give some estimates for the probability of undetected errors to facilitate the selection of an error detection code for the Internet Protocol Small Computer System Interface (iSCSI). We will also attempt to compare Cyclic Redundancy Checks (CRCs) with other checksum forms ..."
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Cited by 6 (0 self)
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In this memo, we attempt to give some estimates for the probability of undetected errors to facilitate the selection of an error detection code for the Internet Protocol Small Computer System Interface (iSCSI). We will also attempt to compare Cyclic Redundancy Checks (CRCs) with other checksum forms (e.g., Fletcher, Adler, weighted checksums), as permitted by available data. 1.
On the Basic Averaging Arguments For Linear Codes
"... Linear codes over F q are considered for use in detecting and in correcting the additive errors in some subset E of F q .(Themost familiar example of such an error set E is the set of all ntuples of Hamming weight at most t.) In this setup, the basic averaging arguments for linear codes are revie ..."
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Cited by 2 (0 self)
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Linear codes over F q are considered for use in detecting and in correcting the additive errors in some subset E of F q .(Themost familiar example of such an error set E is the set of all ntuples of Hamming weight at most t.) In this setup, the basic averaging arguments for linear codes are reviewed with emphasis on the relation between the combinatorial and the informationtheoretic viewpoint. The main theorems are (a correspondingly general version of) the VarshamovGilbert bound and a `randomcoding' bound on the probability of an ambiguous syndrome. These bounds are shown to result from applying the same elementary averaging argument to two different packing problems, viz., the combinatorial `sphere' packing problem and theprobabilistic `Shannon packing'. Some applications of the general bounds are indicated, e.g., hash functions and Euclideanspace codes, and the connection to Justesentype constructions of asymptotically good codes is outlined.
Undetected Error Probability for Data Services in a Terrestrial DAB Single Frequency Network
"... DAB (Digital Audio Broadcasting) is the European successor of FM radio. Besides audio services, other services such as traffic information can be provided. An important parameter for data services is the probability of nonrecognized or undetected errors in the system. To derive this probability, we ..."
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DAB (Digital Audio Broadcasting) is the European successor of FM radio. Besides audio services, other services such as traffic information can be provided. An important parameter for data services is the probability of nonrecognized or undetected errors in the system. To derive this probability, we propose a bound for the undetected error probability in CRC codes. In addition, results from measurements of a Single Frequency Network (SFN) in Amsterdam were used, where the University of Twente conducted a DAB field trial. The proposed error bound is compared with other error bounds from literature and the results are validated by simulations. Although the proposed bound is less tight than existing bounds, it requires no additional information about the CRC code such as the weight distribution. Moreover, the DAB standard has been extended last year by an Enhanced Packet Mode (EPM) which provides extra protection for data services. An undetected error probability for this mode is also derived. In a realistic user scenario of 10 million users, a 8 kbit/s EPM sub channel can be considered as a system without any undetected errors (Pud = 6 · 10 −40). On the other hand, in a normal data sub channel, only 110 packets with undetected errors are received on average each year in the whole system (Pud = 5 · 10 −13). 1
On the Probability of Undetected Error for OverExtended ReedSolomon Codes
"... AbstractWe derive upper and lower bounds on the weight of p, as follows: distribution of OverExtended ReedSolomon (OERS) codes. Using these bounds, we obtain tight upper and lower bounds n on the probability of undetected error for OERS codes on qary Pud(P) Ai P (1 _ p)ni (1) symmetric channels ..."
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AbstractWe derive upper and lower bounds on the weight of p, as follows: distribution of OverExtended ReedSolomon (OERS) codes. Using these bounds, we obtain tight upper and lower bounds n on the probability of undetected error for OERS codes on qary Pud(P) Ai P (1 _ p)ni (1) symmetric channels. q1 where Ai is the number ofcodewords withHamming weight i. I. INTRODUCTION Equation (1) relates the probability of undetected error directly to the weight distribution of the code. the received symbols appear to be uniIn some applications, error correcting codes have been used Whenp = (q1) lq, as pure error detection codes. In particular, ReedSolomon formly distributed no matter which codeword was transmitted.
Binomial Moments of the Distance Distribution: Bounds and Applications
 IEEE Trans. Inform. Theory
, 1999
"... We study a combinatorial invariant of codes vwhich counts the number of ordered pairs of codewords in all subcodes of restricted support in a code. This invariant can be expressed as a linear form of the components of the distance distribution of the code with binomial numbers as coefficients. For t ..."
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We study a combinatorial invariant of codes vwhich counts the number of ordered pairs of codewords in all subcodes of restricted support in a code. This invariant can be expressed as a linear form of the components of the distance distribution of the code with binomial numbers as coefficients. For this reason we call it a binomial moment of the distance distribution. Binomial moments appear in the proof of the MacWilliams identities and in many other problems of combinatorial coding theory. We introduce a linear programming problem for bounding these linear forms from below. It turns out that some known codes (1errorcorrecting perfect codes, Golay codes, NordstromRobinson code, etc) yield optimal solutions of this problem, i.e., have minimal possible binomial moments of the distance distribution. We derive several general feasible solutions of this problem, which give lower bounds on the binomial moments of codes with given parameters, and derive the corresponding asymptotic bounds. Applications of these bounds include new lower bounds on the probability of undetected error for binary codes used over the binary symmetric channel with crossover probability p and optimality of many codes for error detection. Asymptotic analysis of the bounds enables us to extend the range of code rates in which the upper bound on the undetected error exponent is tight. Keywords: Distance distribution, binomial moments, linear programming, extremal codes, undetected error, Rodemich's theorem.
iSCSI CRC/Checksum Considerations
, 2000
"... Cyclic redundancy check (CRC) codes [Peterson] are shortened cyclic codes used for error detection. A number of CRC codes have been adopted in standards: ATM, IEC, IEEE, CCITT, IBMSDLC, and more [Baicheva]. The most important expectation from this kind of code is a very low probability for undetect ..."
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Cyclic redundancy check (CRC) codes [Peterson] are shortened cyclic codes used for error detection. A number of CRC codes have been adopted in standards: ATM, IEC, IEEE, CCITT, IBMSDLC, and more [Baicheva]. The most important expectation from this kind of code is a very low probability for undetected errors. The probability of undetected errors in such codes has been, and still is, subject to extensive studies that have included both analytical models and simulations. Those codes have been used extensively in communications and magnetic recording as they demonstrate good "burst error" detection capabilities, but are also good at detecting several independent bit errors. Hardware implementations are very simple and well known; their simplicity has made them popular with hardware developers for many years. However, algorithms and software for effective implementations of CRC are now also widely available [Williams]. The probability of undetected errors depends on the polynomial selected...
WSEAS TRANSACTIONS on COMMUNICATIONS WACKER H. D., BOERCSOEK J. Binomial and Monotonic Behavior of the Probability of Undetected Error and the 2rBound
"... Abstract: Proper linear codes play an important role in error detection. They are characterized by an increasing probability of undetected error pue(ε,C) and are considered “good for error detection”. A lot of CRCs commonly used to protect data transmission via a variety of field busses are known f ..."
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Abstract: Proper linear codes play an important role in error detection. They are characterized by an increasing probability of undetected error pue(ε,C) and are considered “good for error detection”. A lot of CRCs commonly used to protect data transmission via a variety of field busses are known for being proper. In this paper the weight distribution of proper linear codes on a binary symmetric channel without memory is investigated. A proof is given that its components are upper bounded by the binomial coefficients in a certain sense. Secondly an upper bound of the tail of the binomial is given, and the results are then used to derive estimates of pue(ε,C). If a code is not proper, it would be desirable to have at least subintervals, where pue(ε,C) increases, or where it satisfies the 2rbound. It is for this reason that next the range of monotonicity and of the 2rbound is determined. Finally, applications on safety integrity levels are studied.