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Combined CRC and Bit Framing for Enhanced Error Detection
... Table 1 below presents a comparison of various widely-used checksum algorithms. The linear congruential checksum (LCC) [16] computes individual checksums for updated configuration items at a specified granularity and combines them with the original checksum (see Section IV.2 for more details). This method supports text addition, deletion, and is invariant to the order of configuration items. ...
The virtual private cloud service currently lacks a real-time end-to-end consistency validation mechanism, which prevents tenants from receiving immediate feedback on their requests. Existing solutions consume excessive communication and computational resources in such large-scale cloud environments, and suffer from poor timeliness. To address these issues, we propose a lightweight consistency validation mechanism that includes real-time incremental validation and periodic full-scale validation. The former leverages message layer aggregation to enable tenants to swiftly determine the success of their requests on hosts with minimal communication overhead. The latter utilizes lightweight validation checksums to compare the expected and actual states of hosts locally, while efficiently managing the checksums of various host entries using inverted indexing. This approach enables us to efficiently validate the complete local configurations within the limited memory of hosts. In summary, our proposed mechanism achieves closed-loop implementation for new requests and ensures their long-term effectiveness.
Cyclic Redundancy Check (CRC) is an essential component in various integrated circuits of the electronics industry. This paper is a CRC comprehensive guide that explores various approaches for CRC implementations in hardware, and demonstrates synthesis estimation results for understanding their impact. Finally, it assists the designer to customize and optimize his CRC implementation to meet different project requirements.
This chapter covers topics from the theory of classical error detection and error correction and introduces concepts useful for understanding quantum error correction. Coding theory is an application of information theory critical for reliable communication and fault tolerant information storage and processing; indeed, the Shannon channel coding theorem says that information on a noisy channel can be transmitted with an arbitrarily low probability of error. A code is designed based on a well-defined set of specifications and protects the information only for the type and number of errors prescribed in its design. Reliable communication and fault-tolerant computing are intimately related to each other; the concept of a communication channel, an abstraction for a physical system used to transmit information from one place to another and/or from one time to another, is at the core of communication, as well as information storage and processing. It should, however, be clear that the existence of error correcting codes does not guarantee that logic operations can be implemented using noisy gates and circuits. The strategies to build reliable computing systems using unreliable components are based on John von Neumann's studies of error detection and error correction techniques for information storage and processing. Linear, polynomial, and several other classes of codes are also discussed.
The Cyclic Redundancy Check (CRC) is an efficient method to ensure a low probability of undetected errors in data transmission using a checksum as a result of polynomial division. However, this probability depends extremely on the polynomial used. Although CRC is well established in communication, it is still a challenge to identify suitable polynomials. The determination of their characteristics becomes very complex in safety-critical applications, where many data have to be exchanged with minimal residual error probability. This complexity is handled by means of deterministic and stochastic automata in the presented solution.
For interval estimation of a proportion, coverage probabilities tend to be too large for "exact" confidence intervals based on inverting the binomial test and too small for the interval based on inverting the Wald large-sample normal test (i.e., sample proportion ± z-score × estimated standard error). Wilson's suggestion of inverting the related score test with null rather than estimated standard error yields coverage probabilities close to nominal confidence levels, even for very small sample sizes. The 95% score interval has similar behavior as the adjusted Wald interval obtained after adding two "successes" and two "failures" to the sample. In elementary courses, with the score and adjusted Wald methods it is unnecessary to provide students with awkward sample size guidelines.
The Cyclic Redundancy Check (CRC) is an efficient method to ensure a low probability of undetected errors in data transmission using a checksum as a result of polynomial division. However, this probability depends extremely on the polynomial used. Although CRC is well established in communication, it is still a challenge to identify suitable polynomials. The determination of their characteristics becomes very complex in safety-critical applications, where many data have to be exchanged with minimal residual error probability. This complexity is handled by means of deterministic and stochastic automata in the presented solution.
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 2-r-bound. It is for this reason that next the range of monotonicity and of the 2-r-bound is determined. Finally, applications on safety integrity levels are studied.
Standardized 32-bit cyclic redundancy codes provide fewer bits of guaranteed error detection than they could, achieving a Hamming Distance (HD) of only 4 for maximum-length Ethernet messages, whereas HD=6 is possible. Although research has revealed improved codes, exploring the entire design space has previously been computationally intractable, even for special-purpose hardware. Moreover, no CRC polynomial has yet been found that satisfies an emerging need to attain both HD=6 for 12K bit messages and HD=4 for message lengths beyond 64 Kbits. This paper presents results from the first exhaustive search of the 32-bit CRC design space. Results from previous research are validated and extended to include identifying all polynomials achieving a better HD than the IEEE 802.3 CRC-32 polynomial. A new class of polynomials is identified that provides HD=6 up to nearly 16K bit and HD=4 up to 114K bit message lengths, providing the best achievable design point that maximizes error detection for both legacy and new applications, including potentially iSCSI and application-implemented error checks.
The author presents a five-step methodology that provides insight into the order in which errors should be considered when designing an error detection scheme, which types of error detection mechanisms are most effective, and which layer should be responsible for detecting a given type of error.< >
The theory of cyclic redundancy codes (CRS) is reviewed. Four software algorithms for performing CRC computations are described: table lookup, reduced table lookup, on-the-fly, and wordwise. They are compared in terms of their speeds and storage requirements.< >
Primitive Polynomial
- E W Weisstein
Classical error-correcting codes: Machines should work. People should think
- R Hamming
A comprehensive guide for CRC hardware implementation
- D Alnajjar
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Error Detecting Codes