CRC and its effective
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This document discusses error detection in messages through checksums and cyclic redundancy checks (CRCs). It explains that message corruption can occur through bit flips, duplications, omissions, or disagreements in communication parameters. CRCs are more effective than checksums at detecting errors by increasing the hamming distance between messages. The document outlines choosing a polynomial for CRC calculation and evaluating CRC effectiveness through Monte Carlo simulation of random corruptions and error detection.
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This talk includes both a tutorial and explanation of research results on the proper use of Cyclic Redundancy codes (CRCs) and checksums in an aviation context. More than 50 years since the invention of the CRC, the proper use of these error detection codes is still hampered by a combination of misleading folklore, sub-optimality of standard approaches, general inaccessibility of research results, and the occasional typographical error in key reference materials. However, recent work has been able to exhaustively explore the CRC design space and identify optimal selection criteria based on key system characteristics. This talk will covers the following areas: checksum and CRC theory with an emphasis on intuitive understanding rather than heavy math; why using a standard or widely used CRC can be suboptimal (or worse); how to pick a good checksum/CRC; the key parameters that affect the error detection capability of a checksum/CRC; CRC pitfalls illustrated via examples from Controller Area Network and ARINC-825; an example CRC selection process for achieving a required level of functional criticality; and a “seven deadly sins” list for CRC/checksum use. Some key research findings that are discussed include: a well-chosen CRC is usually dramatically better than a checksum for relatively little additional computational cost; you can usually do a lot better than “standard” CRC (especially CRC-32); Hamming Distance at the target payload length is the predominant selection criterion of interest; and it is important to avoid bit encoding approaches that undermine CRC effectiveness.
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CRC and its effective
- 1. CRC and its effectiveness Part 1 Martin Brenn, 28.04.2012 brenn@depon.net Depon.Net
- 2. Messages • Messages are sent everywhere and everyday. • For example: – CAN (created by automotive industry) – SPI (Inter-CPU) – Wired Ethernet (LAN) – Wireless LAN (IEEE 80211.x) – And many many more
- 3. Corruption • Corruption of messages occurs everywhere and every day! • Typical failure modes: – Loss – Repetition – Wrong order of packets (especially in Internet) – Manipulation of content • Bit flips (0->1 or 1-0) • Duplication or omission of bits (11100->1100) – Disagreement about communication parameters • „What he says?“ or „Ariane 5 Flight 501“
- 4. Ariane 5 Result of converting a 64-Bit float to 16-bit Integer without check for Arithmetic Overflow • http://en.wikipedia.org/wiki/Ariane_5_Flight_501 Source of images: 1) http://www.capcomespace.net/dossiers/espace_europeen/ariane/ariane 5/AR501/V88%20explosion%2003.jpg 2) http://de.wikipedia.org/wiki/Ariane_5
- 5. Scope • Today, we just take care of manipulation of data • Competition against systematic failures is also quite interesting but not in my today‘s scope.
- 6. Result Corrupted cat is corrupt
- 7. Manipulation types • Typical Effects: – Single bit error: Just one bit flips • 0100 1011 -> 0101 1011 – Double bit error: Two bits flips • 0100 1011 -> 1110 1011 • 0100 1011 -> 0100 1000 – Multiple bit error: More bit errors • 0100 1011 -> 1001 0011 – Burst error: Multiple bits flip or get a new value • 0100 1011 -> 1111 1011
- 8. What do? • Create redundandy! – Simple: Repeat message twice and check if content is the same – Problem: 6 Mbit-DSL will just give 3 Mbit. – Does duplication really help against systematic failures? – i.e. Dual-Channel FlexRay • Usually, information about validity of message is enough! – Add checksum for detection!
- 9. Checksum vs. CRC • Checksums are not checksums! • Typically, „checksums“: are a summation of all values multiplied with factors depending on their position: – Checksum = Sum(Value[n] * Lookup[n%m]) – Not very effective (i.e: TCP) • CRC: – Quite funny thing, difficult to explain – http://en.wikipedia.org/wiki/Computation_of_ CRC
- 10. Properties of CRC • Main Properties of a CRC: – Polynomial, implying the length of CRC – Seed [Not Seeed (Dickes B)] – Inverting, +1, etc… • The calculated CRC will be appended to message • CRC increases hamming distance of messages. – Corruption can be detected!
- 11. Choice of Polynomial • So, let‘s choose a CRC… • Where to start? • For example: – http://www.ece.cmu.edu/~koopman/roses/ds n04/koopman04_crc_poly_embedded.pdf – Nice work!
- 12. Task • Task: – Find the probability that a corrupted message will be assumed as corrupt! – We will use „Monte Carlo Method“ • http://en.wikipedia.org/wiki/Monte_Carlo_method • Simple things need complex words! • Do random guessing and take this as the truth • Simple, quite effective
- 13. • Part 1 completed! • Part 2 will present the application!