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.

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!