CRC and Checksum Tutorial Slides

I recently presented an invitation-only webinar on the topic of CRC and Checksum good practices and error detection effectiveness. The talk was for an aviation audience, but it applies almost entirely to other applications as is. The recording didn't work out, but if there is enough demand I'll find time this summer to see if I can do an audio narration recording to go with the slides.

Meanwhile, you can find the slides here:
http://www.ece.cmu.edu/~koopman/pubs/KoopmanCRCWebinar9May2012.pdf

Contents:
- Introduction
  - Motivation -- why isn't this a solved problem?
  - Parity computations as an example
  - Error code construction and evaluation (without scary math)
  - Example using parity codes
- Checksums
  - What's a checksum?
  - Commonly used checksums and their performance
- Cyclic redundancy codes (CRCs)
  - What's a CRC
  - Commonly used CRC approaches and their performance
- Don't blindly trust what you hear on this topic
  - A good CRC is almost always much better than a good checksum
  - Many published (and popular) approaches are suboptimal or just plain wrong
  - There are some topics to be careful of for which we don't know the answers yet

We are also collecting information about how CRCs and checksums are used in real applications (which is not necessarily the same as what researchers study!) If you have anecdotes, examples, or other information about what you do or what you'd like to do, we'd love to hear about it. If you are in the aviation community the FAA is running a much more specific survey just for you; let me know and I'll get you in touch with the appropriate FAA contact.

(We can't necessarily provide immediate answers to specific questions such as "which polynomial should I use for this specific situation." But popular topics and questions that we think are broadly applicable will be put into the research bin and published here or in a report when results are available.) 

Consolidated Wikipedia Pointers for Checksums and CRCs

Here are some starting points within Wikipedia if you are interested in checksum and CRC background. (These articles also point to other places of interest.) Over time I hope to distill the practical application of all this in my blog, but for now these are reasonable starting points.

• List of checksum and CRC algorithms: http://en.wikipedia.org/wiki/List_of_checksum_algorithms

• Longitudinal Redundancy Check (XOR checksum): http://en.wikipedia.org/wiki/Longitudinal_redundancy_check

• Overview of Checksums: http://en.wikipedia.org/wiki/Checksum
  
• Fletcher Checksum: http://en.wikipedia.org/wiki/Fletcher%27s_checksum
• Adler Checksum: http://en.wikipedia.org/wiki/Adler-32

• Overview of CRC: http://en.wikipedia.org/wiki/Cyclic_redundancy_check
• More detailed example of CRC computation: http://en.wikipedia.org/wiki/Computation_of_CRC 
• Mathematics of CRCs: http://en.wikipedia.org/wiki/Mathematics_of_CRC

 Related pages:

• Overview of error detection and correction codes: http://en.wikipedia.org/wiki/Redundancy_check
• Discussion of parity: http://en.wikipedia.org/wiki/Parity_bit
• Check digits (it's like parity for numbers handled by people): http://en.wikipedia.org/wiki/Check_digit

It is important to realize that Wikipedia is not necessarily an authoritative source. For this area it seems there is enough critical mass of authors, editors and reviewers to get the pages into reasonable shape.

CRC for Protecting A Single Value

Some critical applications need to protect a single byte or word of data in memory against corruption. (For example, if you want to be extra-sure about protecting EEPROM values against corruption.) A previous post gives good CRC polynomials for a wide range of circumstances, but it is always nice to know if you can do better for a special case. Below are optimal CRC polynomials for a few special cases involving small data words that might be stored in memory (RAM, EEPROM, or otherwise).

Protecting an 8-bit data word:
8-bit CRC:  HD=5;  0x9C = x^8 + x^5 + x^4 + x^3 + 1  
16-bit CRC: HD=8; 0xE92F = x^16 + x^15 + x^14 + x^12 + x^9 + x^6 + x^4 + x^3 + x^2 + x + 1
32-bit CRC: HD=16; 0xC563942F = x^32 +x^31 +x^27 +x^25 +x^23 +x^22 +x^18 +x^17 +x^16 +x^13 +x^11 +x^6 +x^4 +x^3 +x^2 +x +1

Protecting a 16-bit data word:
8-bit CRC:  HD=4;  0x93 = x^8 + x^5 + x^2 + x + 1  
16-bit CRC: HD=7; 0x978A = x^16 + x^13 + x^11 + x^10 + x^9 + x^8 + x^4 +  x^2 + 1
32-bit CRC: HD=14; 0xB396786D = x^32 +x^30 +x^29 +x^26 +x^25 +x^24 +x^21 +x^19 +x^18 +x^15 +x^14 +x^13 +x^12 +x^7 +x^6 +x^4 +x^3 +x +1

Protecting a 32-bit data word:
8-bit CRC:  HD=4;  0x92 = x^8 + x^5 + x^2 + 1  
16-bit CRC: HD=6; 0x8BFC = x^16 + x^12 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 +  x^4 + x^3 + 1
32-bit CRC: HD=12; 0xB527A43B = x^32 +x^30 +x^29 +x^27 +x^25 +x^22 +x^19 +x^18 +x^17 +x^16 +x^14 +x^11 +x^6 +x^5 +x^4 +x^2 +x +1

The hex number has an implicit +1. "HD" means Hamming Distance. Other information about this topic can be found at my previous post on good CRCs.

Note that for this sort of use it is a good idea to "seed" the CRC computation with a value of that is not zero. That avoids a data word value of zero giving a CRC computed value of zero -- which will result in an undetected error if memory is wiped to all zeros for some reason.