After an extensive editing and approval process, the FAA has released the report that I did with Kevin Driscoll & Brendan Hall from Honeywell. You can see it here:

Selection of Cyclic Redundancy Code and Checksum Algorithms to Ensure Critical Data Integrity

DOT/FAA/TC-14/49

http://www.tc.faa.gov/its/worldpac/techrpt/tc14-49.pdf

# Checksum and CRC Central

Cyclic Redundancy Codes, Checksums, and related issues for computer system data integrity.

## Saturday, April 11, 2015

## Saturday, September 27, 2014

### Data Integrity Techniques: Aviation Best Practices for CRC & Checksum Error Detection

I just presented a session at an FAA sponsored conference on "Data Integrity Techniques: Aviation Best Practices for CRC & Checksum Error Detection" on Sept. 25. Here are the slides:

(Acrobat download: http://users.ece.cmu.edu/~koopman/pubs/koopman14_crc_faa_conference_presentation.pdf)

A recording of an older variant of this presentation can be viewed below:

Webinar download: https://cmu.box.com/s/nn5r9ogwpw100fqkp6g2

Accompanying slides for that older webinar can be found: here

(Acrobat download: http://users.ece.cmu.edu/~koopman/pubs/koopman14_crc_faa_conference_presentation.pdf)

A recording of an older variant of this presentation can be viewed below:

Webinar download: https://cmu.box.com/s/nn5r9ogwpw100fqkp6g2

Accompanying slides for that older webinar can be found: here

## Thursday, August 14, 2014

### Significant update to on-line CRC performance data

I've managed to create a new set of pages with CRC performance data during my hobby time this summer.

"Best" CRC Polynomials:

http://users.ece.cmu.edu/~koopman/crc/index.html

This contains an extensive list of of good CRC polynomials for different CRC sizes and dataword lengths. I re-ran all the computations in light of some data that has become available since the initial publication a number of years back. The table is slightly different than the table I previously published. The old table is OK, but this one is marginally better than the old one for the data that was previously provided, so there is no pressing need to change systems based on the old version so long as you were running at shorter than 2Kbit dataword sizes. More importantly, this new table consideres unlimited dataword lengths and larger CRC sizes. (At this time the 32-bit computations are still running and they'll be updated as they are available.)

CRC Polynomial Zoo with Hamming Weight Data

Contains error detection performance data for a large variety of CRCs, including numerous "standard" and published CRCs. If you see one missing let me know with a citation and I'll add it.

I hope that this data is useful to others. Some of the large polynomials have incomplete or shortened data files, and will be updating those over time as the computations complete.

## Monday, August 4, 2014

### CRC publication errata

Thanks to Prof. Berthold Gick at University of Applied Sciences in Koblenz Germany for finding a few bugs in my published CRC values. (And also thanks for a very thorough second-check of results -- this is an essential part of scholarly publication that is not acknowledged as often as it should be!)

I have updated presentations and papers that I can find with the following corrections:

From my FAA presentation materials:

Polynomial HD=2 HD=3 HD=4

0x80000d | 16,777,212 | 5815 | 509 (length in bits at that HD)

From my 2002 paper:

Polynomial 0x992c1a4c has a maximal HD=6 payload of 32738 bits (originally published as 32737)

From many publications the table of 16-bit and smaller CRCs:

11-bit polynomial 0x5d7 has a maximal HD=5 payload of 26 bits (originally published as 25)

If anyone else spots an error please do let me know. This work happens time-available, but I do strive to eventually fix any bugs I know about.

## Saturday, May 12, 2012

### 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.)

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.)

## Sunday, January 15, 2012

### 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

- 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

## Sunday, January 1, 2012

### 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).

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

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

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.

__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.

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