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A Painless Guide To Crc Error Detection Algorithms

Everything you wanted to know about CRC algorithms

(by ross n. williams)

A very nice guide on CRC algorithms in 21 chapters.
This document is an attempt to provide a clear and simple no-nonsense explanation of CRCs and to absolutely nail down every detail of the operation of their high-speed implementations. In addition to this, this document presents a parameterized model CRC algorithm called the "Rocksoft(tm) Model CRC Algorithm". The model algorithm can be parameterized to behave like most of the CRC implementations around, and so acts as a good reference for describing particular algorithms.
This article is online from 2924 days and has been seen 4833 times





==================================================
A PAINLESS GUIDE TO CRC ERROR DETECTION ALGORITHMS
==================================================
"Everything you wanted to know about CRC algorithms, but were afraid
to ask for fear that errors in your understanding might be detected."

Version : 3.
Date    : 19 August 1993.
Author  : Ross N. Williams.
Net     : ross@guest.adelaide.edu.au.
FTP     : ftp.adelaide.edu.au/pub/rocksoft/crc_v3.txt
Company : Rocksoft^tm Pty Ltd.
Snail   : 16 Lerwick Avenue, Hazelwood Park 5066, Australia.
Fax     : +61 8 373-4911 (c/- Internode Systems Pty Ltd).
Phone   : +61 8 379-9217 (10am to 10pm Adelaide Australia time).
Note    : "Rocksoft" is a trademark of Rocksoft Pty Ltd, Australia.
Status  : Copyright (C) Ross Williams, 1993. However, permission is
          granted to make and distribute verbatim copies of this
          document provided that this information block and copyright
          notice is included. Also, the C code modules included
          in this document are fully public domain.
Thanks  : Thanks to Jean-loup Gailly (jloup@chorus.fr) and Mark Adler
          (me@quest.jpl.nasa.gov) who both proof read this document
          and picked out lots of nits as well as some big fat bugs.

Table of Contents
-----------------
    Abstract
 1. Introduction: Error Detection
 2. The Need For Complexity
 3. The Basic Idea Behind CRC Algorithms
 4. Polynomical Arithmetic
 5. Binary Arithmetic with No Carries
 6. A Fully Worked Example
 7. Choosing A Poly
 8. A Straightforward CRC Implementation
 9. A Table-Driven Implementation
10. A Slightly Mangled Table-Driven Implementation
11. "Reflected" Table-Driven Implementations
12. "Reversed" Polys
13. Initial and Final Values
14. Defining Algorithms Absolutely
15. A Parameterized Model For CRC Algorithms
16. A Catalog of Parameter Sets for Standards
17. An Implementation of the Model Algorithm
18. Roll Your Own Table-Driven Implementation
19. Generating A Lookup Table
20. Summary
21. Corrections
 A. Glossary
 B. References
 C. References I Have Detected But Haven't Yet Sighted


Abstract
--------
This document explains CRCs (Cyclic Redundancy Codes) and their
table-driven implementations in full, precise detail. Much of the
literature on CRCs, and in particular on their table-driven
implementations, is a little obscure (or at least seems so to me).
This document is an attempt to provide a clear and simple no-nonsense
explanation of CRCs and to absolutely nail down every detail of the
operation of their high-speed implementations. In addition to this,
this document presents a parameterized model CRC algorithm called the
"Rocksoft^tm Model CRC Algorithm". The model algorithm can be
parameterized to behave like most of the CRC implementations around,
and so acts as a good reference for describing particular algorithms.
A low-speed implementation of the model CRC algorithm is provided in
the C programming language. Lastly there is a section giving two forms
of high-speed table driven implementations, and providing a program
that generates CRC lookup tables.

(*** download for full text ***)




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