Cyclic redundancy check (CRC) code[13] 

Also known as Frame check sequence (FCS).


A generalization of the single parity-check code in which the generalization of the parity bit is the remainder of the data string (mapped into a polynomial via the Cyclic-to-polynomial correspondence) divided by some generator polynomial. A notable family of codes is referred to as CRC-(\(m-1\)), where \(m\) is the length of the generator polynomial.


Detects any burst error up to the length of the generator polynomial.


CRC-16 and CRC-32 are used in data transmission, e.g., IEEE 802.16e, IEEE 802.3 [4] and TCP/IP communication [5; Sec. 2.3.3].


See Ref. [6] and book [7] for introductions to CRC codes.See Refs. [8,9] for exhaustive lists of CRC polynomials, as well as the CRC Polynomial Zoo website by Philip Koopman.




  • Polar code — CRC codes concataned with polar codes yield improved performance of the SCL polar-code decoder [10,11].


W. Peterson and D. Brown, “Cyclic Codes for Error Detection”, Proceedings of the IRE 49, 228 (1961) DOI
W. W. Peterson and E. J. Weldon, Error-correcting codes. MIT press 1972.
S. Lin and D. J. Costello, Error Control Coding, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2004.
Borrelli, Chris. "IEEE 802.3 cyclic redundancy check." application note: Virtex Series and Virtex-II Family, XAPP209 (v1. 0) (2001).
M. Ergen, “Basics of Cellular Communication”, Mobile Broadband 19 (2008) DOI
S. Sheng-Ju, “Implementation of Cyclic Redundancy Check in Data Communication”, 2015 International Conference on Computational Intelligence and Communication Networks (CICN) (2015) DOI
Wells, Richard B. Applied coding and information theory for engineers. Prentice-Hall, Inc., 1998.
P. Koopman, “32-bit cyclic redundancy codes for Internet applications”, Proceedings International Conference on Dependable Systems and Networks DOI
P. Koopman and T. Chakravarty, “Cyclic redundancy code (CRC) polynomial selection for embedded networks”, International Conference on Dependable Systems and Networks, 2004 (2004) DOI
B. Li, H. Shen, and D. Tse, “An Adaptive Successive Cancellation List Decoder for Polar Codes with Cyclic Redundancy Check”, IEEE Communications Letters 16, 2044 (2012) DOI
I. Tal and A. Vardy, “List Decoding of Polar Codes”, IEEE Transactions on Information Theory 61, 2213 (2015) DOI
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“Cyclic redundancy check (CRC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.
@incollection{eczoo_crc, title={Cyclic redundancy check (CRC) code}, booktitle={The Error Correction Zoo}, year={2024}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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“Cyclic redundancy check (CRC) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2024.