I'm looking at designing a low-level radio communications protocol, and am trying to decide what sort of checksum/crc to use. The hardware provides a CRC-8; each packet has 6 bytes of overhead in addition to the data payload. One of the design goals is to minimize transmission overhead. For some types of data, the CRC-8 should be adequate, for for other types it would be necessary to supplement that to avoid accepting erroneous data.
If I go with a single-byte supplement, what would be the pros and cons of using a CRC8 with a different polynomial from the hardware CRC-8, versus an arithmetic checksum, versus something else? What about for a two-byte supplement? Would a CRC-16 be a good choice, or given the existence of a CRC-8, would something else be better?
In 2004 Phillip Koopman from CMU published a paper on choosing the most appropriate CRC, http://www.ece.cmu.edu/~koopman/crc/index.html
This paper describes a polynomial selection process for embedded network applications and proposes a set of good general-purpose polynomials. A set of 35 new polynomials in addition to 13 previously published polynomials provides good performance for 3- to 16-bit CRCs for data word lengths up to 2048 bits.
That paper should help you analyze how effective that 8 bit CRC actually is, and how much more protection you'll get from another 8 bits. A while back it helped me to decide on a 4 bit CRC and 4 bit packet header in a custom protocol between FPGAs.
来源：https://stackoverflow.com/questions/7974082/best-8-bit-supplemental-checksum-for-crc8-protected-packet