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?