Packet Error Check Codes

Question 1

A CRC is not processor-intensive. All it adds to your exclusive-or is a table lookup. The operation on each byte is simply: crc = crc8_table[crc ^ *data++]. See below.

The downside of doing just an exclusive-or is that there are many simple errors that cancel each other, resulting in a false-positive check. A CRC is much better.

#include <stddef.h>

/* 8-bit CRC with polynomial x^8+x^6+x^3+x^2+1, 0x14D.
   Chosen based on Koopman, et al. (0xA6 in his notation = 0x14D >> 1):
   http://www.ece.cmu.edu/~koopman/roses/dsn04/koopman04_crc_poly_embedded.pdf
 */

static unsigned char crc8_table[] = {
    0x00, 0x3e, 0x7c, 0x42, 0xf8, 0xc6, 0x84, 0xba, 0x95, 0xab, 0xe9, 0xd7,
    0x6d, 0x53, 0x11, 0x2f, 0x4f, 0x71, 0x33, 0x0d, 0xb7, 0x89, 0xcb, 0xf5,
    0xda, 0xe4, 0xa6, 0x98, 0x22, 0x1c, 0x5e, 0x60, 0x9e, 0xa0, 0xe2, 0xdc,
    0x66, 0x58, 0x1a, 0x24, 0x0b, 0x35, 0x77, 0x49, 0xf3, 0xcd, 0x8f, 0xb1,
    0xd1, 0xef, 0xad, 0x93, 0x29, 0x17, 0x55, 0x6b, 0x44, 0x7a, 0x38, 0x06,
    0xbc, 0x82, 0xc0, 0xfe, 0x59, 0x67, 0x25, 0x1b, 0xa1, 0x9f, 0xdd, 0xe3,
    0xcc, 0xf2, 0xb0, 0x8e, 0x34, 0x0a, 0x48, 0x76, 0x16, 0x28, 0x6a, 0x54,
    0xee, 0xd0, 0x92, 0xac, 0x83, 0xbd, 0xff, 0xc1, 0x7b, 0x45, 0x07, 0x39,
    0xc7, 0xf9, 0xbb, 0x85, 0x3f, 0x01, 0x43, 0x7d, 0x52, 0x6c, 0x2e, 0x10,
    0xaa, 0x94, 0xd6, 0xe8, 0x88, 0xb6, 0xf4, 0xca, 0x70, 0x4e, 0x0c, 0x32,
    0x1d, 0x23, 0x61, 0x5f, 0xe5, 0xdb, 0x99, 0xa7, 0xb2, 0x8c, 0xce, 0xf0,
    0x4a, 0x74, 0x36, 0x08, 0x27, 0x19, 0x5b, 0x65, 0xdf, 0xe1, 0xa3, 0x9d,
    0xfd, 0xc3, 0x81, 0xbf, 0x05, 0x3b, 0x79, 0x47, 0x68, 0x56, 0x14, 0x2a,
    0x90, 0xae, 0xec, 0xd2, 0x2c, 0x12, 0x50, 0x6e, 0xd4, 0xea, 0xa8, 0x96,
    0xb9, 0x87, 0xc5, 0xfb, 0x41, 0x7f, 0x3d, 0x03, 0x63, 0x5d, 0x1f, 0x21,
    0x9b, 0xa5, 0xe7, 0xd9, 0xf6, 0xc8, 0x8a, 0xb4, 0x0e, 0x30, 0x72, 0x4c,
    0xeb, 0xd5, 0x97, 0xa9, 0x13, 0x2d, 0x6f, 0x51, 0x7e, 0x40, 0x02, 0x3c,
    0x86, 0xb8, 0xfa, 0xc4, 0xa4, 0x9a, 0xd8, 0xe6, 0x5c, 0x62, 0x20, 0x1e,
    0x31, 0x0f, 0x4d, 0x73, 0xc9, 0xf7, 0xb5, 0x8b, 0x75, 0x4b, 0x09, 0x37,
    0x8d, 0xb3, 0xf1, 0xcf, 0xe0, 0xde, 0x9c, 0xa2, 0x18, 0x26, 0x64, 0x5a,
    0x3a, 0x04, 0x46, 0x78, 0xc2, 0xfc, 0xbe, 0x80, 0xaf, 0x91, 0xd3, 0xed,
    0x57, 0x69, 0x2b, 0x15};

unsigned crc8(unsigned crc, unsigned char *data, size_t len)
{
    unsigned char *end;

    if (len == 0)
        return crc;
    crc ^= 0xff;
    end = data + len;
    do {
        crc = crc8_table[crc ^ *data++];
    } while (data < end);
    return crc ^ 0xff;
}

/* this was used to generate the table and to test the table-version

#define POLY 0xB2

unsigned crc8_slow(unsigned crc, unsigned char *data, size_t len)
{
    unsigned char *end;

    if (len == 0)
        return crc;
    crc ^= 0xff;
    end = data + len;
    do {
        crc ^= *data++;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
        crc = crc & 1 ? (crc >> 1) ^ POLY : crc >> 1;
    } while (data < end);
    return crc ^ 0xff;
}
*/

#include <stdio.h>

#define SIZE 16384

int main(void)
{
    unsigned char data[SIZE];
    size_t got;
    unsigned crc;

    crc = 0;
    do {
        got = fread(data, 1, SIZE, stdin);
        crc = crc8(crc, data, got);
    } while (got == SIZE);
    printf("%02x\n", crc);
    return 0;
}

Question 2

The table look up method for generating the PEC value is certainly faster. My tests on a a PIC32 running at 80 MHz for a 4 byte packet indicates that the table method required 2.8us while the algorithm method needed 11.5us. The memory requirements shows the cost of of speed: The table method requires 348 bytes while the algorithm method on;y 216 bytes. So if memory is scarce - consider the algorithm approach shown here. (BYTE is an unsigned char)

/* bit_crc8 FUNCTION DESCRIPTION ************************************
 * SYNTAX:          BYTE bit_crc8( BYTE *data, BYTE len);
 * KEYWORDS:        PEC, CRC, error checking
 * DESCRIPTION:     Returns the PEC for an array of bytes.  This method does
 *                  not use a lookup table
 * PARAMETER 1:     BYTE pointer to data array
 * PARAMETER 2:     BYTE - Number of bytes in array
 * RETURN VALUE:    BYTE - PEC value
 * NOTES:           SMBus limits the number of bytes in the packet to 256
 *                  Primitive polynomial is set by the definition of PEC.
 * END DESCRIPTION **********************************************************/

BYTE bit_crc8( BYTE *data, BYTE len)
{
   #define PEC 0x07    // Implements Polynomial X^8 + X^2 + X^1 +1
   BYTE crc = 0;
   BYTE loop, b8;

   while (len--)
   {
      crc ^= *data++;
      for(loop=0; loop <8; loop++)
      {
          b8 = crc & 0x80;    /* Test for MSB set to 1 */
          crc <<= 1;          /* Left shift CRC */
          if(b8)
          {
              crc ^= PEC;     /* Divide by PEC if bit 8 was set */
          }
      }
   }
   return crc;

}