FCS Sample Clauses

FCS. The FCS field contains a 32-bit value that represents a CRC polynomial of degree 31. The CRC is calculated over a calculation field, which is the entire Frame Payload field for this specification. The calculation field is mapped to a message polynomial M(x) of degree k-1, where k is the number of bits in the calculation field. The least-significant bit of the first octet presented to the PHY SAP is the coefficient of the xk-1 term, and the most-significant bit of the last octet transmitted is the coefficient of the x0 term. The CRC is calculated using the following standard generator polynomial of degree 32: G(x) = x32 + x26 + x23 + x22 + x16 + x12 + x11 + x10 + x8 + x7 + x5 + x4 + x2 + x + 1 The CRC polynomial is the one's complement of the modulo 2 sum of the following remainders: — The remainder resulting from xk × (x31 + x30 + ... + x + 1) divided (modulo 2) by G(x). — The remainder resulting from x32 × M(x), divided (modulo 2) by G(x). The FCS field value is derived from the CRC polynomial such that the least-significant bit is the coefficient of the x31 term and the most-significant bit is the coefficient of the x0 term. Figure 16 illustrates the encoding of the FCS field for the CRC polynomial: a31x31 + a30x30 + a29x29 + … + a2x2 + a1x + a0 bits: b31 b30 b29 … b2 b1 b0 a0 a1 a2 … a29 a30 a31 Figure 16 — FCS field encoding In a common implementation, at the transmitter, the initial remainder of the division is preset to all ones and is then modified via division of the calculation field by the generator polynomial G(x). The one’s complement of this remainder is the FCS field. At the receiver, the initial remainder is preset to all ones. The serial incoming bits of the calculation field and FCS, when divided by G(x) in the absence of transmission errors, results in a unique non-zero remainder value. The unique remainder value is the polynomial: x31 + x30 + x26 + x25 + x24 + x18 + x15 + x14 + x12 + x11 + x10 + x8 + x6 + x5 + x4 + x3 + x + 1