Error Detection

The error detection uses both Cyclic Redundancy Check (CRC) and checksum methods. SDLC/HDLC supports 16 bit CRC error detection. CRC can detect all the single errors, double errors and burst errors up to 16 bits in length and can also detect 99% of burst errors of lengths greater than 16 bits.

The way this works is as follows. A cyclic code message consists of a specific number of data bits $G(X)$ and a Block Check Character (BCC). Let $n$ equal the total number of bits in the message, $k$ equal the number of data bits, i.e. $n-k$ is the number of bits in the BCC. The code message is derived from two polynomials which are algebraic representations of two binary words, the generator polynomial $P(X)$ and the message polynomial $G(X)$. The generator polynomial $P(X)$ is a type of code used in CRC-12, CRC-16 and CRC-CCITT.

For example, $n$ bits of binary data can be represented as a message polynomial of degree $n-1$. Thus, an eight-bit long message $10101010$ is represented as

$$G(X) = X^7 + X^5 + X^3 + X^1.$$ (24.3.1)

The code message can be constructed as follows:

1. Multiply the message $G(X)$ by $X^{n-k}$ where $n-k$ is the number of bits in the BCC.
2. Divide the resulting product $X^{n-k}[G(X)]$ by the generator polynomial $P(X)$.
3. Disregard the quotient and add the remainder $C(X)$ to the product to get the code message polynomial $F(X)$, which is represented as $X^{n-k}[G(X)]+C(X)$.

The division is performed in binary without carries or borrows. The code message $F(X)$ is transmitted as binary data and the receiver at the other end retrieves the message using the same generator polynomial and accepts the data if the remainder is zero.