Error Detection And Correction For Cyclic Code Code

3.6  Error Detection And Correction For Cyclic                 Code

We will illustrate this operation with the following example.

Example 3.5

Consider the syndrome circuit for (7, 4) cyclic code generated by

g(x) = 1+ x + x³

The code has d_min =3  and is capable of correcting any single error in e(x).

Since the error patterns consist of the cyclic shifts of  (0 0 0 0 0 0 1), the decoder needs only to be able to recognize one of the seven nonzero syndromes to be able to correct all of the nonzero error patterns.

The syndrome s = (1 0 1), corresponding to the error pattern

 e = (0 0 0 0 0 0 1), is the best choice since it allows one to release the

corrected codeword bits before the error location actually is identified.

The circuit shown in figure 3.4 is capable to detect errors in received code vector and correct it.

Decoding begins by first setting all of the shift register cells to zero. The received word r is then shifted bit-by-bit into the 7-bit received word buffer and the syndrome computation circuit, simultaneously.

Once the received word is completely shifted into the buffer, the Shift registers of the syndrome computation circuit contain the Syndrome for the received word. As one continues to shift cyclically the contents of the received-word buffer and the syndrome computation circuit.

The syndrome computation circuit computes the syndrome for the cyclically shifted versions of the received word.

If at any point the computed syndrome is s = (1 0 1), it is detected by the AND gate when its output goes to 1. This value is then used to complement and correct the error in the rightmost bit in the buffer as it leaves the buffer.