LINEAR BLOCK CODES   (cont)

Parity Check Matrix H and Error Correction Decoding

Parity Check Matrix is a (n-k) ´n matrix defined as

.......(2.4)

and x is a code vector generated by matrix G is, if and only if,.

     Suppose vector x was sent over a noisy channel. Let y be the received vector which can be expressed as y = x + e, where e is the error vector (or pattern). To determine the error vector e, a 1´(n-k) vector s, which is referred to as the syndrome, is computed.

     For any error vector e, there are 2k distinct vectors: e + xi, i = 0,1, …, 2k-1, which is known as coset and e is the coset leader. Each coset has a unique syndrome. Once the syndrome is computed, the error vector (which is the coset leader) is known. The corrected vector is then computed: x = y + e.