ENCODING CIRCUIT FOR (n,k) LBC

ENCODING CIRCUIT FOR (6,3) LBC

SYNDROME CALCULATION CIRCUIT

SYNDROME CALCULATION CIRCUIT FOR (6,3) LBC

ERROR DETECTION & CORRECTION CAPABILITY OF LBC

• THEOREM 1: “The minimum distance of a LBC is equal to the minimum hamming weight of a non zero vector”.

• THEOREM 2 (a):“Let C be a (n,k) LBC with parity check matrix H. For

each code vector of Hamming weight ‘l’, there exist ‘l’ column of H such that the vector sum of these columns is equal to the ZERO Vector”.

• THEOREM 2(b): converse of theorem 2 a.“Let C be a (n,k) LBC with parity check matrix H. If there exist ‘l’

column of H such that the vector sum of these columns is equal to the ZERO Vector, then there exist a code vector of hamming weight ‘l’ in C”.

COROLLARY 2(c): “let C be a LBC with parity check matrix H. If no ‘(d-1)’ or fewer columns of H add to zero, the code has minimum Hamming weight of at least “d’”.

COROLLARY 2(d): “let C be a LBC with parity check matrix H. The minimum hamming weight (equal to Minimum distance) of C is equal to smallest number of columnns of H that add up to ZERO”

• THEOREM 3:“ A LBC with a minimum distance dmin can detect up to (dmin – 1) errors in each code vector & can correct up to (dmin – 1) /2 errors.