receiver matched filter.For BPSK transmission over the AWGN channel,a simple measure of the reliability of a received symbol yis its magnitude the larger the magnitude,the larger the reliability of the hard-decision bit measure has been used in many reliability-based algorithm for decoding linear block codes. Let H be the parity-check matrix of a (d,de)-regular LDPC code C of length n.For 0sI<n consider the set A={h”,h9,h} ofd,rows in H that are orthogonal on the bit position I.For 1s j<d,consider the jth row in h=(h8,纷，9-) For simplicity of notation,we will use p to<nbe the locations where=.h=1.Then h checks the code bits,c.cc.Then the syndrome bit computed from zand h is ”=zh9=h州+h城+.+nh9 =e,hg+eh+.+e,hg We measure the reliability of the received symbol with For /<and 1sj<d,define ly,a=min1y卡1≤k≤p} (4.13) The numbery is used as a measure of the reliability of the syndrome bits Define the following sum E∑”s29-ly巴 (4.14) Then E is simply a weighted check-sum that is orthogonal on the bit position I.The weighted check-sums can be incorporated into the BF decoding algorithm to improve the decoding performance.Such a BF decoding is called weighted BF decoding.It is carried out as follows. 1)Compute the parity-check sums based on(4.10).If all the parity-check sums are zero,stop the decodin 2)Compute the weighted check-sums Ebased on (4.14)fors/<n 3)Find the bit position for which Er is the largest. 4)Flip the received bit=. 5)Repeat steps 1)through 4).This processing of bit flipping continues until all the 16 16 receiver matched filter. For BPSK transmission over the AWGN channel, a simple measure of the reliability of a received symbol yl is its magnitude | yl |: the larger the magnitude, the larger the reliability of the hard-decision bit zl. This reliability measure has been used in many reliability-based algorithm for decoding linear block codes. Let H be the parity-check matrix of a (dv, dc)-regular LDPC code C of length n. For 0 ≤ <l n , consider the set { } () () () 1 2 , ,., v ll l A hh h l d = of dv rows in H that are orthogonal on the bit position l. For 1 v ≤ j < d , consider the jth row in Al, ( ) () () () () ,0 ,1 , 1 , ,., l ll l j j j jn hh h h = − For simplicity of notation, we will use ρ to denote dc. Let 1 2 0 , ,., ii i n ≤ ρ < be the locations where () () () ,0 ,1 , 1 . 1. ll l j j jn hh h = == = − Then ( )l h j checks the code bits, 1 2 , ,., ii i cc c ρ . Then the syndrome bit computed from z and ( )l h j is 11 2 2 () () () () () , , l lll l j j i ji i ji i ji s zh zh z hρ ρ =⋅ = + + + z h " 11 2 2 () () () , , ll l i ji i ji i ji eh eh e hρ ρ = + ++ " We measure the reliability of the received symbol with | | k k i i z y . For 0 ≤ <l n and 1 v ≤ <j d , define { } ( ) min | | min | |: 1 k l j i y yk = ≤≤ ρ (4.13) The number ( ) | | l j y is used as a measure of the reliability of the syndrome bit ( )l j s . Define the following sum ( ) ( ) () () min 2 1| | l j l l l l jj s E sy ∈  ∑ − S (4.14) Then El is simply a weighted check-sum that is orthogonal on the bit position l. The weighted check-sums can be incorporated into the BF decoding algorithm to improve the decoding performance. Such a BF decoding is called weighted BF decoding. It is carried out as follows. 1) Compute the parity-check sums based on (4.10). If all the parity-check sums are zero, stop the decoding. 2) Compute the weighted check-sums El based on (4.14) for 0 ≤ l n < . 3) Find the bit position l for which El is the largest. 4) Flip the received bit zl. 5) Repeat steps 1) through 4). This processing of bit flipping continues until all the