(4.53) denotes the average number of bit errors caused by transitions between the all-zero codeword and codewords of weight d.The set of all pairs (d.B)is called the code distance spectrum. With (d)s(4.51)becomes (4.54) where Ris the code rate.Using IOWEF,we can also express (4.52)(or(4.51as RA) (2drE 台K (4.55) With the property that +y)sy)e2,a tighter upper bound on bit error probability can be expressed as P,so dad. (WZ) K oW w=Z-eM-R.F!No) (4.56) Information Weight Distribution of PCC We now proceed to consider the weight spectrum of PCC.Let(Z),=1,2,denote the conditional weight enumerating function for the constituent codes C in the PCBC.We want now to obtain the conditional WEF(Z)of the PCBC.For a given interleaver.this operation is exceedingly complicated.To facilitate the analysis,we consider the ensemble performance,where the ensemble of codes is generated by a uniform interleaver of length N and the component codes are fixed block codes. Definition [Benedetto]:A uniform interleaver of length K is a probabilistic device which maps a given input word of weight w into all distinct K permutations of it with equal N 4-41 d wz, wzd w B A   K   (4.53) denotes the average number of bit errors caused by transitions between the all-zero codeword and codewords of weight d. The set of all pairs (d, Bd) is called the code distance spectrum. With 0 / 2 1 ( ) 2 s dE N Pd e  , (4.51) becomes 0 0 / / , 1 0 1 2 cb cb K NK wR E N zR E N b wz w z w P e Ae K         / 0 1 1 ( ) 2 RE N c b K w w WZe w w WAZ K       (4.54) where Rc is the code rate. Using IOWEF, we can also express (4.52) (or (4.51)) as min , 1 0 2 K N c b b wd w dd w dR E P AQ   K N          (4.55) With the property that / 2 ( ) () x Q x y Q ye   , a tighter upper bound on bit error probability can be expressed as min 0 0 min min / / 0 2 cb cb N c b d R E N dR E N b d d d d RE P Q e Be N           min 0 0 min / 0 exp( / ) 2 (,) c b c b c b d RE N W Z RE N d RE W AW Z Q e N KW            (4.56)  Information Weight Distribution of PCC We now proceed to consider the weight spectrum of PCC. Let ( ) Ci A Z w , i=1, 2, denote the conditional weight enumerating function for the constituent codes i in the PCBC. We want now to obtain the conditional WEF ( ) CP A Z w of the PCBC. For a given interleaver, this operation is exceedingly complicated. To facilitate the analysis, we consider the ensemble performance, where the ensemble of codes is generated by a uniform interleaver of length N and the component codes are fixed block codes. Definition [Benedetto]: A uniform interleaver of length K is a probabilistic device which maps a given input word of weight w into all distinct         w K permutations of it with equal