up to Pass t 1 Sample Clauses

up to Pass t 1. ≤ ≤ − (2) × × × H(1)

up to Pass t 1. For Pass 1, the initial bit error probability is given by p (= p(0)). Since the bit error probability does not change with the pass going on, the optimal weight deter- mined by (2.28) remains constant during the whole pass. As shown in Figure 2.3 in Subsection 2.5.1, w = 2 as long as the bit error probability is at least 0.20. Pass 1 up to Pass t − 1 are described in the following algorithm. Algorithm 2.5.1 Initialize i = 1; While p(i—1) ≥ 0.20 (1) Determine wopt = 2; (2) Construct H(i) according to the protocol; (3) Run the BPD p(i—1), H(i) algorithm and output p(i) with p(i) = p(i) = p(i—1) 2 + 1 − p(i—1) 2 , j = 1, 2, . . . , n; (4) Determine the information rate by (5) i ← i + 1. t ← i. In these passes, the individual bit error probabilities in vector p(i) are all equal, so the average bit error rate p(i) is also equal to the individual ones. Pass t and Pass t + 1 Pass t is the first pass with an initial bit error probability p(t—1) < 0.20. The optimal weight determined by (2.28) should have been larger than 2. However, the rule for selecting the optimal weight by (2.28) assumes that the row vectors constructed in some pass are involved in error corrections only in this very pass. Pass t is an exception to this assumption since the row vectors of Pass t may also be involved in the error corrections during Pass t + 1. The selection of the optimal weight wt should minimize the total amount of leaked information to remove all remaining errors. Since the bit error probability for the remaining bits is constant during Pass t, the optimal weight wopt is fixed as well. On the other hand, Equation (2.28) does apply to Pass t + 1 because almost all remaining errors will be corrected in this pass. There may be some (very few) errors left for subsequent passes to correct. Correcting these errors may also involve the vectors of Pass t + 1, but the number of errors left is so small (this has been verified by simulation results in [73]) that determining the optimal weight for Pass t + 1 by (2.28) gives negligible deviation. Pass t + 1 and Pass t are correlated in two aspects: first of all, the value of wt influences the initial average bit error rate p(t) for Pass t + 1. Secondly, error corrections in vectors of Pass t resulting from error corrections during Pass t + 1 decrease the average bit error rate of Pass t + 1. Now we are ready to describe how to estimate the amount of the information leaked to Eve from Pass t onwards until all errors are removed, given that...