re denoted by do, d1 dN-1 where N = 66Z for base graph 1 and 50Z- for base graph 2, where the value of lifting factor Z is given in Table 4.7. A code block is encoded by the LDPC encoder based on the following procedure [7]: 534 Chapter 4 1. Find the set with index iLS in Table 4.7 which contains Zc. 2. Set dk-2Z = Ck, Ak 2Zc,..., K - 1. 3. Generate N 2Z parity bits W = H[c w] T =0. 4. The encoding is performed in GF(2). For base graph 1, matrix HBG (representing the base graph) has 46 rows and 68 columns. For base graph 2, matrix HBG has 42 rows and 52 columns. The elements of HBG matrices are given in [7]. The PC matrix H is obtained by replacing each element of HBG with a Z X Z matrix such that each ele- ment of value 0 in HBG is replaced by an all zero matrix 0 of size Z X Zc; and each ele- ment of value 1 in HBG is replaced by circular permutation matrix I(Pij) of size Z X Z, where i and j are the row and column indices of the element, and I(Pi.j) is obtained by circularly shifting the identity matrix I of size Z X Z to the right Pij times. The value of Pij is given by Pij = Vij mod Z and the value of Vi.j is given in [7]. 5. Set dk-2Zc = Wk-K, = K, N + 2Z - 1. The performance of the NR LDPC codes over an AWGN channel was evaluated using a normalized min-sum decoder, layered scheduling, and a maximum of 20 decoder iterations. Fig. 4.51 shows the required SNR to achieve certain BLER targets as a function of informa- tion block size K for code rate 1/2 and QPSK modulation. The results show that the NR LDPC codes provide consistently good performance over a large range of block sizes. For this code rate, base graph 2 is used for all K for which it is defined, that is, for K < 3840, while base graph 1 is used for larger values of K (note the discontinuity point in the curves at K = 3840). As shown in the figure, there is a small gap in performance at the block size where the transition occurs between base graph 1 and base graph 2 [55]. Target BLER = 10-1 Target BLER = 10-2 Target BLER = 10-3 Information block si