pressions, sequence ON denotes the set of information bit indices in the polar sequence QN-1, and OF is the set of other bit indices in polar sequence QN-1 where Q and OF are derived through subblock interleaving, (i.e., cardinality of the set or the length of the sequence), and NPC is the number of PC bits (see Table 4.15). Table 4.15: Polar sequence QNmax 1 and the associated reliability factor W(QNmax) [7]. QNmax W(QNmax) QNmax W(QNmax) QNmax QNmax W(QNmax) QNmax QNmax QNmax QNmax 528 Chapter 4 K/E 59/512 K/E 56/864 K/E 43/184 K/E =43/180 K/E 67/128 K/E 54/124 K/E 163/240 K/E 164/240 K/E 307/360 K/E 164/184 SNR (dB) SNR (dB) Downlink polar coding, CRC-24, and list size = 8 Uplink polar coding, CRC-11, list-size = 8 Figure 4.48 Downlink/uplink polar coding with various K/E ratios [67]. Once the input bits are reordered and moved to the reliable positions according to the above reliable bit positions determination procedure, the reordered bits are passed through the polar encoder [7]. As we defined earlier, the polar code generator matrix GN = (G2) is constructed as the nth Kronecker power of matrix G=1|] For a bit index j = 0,1,...,N - 1, let gj denote the jth row of GN and w(g) the row weight of gj, where w(gj) is the number of ones in gj. Let us further assume that QPC is the set of bit indices for PC bits, where the car- dinality of the set is Qpc NPC. number of PC bits are placed in the (npc - nxm) least reliable bit indices in Q . . Other PC bits are placed in the bit indices of minimum row weight in ON where ON denotes the e npc) most reliable bit indices in Q If there are more than NPC bit indices of the same minimum row weight in ON the other PC bits are placed in the NPC bit indices of the highest reliability and the minimum row weight in Q . The output bit sequence following polar encoding d = [do,d1,..., dN-1] is obtained as = uGN where vector u = [uo,U1,..., UN-1] is derived from interleaved sequence following the above bit reordering process. The encoding is performed in GF(2)¹. The performance of 