 shortening, or repetition are applied to change the N-bit vector y into the E-bit vector A channel interleaver is finally applied to compute the vector f that is now ready to be mod- ulated and transmitted [36]. The NR polar encoder relies on several parameters that depend on the amount and type of information to be transmitted and the physical channel used. The first parameter that needs to be identified is the code length of the polar code, N = 2n. The number n is calculated as n = max {min {n1, N2, nmax}, nmin}, where nmin and nmax provide a lower and an upper bound on the code length, respectively. In particular, nmin=5 and nmax = 9 for the downlink control channel, whereas nmax 10 for the uplink control channel. The parameter N2 = log2 (K/Rmin) gives an upper bound on the code rate based on the minimum code rate admitted by the encoder, that is, 1/8. The value of parameter n1 is dependent on the rate-matching scheme. It is usually calculated as n1 = log2E SO that 2nd is the smallest power of two larger than E. However, a correction factor is introduced to avoid too severe rate matching: if log2E < 0.17, that is, if the smallest power of two larger than E is too far from E, the parameter is set to n1 = log2E In this case, an additional constraint on the code dimension is added by imposing KE <9/16 to ensure that K < N. If a code length New Radio Access Physical Layer Aspects (Part 2) 525 Table 4.14: 3GPP NR polar encoding parameters [7]. PUCCH/PUSCH PDCCH/PBCH No 20 12 < Nc 19 E - No VI 175 E - Nc > 175 N > E is selected, the polar code will be punctured or shortened, depending on the code rate before the transmission. In particular, if the code will be punctured; otherwise it will be shortened. If N < E, repetition is used, and some encoded bits will be transmitted twice. In this case, the code construction ensures that K <N. As shown in Table 4.14, a set of parameters are defined to differentiate between different type of control information. The parameters I LL and IBIL refer to the activation of the inpu