 block CRC generator appends a 16-bit FEC block CRC to each FEC block. The cyclic generator for FEC block CRC encoding is given by GFB-CRC (D) = D16+D15 + D2 + 1. The step-by-step procedure for calculation of the modulation and coding schemes in IEEE 802.16m is shown in Figure 9-46. The FEC encoder input bits are denoted by d1, d2, d3, dNFB with d1 representing the MSB and NFB being the size of the FEC encoder input inclusive of 16-bit FEC block CRC and the parity bits produced by the FEC block CRC generator being denoted by p1, P2, P3, P16. The FEC block CRC encoding is performed in a systematic form, which means that in GF(2), the polynomial viA finite field is a field with a finite number of elements, which is also called a Galois field. The order or the number of elements of a finite field is always a prime or a power of a prime. For each prime power, there exists exactly one finite field GF(p"), which is often expressed as Fp m in the literature, where GF(p) is called the prime field of order p, and is the field of residue classes modulo p, where the p elements are denoted 0, 1, 2, p 1. In GF(p) the two expressions a III b and a = b modp are equivalent. The finite field GF(2) consists of elements 0 and 1 which satisfy the following addition and multiplication properties: [67,68] 9.12 Channel coding and modulation Obtain /size-offset 2 and Allocation Size from A-MAP IE Obtain Modulation Order M from Table 9-8 Obtain minimum-size from Table 9-7 Calculate Index= !minimum-size / /size-off Obtain NDB and KFB from Table 9-6 FIGURE 9-46 The procedure for calculation of coding and modulation parameters + ... + + P15D + P16 yields a remainder of zero when divided by GFB-CRC (D). Each FEC block is encoded using the convolutional turbo coder. The IEEE 802.16m CTC encoder uses a double binary Circular Recursive Systematic Convolu- tional (CRSC) code. Duo-binary turbo codes are built from parallel concatenation of two RSC component codes, each with two inputs. There are several advantages for this construction compared t