hing PCM at the decoding side. In the following section, we provide a quick overview of basic code construction details and the 5G coding chain. 6.13.1.1 5G LDPC Code Design The 5G LDPC design [5] is mainly based on two base graphs, where each base graph has eight different shift coefficient designs. Each of these shift coefficient designs is further extended to support multiple lifting sizes. To explain this in more detail, we have to consider the fundamentals of QC-LDPC codes. 6 5G Physical Layer The representation of an QC-LDPC PCM, H, can be as follows: P(N-K)),1 P(N-Kj),2 P(N-K),3 P(N-K1),N where Pi,j is a cyclic-permutation matrix obtained from the zero matrix and Z by the Z cyclically shifted identity matrix to the right (z is the lifting size). Also, Pi,j often repre- sented as a numerical entry which is the value of the shift. All the nonzero entries of H define the connections between check and variable nodes, and this is generally known as the base graph. For base graph #1 in NR, N = 68 and Kb = 22, which in turn provides the dimensions mentioned in Figure 6.46. In general, the base graph defines the structure of the code and defines the basic frame- work for the hardware dimensions of the encoding/decoding. 5G LDPC base graphs contain specific design components that can be illustrated as in Figure 6.47 The 1's in the matrix represent the nonzero elements of the shift coefficient designs, where each shift coefficient design has a numeric value that defines the cyclic shift used in the parity PCM. The 0 represents a zero matrix with the dimension used in the lifting Figure 6.47 Structure of 5G LDPC base graph #1 6.13 Channel Coding with 5G size. The parts of the base graph #1 (base graph #2 also has similar parts with different dimensions) are as follows: Matrix A and B correspond to the kernel part, where the highest code rate is defined. Matrix A further corresponds to the systematic bits. Matrix B is a square matrix and corresponds to the parity bits; it has a dual diagonal structure (i.e. main diago