the polar codes with different K/E ratios is shown in Fig. 4.48. GF(2) is the Galois field comprising two elements and the smallest finite field. One may also define GF(2) as the quotient ring of the ring of integers Z by the ideal 2Z of all even numbers GF(2) = Z/2Z. New Radio Access Physical Layer Aspects (Part 2) 529 4.1.7.3 Principles of Low Density Parity Check Coding LDPC codes belong to the class of forward error correction codes which are used for send- ing a message over noisy transmission channel. These codes can be described by a parity check matrix which contains mostly zeros and a relatively small number of ones. Thus the decoding complexity is small when compared to other code constructions. A very efficient iterative decoding algorithm known as belief propagation is used in the decoder. The LDPC codes can be divided into two groups: regular LDPC codes when the column weight and the row weight of the PC matrix are constant and equal and irregular LDPC codes when the column weight and the row weight are not constant and equal, meaning that the number of ones per row and column is different. The LDPC codes are represented in different ways. Similar to all linear block codes, a matrix representation by the corresponding generator matrix G or the PC matrix H is possible. Thus if the number of input information bits is K and the number of output bits is N, the PC matrix H is expressed as an M X N matrix, where M = N K. The resultant code rate K/N defines the size of the PC matrix. The LDPC codes can be further graphically represented with a Tanner graph, which is one of the most common graphical representations for the LDPC codes. It provides the complete representation of the code and helps to describe the decoding algorithm. Tanner graphs are bipartite graphs, that is, there are two disjunct sets of nodes. The two types of nodes are variable nodes (VND) and check nodes (CND). The VNDs represent the code bits, thus, each of the N columns of matrix H is represented by one VND. The CNDs represent the code