posed schemes. Lastly, Section 9.5 concludes the chapter. 9.2 System Model In this section, we introduce the FL model update and FL model compression schemes including quantization and sparsification. The main notations used in the chapter are sum- marized in Table 9.1. 9.2.1 FL Model Update The system considers a total of N edge devices that distributively and collaboratively build a global learning model [178]. Each device or user collects and maintains its own raw data Table 9.1 Summary of notations. Notation Definition N; K; C Number of edge devices connected to PS; number of edge devices participating FL in each round; fraction of participating devices, i.e. C = K/N, 0 < C < 1 Features of data point j; label of data point j; parameter set describe the mapping from Xi to y f(.); n Loss function; learning rate Dk; IDkl Dataset on user k; cardinality of the dataset Dk hk; ho Channel coefficient of user k; large-scale fading of user k; small-scale fading, ho~CN(0,1) ~ Power of user k; transmitter and receiver antenna gain; distance between user and PS A; a;nt Signal wavelength; path-loss exponent; additive noise gkist;Rk Gradient of user k; encoded gradient update from user k at communication round t; data rate of user k GS(.); GQ(.) Gradient sparsification function; gradient quantization function 9.2 System Model locally. ML generally finds the mapping between features Xj and label yj. A loss function f(xj, yj; ij) is used to capture the error between this mapping. Typical loss functions used include linear regression and root-mean-squared error. Each user performs learning algorithms locally. Essentially, local learning at user n aims to solve the following problem: (9.1) Different from the traditional learning process where e{D1,D2,...,DN} , are placed in the same location, FL can rely on the distributed stochastic gradient descent (SGD) method to perform update in each iteration. Specifically, the loss function in (9.1) can be generalized across multiple devices as: (9.2) where |D|= In each training round, F