## 1 Introduction  
The theory of information transmission has experienced huge growth since the work of [PERSON] (1948) demonstrated the theoretical possibility of reliable transmission [1]. Two main classes of technique make it possible to ensure the reliability of a transmission: channel coding, which aims to code the transmitted message in such a way that the receiver can correct most transmission errors; and equalization, the objective of which is to make the best use of the bandwidth of the medium (transmission channel) [2, 3]. In practical communication systems, transmitted signals are subject to various distortions, such as noise, inter-symbol interference (ISI) due to multipath propagation, and the nonlinear effects of amplifiers. All these factors alter the original signal, so it is essential to restore the channel's input by observing its output. The process of restoring the original signal consists of the application of a channel equalizer [4, 5]. This is where the techniques of equalization and channel estimation come in, the purpose of which is to determine the disturbances of the channel to eliminate them or at least limit their impact on the transmitted signal. These systems are sized to optimize certain transmission quality criteria, thanks to very powerful mathematical tools and sophisticated algorithms. The role of the equalizer filter is to use the observations of the channel to restore the transmitted signal and reduce the distortions caused by the channel as much as possible [6, 7, 8, 9, 10, 11]. The problem is to estimate the values of the coefficients of the equalizer filter, to allow restoring the transmitted signal with a low probability of possible error. An optimization of the coefficients of the equalizer filter that minimizes in the most precise manner the probability of the appearance of these errors is strongly desired. Several criteria for optimizing these coefficients are recommended; the most used being that of minimizing the mean square error (MMSE). Although an MMSE equalizer provides a good performance, a simple approach to designing a zero forcing equalizer at the level of the receiver was considered in [12]. Optimization theory also offers various algorithms; examples include gradient algorithms, the Viterbi algorithm, etc. [10; 13]. The choice of algorithm is essentially linked to the choice of the criterion. The Viterbi algorithm, for example, is applied to a maximum likelihood criterion, while the gradient algorithms are related to non-linear criteria, such as the mean square error (MSE) [14; 15]. The choice of structure is determined by both the criterion and the optimization algorithm. Two fundamental structures are presented in the literature: the transverse structure, and the lattice structure. These structures are designed using finite impulse response filters (FIR) or infinite impulse response (IIR) [15]. Structures of the non-linear type are filter-based but have a non-linear behavior, such as architectures with decision feedback [10; 15]. These equalizers have the main function of inverting the response of the transmission channel, so that the \"channel-equalizer\" couple can be considered an ideal channel. The equalization operation can cause, depending on the nature of the equalizer used, more or less significant increases in the noise present at its input [10]. This research investigates the situation when error correcting codes, such as turbo codes, LDPC codes, and polar codes are applied over the AWGN channels that present ISI. More precisely, it was proposed to research the equalization and the estimation of an AWGN channel in the context of the use of the three most efficient codes; and indeed the turbo codes, LDPC codes, and polar codes proposed in [16; 17; 18] make it possible to achieve performances quite close to the Shannon limit, even over the AWGN channels. Some aspects related to coding and decoding the fields of use of turbo codes, LDPC codes, and polar codes were treated in [19; 20].