## 1 Introduction
In a few words, two recursive systematic convolution encoders separated by an interleaver are used to build a turbo encoder. Polar codes are constructed based on the concept of channel polarization. In the case of decoding, the turbo decoder is based on the BCJR (Bahl, Cocke, Jelinek, and Raviv) or MAP algorithms [16]. On the other hand, the decoding of polar codes is based on the successive cancellation algorithm [18]. Regarding LDPC encoding, both the base matrix and expand factor were utilized in order to exemplify the parity check matrix H [17]. The encoding of LDPC in the 5G standard implied the usage of a base matrix of 42 \(\times\) 52 size (base graph 2). In preparation for LDPC, codes decoding the algorithm of sum product (or message passing) was applied. The simple enhancements made in this paper to 5G LDPC codes, polar codes, and 3G and 4G turbo codes using equalization techniques could also be considered, for example, to improve performance in the field of digital communications. The landmark codes such as turbo, LDPC, and polar are widely used in modern communication system standards. Starting from the general results obtained in Section 5 of this paper, further results could be obtained using specific standards such as 3 GPP-LTE, WiMAX, and WiFi, concerning turbo codes, or 5G machine type communication applications, such as ultra-reliable low-latency communications (URLLC) and massive machine-type communication (mMTC) concerning the LDPC and polar codes [19; 20]. Several decoding and equalization receiver schemes designed for different standards have been proposed in the literature [21; 22; 23]. Depicting the performance of AWGN channels in the presence of ISI, the paper focused on only the most advanced forward error correction schemes, such as turbo codes, LDPC codes, and polar codes, due to their great effect on the existing communications standards (long term evolution (LTE) and 5G standards) and their high efficiency, since they can perform near the channel capacity [24]; this analysis also applies to the other codes, such as RS codes (Reed-Solomon), Raptor codes, and so on. The main purposes of this paper are summarized as follows:* This paper presents a novel LDPC least square (LS) channel estimator, using the LLR (log-likelihood) fed back from the LDPC decoder to iteratively improve the channel estimation. * In addition, this paper presents a novel polar least square (LS) channel estimator, achieved based on the sequence obtained at the output of the polar decoder to iteratively improve the channel estimation. * In the working SNR range, the iterative LS estimation of the channel response to the impulse offers substantial improvements regarding the performance of all three types of codes (LDPC codes, polar codes, and turbo codes) compared to estimation only once, and the LDPC codes seemed to give the best results. Additionally, computer simulation results are presented to confirm this assertion. It should be noted that there are works, such as those previously mentioned, that individually evaluated the performance of turbo codes, LDPC codes, or polar codes using specific standards, but this paper is the first to highlight the performance of the three codes simultaneously using the same AWGN channel model and applying different equalization techniques. It BPSK (binary phase-shift keying) modulation was assumed in this paper, but the analysis could be applied to other modulation methods as well. Thus, in future, these results will help in choosing or implementing different types of codecs, depending on the application. For the moment, this integrative paper can be considered a good starting point for researchers who are focused on increasing the accuracy of the application of signal equalization techniques at the reception side.