## 1 Introduction  
The initial approaches to reduce the effect of multipath impairment are broadly categorized into three main groups: diversity, multicarrier transmission, and their combinations. Diversity considerably reduces the probability of simultaneous fade on several replicas of the same information signal. Various diversity transmission techniques for fading environments have been extensively studied in [1, 2, 3, 4, 5]. In multicarrier modulation schemes like orthogonal frequency division multiplexing (OFDM), employing longer symbol durations effectively reduces the intersymbol interference (ISI), which can further be mitigated by utilizing cyclic prefixes. The effectiveness of OFDM and its application in combating ISI channels has been well investigated in [6]. Additionally, the combination of multicarrier modulation and diversity techniques has also been well addressed in the literature, e.g., [7, 8]. Later, with the emergence of machine learning algorithms like expectation propagation (EP), new attempts to mitigate multipath phenomena in both time and frequency domains have been pursued [9, 10]. However, EP has its drawbacks, such as numerical instabilities when performing distribution divisions [11]. As a result, our focus shifts toward the fundamental aspects of wireless communications. More recently, AI-assisted algorithms have been proposed to handle multipath channels [12]. In the first two studies, the channel parameters, such as the number of paths, path gains, and delays, are known as the receiver. To provide additional clarity, we will briefly outline the algorithm proposed in [9]. The receiver utilizes an equalizer based on EP. This equalizer employs the decoder feedback to execute the EP. Specifically, the posteriors generated by the decoder are mapped into Gaussian messages, with their means and variances dependent on channel impairments, such as channel taps. A similar methodology is applied in the frequency domain in [10]. In the last work, the number of channel taps is fixed, and it is assumed that the channel taps follow a Gaussian distribution with an exponential power profile, but the channel is not dense over a block of the received signal. The main contribution of this paper is the design of a receiver that, instead of depending on the low-pass equivalent of the channels, is based on front-end communication systems. This design allows for the use of the sum-product algorithm (SPA) to simultaneously track all multipath channel parameters. In addition, a discretization and modeling technique for unknown channel parameters is introduced, where the parameters are represented as Bernoulli random variables. The SPA is then used to track the unknown parameters. Notably, the receiver does not require prior knowledge of the channel parameters, such as the number of paths or Gaussian channel taps. Moreover, extending this algorithm to the general multipath channels is straightforward. This paper introduces a novel approach for performing joint partial path overlapping detection and channel decoding symbol by symbol in a dense partial path overlapping over a block of received symbols, utilizing the SPA on factor graphs. By focusing on front-end communication systems, we can track all unknown channel parameters through SPA on factor graphs. While this approach, i.e., the front-end receiver design using SPA, was initially proposed by the authors of this paper in [13], its advantages quickly gained the attention of researchers [14], where it has been named as discrete time models. In our study, we discretize channel parameters such as channel paths and attenuation coefficients, both in the channel low-pass equivalent (for illustrative purposes) and in the front-end strategy. These parameters are modeled as Bernoulli random variables with priors set to 0.5, denoted as path existence (_PE_) and attenuation existence (_AE_). Given a vector of observations, we factorize the joint posterior distribution of channel model parameters and codeword bits.