# Memory-Based LT Codes for Efficient 5G Networks and Beyond
###### Abstract  
The next-generation networks (5G and beyond) require robust channel codes to support their high specifications, such as low latency, low complexity, significant coding gain, and flexibility. In this paper, we propose using a fountain code as a promising solution to 5G and 6G networks, and then we propose using a modified version of the fountain codes (Luby transform codes) over a network topology (Y-network) that is relevant in the context of the 5G networks. In such a network, the user can be connected to two different cells at the same time. In addition, the paper presents the necessary techniques for analyzing the system and shows that the proposed scheme enhances the system performance in terms of decoding success probability, error probability, and code rate (or overhead). Furthermore, the analyses in this paper allow us to quantify the trade-off between overhead, on the one hand, and the decoding success probability and error probability, on the other hand. Finally, based on the analytical approach and numerical results, our simulation results demonstrate that the proposed scheme achieves better performance than the regular LT codes and the other schemes in the literature. 5G; LT codes: channel codes; network coding; fountain code +
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result, there will be no collisions on such a network. Moreover, these three links are modeled as binary erasure channels (BECs) with different erasure probabilities. In the fountain codes, the transmitter sends a stream of encoded symbols over the channel and then adjusts the number of encoded symbols (i.e., code rate) depending on the channel's properties. Such a process is achieved without prior knowledge of the channel's properties (e.g., CSI) at the transmitter. In other words, fountain codes can work in the absence of a feedback channel, even in nasty channels [8; 9; 10]. Such codes work on erasure channels such as binary erasure channels (BECs) [9; 11; 12], as well as noisy channels such as AWGN channels [13; 14; 15] and fading channels [16; 17]. In practice, Luby transform (LT) codes [9] and Raptor codes [18], which are the most well-known and widely used fountain codes, are utilized to enrich the transmission efficiency of the point-to-point communications. LT codes can potentially generate an endless number of encoded bits/symbols from the source data and then send these encoded bits/symbols to the destination. Once the destination receives an adequate number of encoded bits, it can decode them and obtain the source bits. Therefore, one of the most essential design parameters of LT codes is the degree distribution that defines the encoding and decoding complexities. Luby proposes two types of distributions, namely ideal soliton distribution (ISD) and robust soliton distribution (RSD) [9]. Additionally, shaping the left degree distribution (i.e., the degrees of the source nodes) of LT codes improves the performance of the point-to-point communications [19]. Hence, this algorithm is referred to as memory-based-LT (MBLT). Recently, the concept of distributed fountain codes (DFC) has been used to send data from multiple sources to a destination through a common relay [20; 21; 22; 23; 24]. However, the concept of DFC deals with sources of different data. Therefore, to deal with sources of the same data in the Y-network topology (Figure 1), we propose using the MBLT codes in both sources and then using a buffer-and-forward (BF) strategy at the relay. Moreover, the proposed scheme can be used in other topologies, such as a multi-source single-sink relay network with an arbitrary number of sources [25; 26; 27]. In this paper, we analyze coding schemes for the Y-network. Then, we present a novel approach to designing LT code over the Y-network where the concept of memory-based is applied at both sources, and then the relay uses a buffer-and-forward strategy.