Abstract Recent advances in deep learning have significantly improved recommendation systems. However, these methods often rely heavily on labeled data, leaving challenges like data sparsity and the cold-start problem unresolved. Self-supervised learning, particularly Graph Contrastive Learning (GCL), has emerged as a powerful approach to mitigate these issues by generating informative views from unlabeled data, attracting considerable attention in recent years. This survey provides a timely and comprehensive review of current GCL-based recommendation methods. First, it introduces a comprehensive framework and taxonomy for view construction in GCL for recommendation systems, dividing it into three main types: structure generation, feature generation, and modality generation. Each category is analyzed in detail, offering insights into their methodologies, strengths, and limitations. Comparative experiments and visualization experiments are conducted on three public datasets, analyzing the complexity of various methods to guide the selection of appropriate approaches. The survey also highlights existing limitations and proposes future research directions along with potential roadmaps to inspire innovative solutions in recommendation systems.

Multimodal recommendation systems struggle to effectively integrate heterogeneous modalities and select informative negative samples, which limits their ability to capture users' true preferences. To address these challenges, we propose Preference-Aware Multimodal Contrastive Learning (PAMCL), a novel framework that leverages a lightweight large language model (LLM) to generate explicit user preference descriptions for guiding the recommendation process. Our approach introduces a simplified multimodal graph aggregation mechanism that unifies feature propagation and contrastive learning, enhancing semantic consistency while reducing computational complexity. Addition ally, we develop a preference-guided multiple negative sampling strategy that utilizes LLM-generated preference embeddings to identify challenging negative samples while avoiding false negatives. Experimental results on three public multimodal recommendation benchmarks demonstrate that PAMCL significantly outperforms state-of-the-art methods by effectively addressing false negative issues in sampling and noise contamination in multimodal fusion.

We study the analog network coding (ANC), which is a well-known amplify-and-forward (AF)-based bidirectional protocol, for a bidirectional network consisting of two different sources and a relay. In this protocol, the two sources exchange information with the help of the relay during two time slots in a half-duplex mode. For this system, we first derive a tight lower bound of outage probability, which is very close to the exact outage probability in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Using the tight lower bound, we obtain finite-SNR diversity-multiplexing tradeoff of the ANC protocol. Furthermore, we propose an optimum power allocation scheme, which simultaneously minimizes the outage probability and maximizes the total mutual information of the ANC protocol.

Time division broadcasting (TDBC) is a well-known bidirectional protocol. In this protocol, two sources exchange information with the help of a relay terminal. For amplify-and-forward (AF)-based TDBC, we first derive a tight lower bound of the outage probability in closed-form, and it is very close to the exact outage probability in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Using the tight lower bound, diversity-multiplexing tradeoff of the TDBC protocol is obtained for finite-SNR. Furthermore, we investigate how to optimize the TDBC protocol; specifically, an optimum method to combine the received signals at the relay terminal is developed. This method minimizes the outage probability and maximizes the total mutual information of the TDBC protocol at the same time.

This paper focuses on the average bit error rate (BER) and diversity order analysis of the distributed Alamouti's code in dissimilar cooperative networks with channel state information (CSI)-assisted relays. We first assume that the relays adopt the amplifying coefficient proposed in . Lower and upper bounds of the average BER of the distributed Alamouti's code are derived. Those two bounds tightly bound the exact average BER. Then we show that, surprisingly, the distributed Alamouti's code achieves only diversity order one when the relays use the amplifying coefficient proposed in . To resolve this problem, we propose a new threshold-based amplifying coefficient for the distributed Alamouti's code based on the work in . This new amplifying coefficient makes the distributed Alamouti's code achieve the full diversity order two. Moreover, based on three different CSI assumptions, four amplifying schemes are developed in order to determine the value of the threshold used in the new amplifying coefficient.

Recently, single-symbol maximum-likelihood (ML) decodable distributed space-time block coding (DSTBC) has been developed for use in cooperative diversity networks. However, the symbol rate of the DSTBC decreases with the number of relays. This issue can be addressed if the channel phase information (CPI) of the first-hop is exploited, and such code is referred to as DSTBC-CPI. Some complex single-symbol decodable DSTBCs-CPI were reported in the literature. However, no upper-bound on the symbol rate of such DSTBC-CPI has been derived, although it is a fundamental issue. Furthermore, finding a tight (more preferably achievable) upper-bound is essential to check if any developed code is optimum or not. In this letter, we derive an upper-bound on the symbol rate of real single-symbol decodable DSTBC-CPI and show that the bound is independent of the number of relays in the network. Finally, we demonstrate that our derived bound is actually achievable.

Analog network coding (ANC) and time division broadcasting (TDBC)are two major protocols used in bidirectional cooperative networks with half-duplex terminals. Most previous work on those two protocols was based on the assumption that there was no direct channel between the two sources. In this paper, we remove this limitation and investigate both protocols in a general bidirectional cooperative network with a direct channel between the two sources. Lower bounds on the outage probabilities of the two protocols are derived first. These lower bounds are very close to the exact outage probabilities in the whole signal-to-noise ratio (SNR) range irrespective of the values of channel variances. Based on the lower bounds, the finite-SNR diversity-multiplexing tradeoffs (DMTs) of the ANC and TDBC protocols are obtained. These tradeoffs establish a framework which enables us to make a comprehensive comparison between both protocols.

An amplify-and-forward, multi-branch, multi-hop relay system with K relays, in which the relays broadcast to other relays as well as the destination, is analyzed. An approximate symbol-error-rate (SER) expression, which is valid for any number of relays and for several modulation schemes, is found for the multi-hop system. Also, the cumulative density function (CDF) and probability density function (PDF) are found for the random variable, Z = XY/(X + Y + c), where X and Y are sums of independent, Erlang random variables, and c is a constant. The moment generating function (MGF) of Z is found for the special case in which c = 0. It is shown that these results are generalizations of previously published results for special cases of Z. The MGF of Z is used to develop the approximate SER expression. Results for the analytic SER expression are included and compared with simulation results for various values of K, for various modulation schemes, and for two choices of system parameters (channel variances). Results for the multi-hop system are also compared to results for the two-hop system (in which relays transmit only to the destination).

In this paper, we first propose an optimum relay ordering algorithm for the multi-branch multi-hop cooperative diversity networks. This optimum algorithm has a high complexity that makes it hard to implement. Therefore, a suboptimum relay ordering algorithm, which considerably reduces the complexity, is then developed. Furthermore, for a cooperative network with two relays, we analytically evaluate the performance of the suboptimum algorithm by using an approximate end-to-end signal-to-noise ratio expression. Specifically, an approximate probability of wrong selection and an approximate expression of the symbol error rate are derived. The analysis and the numerical results demonstrate that the suboptimum algorithm performs very well as the optimum one at a much lower complexity.

This paper focuses on error performance analysis of distributed Alamouti's code. Recently, many works have been devoted to the performance analysis of this code. In order to simplify the analysis, however, they either assumed the channels in the cooperative network had the same variances or only considered asymptotic error performance at high signal-to-noise ratio (SNR) range. In this paper, we study a general dissimilar cooperative network, where the channels have different variances. Two accurate approximate bit error rate (BER) expressions are proposed in order to evaluate the error performance of the distributed Alamouti's code. We also investigate how the values of channel variances affect the accuracies of the proposed approximate BER expressions. Our results demonstrate that the proposed approximate BER expressions are very close to the exact BER over the whole SNR range. Furthermore, we show that the average BER of the distributed Alamouti's code behaves like(ln(E)/E)2when the transmission powerEis sufficiently large.

In this paper, a new opportunistic source selection (OSS) protocol is studied in bidirectional cooperative networks. Unlike existing protocols, this protocol exploits multiuser nature of the bidirectional cooperative networks and it opportunistically supports two traffic flows based on instantaneous channel conditions. This makes the OSS protocol much more reliable than existing protocols. In order to show the performance improvement, we first derive a lower bound of the outage probability of the OSS protocol. Numerical results demonstrate that this lower bound is extremely tight and it indicates that the OSS protocol achieves full diversity order two in a bidirectional cooperative network with two sources and one relay. Then exact and approximate lower bounds of average bit error rates (BERs) at both sources in the OSS protocol are derived. Those lower bounds are very close to the exact average BERs as shown by numerical results. Lastly, an optimum power allocation scheme is developed for the OSS protocol. This scheme can optimize the outage probability, average BER, and data-rate of the OSS protocol at the same time.

This letter focuses on the broadcasting phase of bidirectional cooperative networks with multiple decode-andforward relays. In this phase, the relays first combine the information-bearing symbols transmitted by the sources, and then broadcast them back to the sources in order to achieve bidirectional communications. Two different combining methods at the relays are considered. The first one is that the relays transmit linear combinations of the information-bearing symbols to the sources by beamforming. We develop an algorithm that can compute the optimum beamforming vector in closed form and this beamforming vector minimizes the outage probability of the bidirectional cooperative network. The second method is that the relays combine the information-bearing symbols by exclusive-or and then transmit them to the sources by beamforming. For this case, we show that the instantaneous signal-to-noise ratios at the sources depend on the values of the information-bearing symbols. Based on [1], the optimum beamforming vector is computed and it minimizes an upper bound of the outage probability of the bidirectional cooperative network.

Very recently, we proposed the row-monomial distributed orthogonal space-time block codes (DOSTBCs) in [1] and showed that the codes achieved approximately twice higher bandwidth efficiency than the repetition-based cooperative strategy. In [1], we assumed that the relays did not have any channel state information (CSI) of the channels from the source to themselves, i.e. the channels of the first hop. However, we notice that this CSI can be readily obtained at the relays without any additional pilot signals or any feedback overhead. Therefore, in this paper, we assume that the relays have partial CSI of the first hop and use this information to construct the codes. We refer to those codes as the row-monomial DOSTBCs with channel phase information (DOSTBCs-CPI) and derive an upper bound of the data-rate of the codes. This upper bound suggests that the row-monomial DOSTBCs-CPI have higher bandwidth efficiency than the row- monomial DOSTBCs in [1], especially in a cooperative network with many relays. Furthermore, we find the actual row-monomial DOSTBCs-CPI achieving the upper bound of the data-rate.

Very recently, we proposed the distributed orthogonal space-time block codes (DOSTBCs) in [1]. We showed that the DOSTBCs achieved the single-symbol maximum likelihood (ML) decodability and the full diversity order. Furthermore, we studied some special DOSTBCs, namely the row- monomial DOSTBCs, which generated uncorrelated noises at the destination. We showed that the row-monomial DOSTBCs achieved approximately twice higher bandwidth efficiency than the repetition-based cooperative strategy. However, the data-rate of the DOSTBC was not analyzed in [1]. In this paper, we consider the general DOSTBCs, which possibly generate correlated noises at the destination. We derive an upper bound of the data- rate of the DOSTBC. This upper bound is larger than that of the row-monomial DOSTBC, and hence, the DOSTBCs can potentially improve the bandwidth efficiency of the cooperative network.

In this paper, we focus on the diversity order of the decode-and-forward (DF) cooperative networks with relay selection. Many detection schemes have been proposed for the DF; but it has been shown that the cooperative maximum ratio combining (C-MRC) can achieve almost the same performance as the optimum maximum likelihood detector and has a much lower complexity. Therefore, we first combine the C-MRC with the relay selection and show that it achieves the full diversity order by deriving an upper bound of its average bit error rate (BER). In order to reduce the signaling overhead, we then combine the link-adaptive regeneration (LAR) with the relay selection. By deriving an upper bound of the average BER, we show that, when there are two relays, the diversity order of the LAR with relay selection is upper-bounded by three and lower-bounded by 3 - epsiv, where xi is an arbitrarily small positive number.

In this paper, we focus on the decode-and-forward (DF) cooperative networks with relay selection. Many detection schemes have been proposed for the DF; but it has been shown that the cooperative maximum ratio combining (C-MRC) can achieve almost the same performance as the optimum maximum likelihood detector and has a much lower complexity. Therefore, we first combine the C-MRC with the relay selection and show that it achieves the full diversity order by deriving an upper bound of its average bit error rate (BER). In order to reduce the signaling overhead in the C-MRC with relay selection, a novel detection scheme, namely product MRC (P-MRC), is proposed for the DF and it achieves the same diversity order as the C-MRC. Then we combine the P-MRC with the relay selection and show that it achieves the full diversity order by deriving an upper bound of its average BER.

We jointly optimize the relay-precoders and decoders with full or partial channel side information (CSI) in a cooperative network. Specifically, three different CSI assumptions are considered: 1) full CSI at the destination terminal and the relay terminals; 2) full CSI at the destination terminal and partial CSI at the relay terminals; 3) partial CSI at the destination terminal and the relay terminals. We show that, under the assumption of full CSI at the destination terminal and the relay terminals, the optimum relay-precoder is the cooperative transmission beamforming and the optimum decoder is a maximum ratio combiner. Under the two partial CSI assumptions, the optimum relay-precoders and decoders work in a fashion of channel selection. It is demonstrated that the proposed optimum relay-precoders and decoders improve the performance considerably

In this correspondence, the distributed orthogonal space-time block codes (DOSTBCs), which achieve the single-symbol maximum likelihood (ML) decodability and full diversity order, are first considered. However, systematic construction of the DOSTBCs is very hard, since the noise covariance matrix is not diagonal in general. Thus, some special DOSTBCs, which have diagonal noise covariance matrices at the destination terminal, are investigated. These codes are referred to as the row-monomial DOSTBCs. An upper bound of the data-rate of the row-monomial DOSTBC is derived and it is approximately twice higher than that of the repetition-based cooperative strategy. Furthermore, systematic construction methods of the row-monomial DOSTBCs achieving the upper bound of the data-rate are developed when the number of relays and/or the number of information-bearing symbols are even.