Systems, methods and computer-accessible medium for providing learning-based compress-and-forward schemes for relay channel(s)

Abstract

Exemplary systems, methods and computer-accessible medium according to the exemplary embodiments of the present disclosure are provided for creating a compress-and-forward communication format. Thus, the exemplary systems, methods, and computer-accessible medium observe the signal transmitted from a source configuration at a relay configuration and the destination, compress the signal observed by the relay configuration using an artificial intelligence (AI) model based on a correlation of the relay to the destination. The AI-based model can exploit the correlation at the relay's compressor and the destination's demodulator. In addition, the compressor at the relay works without visibility of the signal observed by the destination configuration. The relay configuration can forward the compressed signal to the destination, and the destination configuration can demodulate information associated with the transmitted signal based on a combination of the signal observed by the destination configuration and the compressed signal received from the relay.

Description

P300735 - 109197.0000195PATENT APPLICATION SYSTEMS, METHODS AND COMPUTER-ACCESSIBLE MEDIUM FOR PROVIDING LEARNING-BASED COMPRESS-AND-FORWARD SCHEMESFOR RELAY CHANNEL(S)CROSS-REFERENCE TO RELATED APPLICATION(S)

[0001] This application relates to and claims priority from U. S. Patent Application No.63 / 745,618, filed on January 15, 2025, the entire disclosure of which is incorporated herein by reference.STATEMENT REGARDING FEDERALLY FUNDED RESEARCH

[0002] This invention was made with government support under 1925079 and 2003182 awarded by the National Science Foundation. The government has certain rights in the invention.FIELD OF THE DISCLOSURE

[0003] The present disclosure relates generally to multi-user communications, and more specifically to systems, methods and computer accessible medium for facilitating compress-and-forward schemes on relay channel(s).BACKGROUND INFORMATION

[0004] A relay channel, as introduced by van der Meulen (see, e.g., Ref. 2), can be considered as a building block of multi-user communications. In this model, a relay facilitates communication between a source and a destination by forwarding its “overheard” received signal to the destination. As such, the relay channel comprises a broadcast channel, from the source to both the relay and the destination, and a multiple access channel, from both the source and the relay to the destination. The relay channel forms the foundation of cooperative networking, which has been shown to be effective in mitigating fading (see, e.g., Refs. 3, 4), increasing data rates (see, e.g., Ref. 5), and managing interference (see, e.g., Ref. 6). With the advent of 6G, new forms of relaying and cooperation are envisioned for communicating in highly dynamic settings. (See, e.g., Refs. 7, 8).

[0005] Despite decades of research, the capacity of the general relay channel may still currently be unknown. Cover and El Gamal (see, e.g., Ref. 9) provided upper and lower boundsP300735. W0.01 - 109197.0000195PATENT APPLICATIONfor the general relay channel by invoking information theoretic achievability and converse arguments. These bounds coincide only in a few special cases, such as the physically degraded Gaussian relay channel. Even though optimum relaying strategies are not known in general, various effective relaying techniques have been proposed, which can be broadly categorized into two main classes: decode-and-forward (DF) and compress-and-forward (CF); (see, e.g., Ref. 9) for a detailed analysis of DF, CF, their variations and combinations. While DF can be efficient in certain scenarios (see, e.g., Ref. 5), its achievable rate is bounded by the capacity of the source-to-relay channel since the relay is required to perfectly decode the source information.

[0006] On the other hand, in CF, the relay refrains from directly decoding the source and instead, compresses its received signal to send to the destination. Upon reception of the compression index, the destination combines it with its own received signal to decode the source information. Given that the received signals at the relay and destination are correlated, the relay can leverage distributed compression techniques to reduce the compression rate without requiring explicit knowledge of the received signal at the destination. As such, it can utilize Wyner-Ziv (WZ) source coding (see, e.g., Ref. 10), also known as source coding with decoder-only side information, to efficiently describe its received signal. Unlike DF, CF relaying consistently outperforms direct transmission since the relay always aids in communication, even when the source-to- relay channel is poor. See e.g., Ref. 11 for additional discussion on scenarios where CF has been proven to be optimal. Despite its benefits, the limitations of practical WZ implementations operating in the finite block length regime have hampered the widespread use of CF relaying.

[0007] Accordingly, there is a need to address and / or improve at least the abovedescribed deficiencies which exist in the previous systems, methods and computer-accessible medium by providing systems, methods and computer-accessible medium that can generate and / or implement, e.g., a learned task-aware Wyner-Ziv compressor for compress-and-forward schemes on relay channel(s).SUMMARY OF EXEMPLARY EMBODIMENTS

[0008] The following is intended to be a brief summary of the exemplary embodiments of the present disclosure and is not intended to limit the scope of the exemplary embodiments.

[0009] In some exemplary embodiments of the present disclosure, the exemplaryP300735. W0.01 - 109197.0000195PATENT APPLICATIONsystems, methods, and computer accessible medium can be provided for facilitating a compress-and-forward communication format. The exemplary systems, methods, and computer accessible medium can observe a signal provided from a source configuration at a relay configuration and a destination configuration. At the relay configuration, it is possible to implement an artificial intelligence (Al) model to compress the signal observed by the relay based on a correlation of the relay configuration to the destination configuration even though the relay configuration cannot observe the destination configuration and does not know the correlation. The Al-based model can be used to determine the compression strategy without visibility of the signal observed by the destination configuration. The relay configuration can forward the compressed signal to the destination configuration. The destination configuration can determine information associated with the transmitted signal based on a combination of the signal observed by the destination configuration and the compressed signal received from the relay.

[0010] The determination by the destination configuration can be configured to reduce or minimize error(s) between the transmitted signal and the determined transmitted signal.Additionally, the Al-based model compression determination can be further based on a delivery of a maximum number of bits per second to the destination. The amount of compression performed by the Al-based model can be further based on a determined trade-off between a probability of error and an available bandwidth between relay and destination. The amount of compression performed by the Al-based model is dictated by the correlation of the relay to the destination configuration. Further, the Al-based model can be linked to the relay and destination configurations, and can perform the demodulation at the destination configuration.

[0011] In some exemplary embodiments of the present disclosure, the exemplary systems, methods, and computer accessible medium can be provided for facilitating a compress-and-forward communication format. The exemplary systems, methods, and computer accessible medium can generate, modify and / or utilize an artificial intelligence (Al) model to (i) compress a signal observed by a relay configuration based on a correlation of the relay configuration to a destination configuration, where the correlation is unknown, and without visibility to the signal observed by the destination, and (ii) demodulate the compressed signal at the destination configuration. For real-valued channels, the exemplary Al-based model can be trained on synthetic data comprising binary phase shift keying (BPSK), Pulse Amplitude Modulation 4-level (4-PAM) and Pulse Amplitude Modulation 8-level (8-PAM) modulations, havingP300735. W0.01 - 109197.0000195PATENT APPLICATIONconstellations X = {±A} for BPSK, X ={±A, ±3A} for 4-PAM, X = {±A, ±3 A, ±5 A, ±7A} for 8-PAM, where A is determined by system power requirements to satisfy a power constraint. For complex-valued channels, the exemplary Al-based model can be trained on synthetic data comprising 4-Quadrature Amplitude Modulation (QAM) and 16-QAM modulations, also subject to a power constraint. Additionally, or alternatively, the exemplary Al-based model can be trained on synthetic data comprising a plurality of additive white Gaussian channels, where one or more input signals come from a finite order fixed modulation scheme

[0012] In some exemplary embodiments of the present disclosure, the exemplary systems, methods, and computer accessible medium can be provided for a compress-and-forward communication format comprising integrating a task-aware entropy-constrained vector quantization (ECVQ) with a side information so as to the compress-and-forward communication format, wherein a compressor that generates information associated with the compress-and-forward communication format is integrated in a relay, and wherein a demodulator receiving and demodulating the information is integrated in a destination configuration. The ECVQ can be implemented with either a hand-design technique or an end-to-end learning-based technique.

[0013] These and other objects, features and advantages of the exemplary embodiments of the present disclosure will become apparent upon reading the following detailed description of the exemplary embodiments of the present disclosure, when taken in conjunction with the appended claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Further objects, features and advantages of the present disclosure will become apparent from the following detailed description taken in conjunction with the accompanying Figures showing illustrative embodiments of the present disclosure, in which:

[0015] Fig. 1 is an exemplary block functional diagram of an exemplary primitive relay channel (PRC) under consideration according to an exemplary embodiment of the present disclosure;

[0016] Figs. 2(a)-2(c) are exemplary graphs for exemplary neural compress-and-forward schemes, according to an exemplary embodiment of the present disclosure;

[0017] Fig. 3 is a set of exemplary graphs showing symbol error rate (SER) and mutual information as a function of the relay-to-destination rate R, for the 4-PAM modulation with YDP300735. W0.01 - 109197.0000195PATENT APPLICATION= YR = 13 dB according to an exemplary embodiment of the present disclosure;

[0018] Fig. 4 is a set of exemplary graphs showing symbol error rate (SER) and mutual information as a function of the relay -to-destinati on rate R, for the 16-QAM modulation with YD = YR = 7 dB according to an exemplary embodiment of the present disclosure;

[0019] Fig. 5 is an exemplary graph showing mutual information for the marginal model (see Fig. 2(a)) in case of BPSK, 4-PAM and 8-PAM modulations with YD = YR = 3 dB according to an exemplary embodiment of the present disclosure;

[0020] Fig. 6 is an exemplary graph showing mutual information for the marginal model (see Fig. 2(a)) in case of BPSK, 4-PAM and 8-PAM modulations with YD = YR = 13 dB according to an exemplary embodiment of the present disclosure;

[0021] Fig. 7 is an exemplary graph providing mutual information for the marginal model (illustrated in Figs. 2(a)-2(c)) in case of BPSK, 4-PAM and 8-PAM and 16-QAM modulations with YD = YR = 7 dB according to an exemplary embodiment of the present disclosure;

[0022] Fig. 8 is an exemplary graph providing an exemplary visualization of the learned CF strategy (marginal scheme in Fig. 2(a)) and demodulation decisions for the 4-PAM modulation with y = 13 and relay rate R ~ 1 according to the exemplary embodiments of the present disclosure;

[0023] Figs. 9(a)-9(c) are exemplary graphs providing exemplary visualizations of the learned CF strategy (see, e.g., marginal scheme illustrated in Fig. 2(a)) and demodulation decisions for the 4-PAM modulation with y = 13 and relay rate R ~ 1 according to the exemplary embodiments of the present disclosure;

[0024] Fig. 10 is an exemplary graph showing an exemplary robustness analysis when the destination and the relay have the same test signal-to-noise ratio (SNR) YD = YR = y according to an exemplary embodiment of the present disclosure;

[0025] Fig. 11 is an exemplary graph showing an exemplary robustness analysis when the relay signal-to-noise ratio (SNR) is fixed yR = 3 dB, and the destination SNR changes yD G {0, 1,...., 6} dB according to an exemplary embodiment of the present disclosure;

[0026] Fig. 12 is an exemplary graph showing an exemplary robustness analysis when the relay signal-to-noise ratio (SNR) is fixed yD = 3 dB, and the relay SNR changes yR G {0, 1,...., 6} dB according to an exemplary embodiment of the present disclosure; andP300735. W0.01 - 109197.0000195PATENT APPLICATION

[0027] Fig. 13 is an illustration of an exemplary block diagram of an exemplary system in accordance with certain exemplary embodiments of the present disclosure.

[0028] Throughout the drawings, the same reference numerals and characters, unless otherwise stated, are used to denote like features, elements, components or portions of the illustrated embodiments. Moreover, while the present disclosure will now be described in detail with reference to the figures, it is done so in connection with the illustrative embodiments and is not limited by the particular embodiments illustrated in the figures and the appended claims.DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

[0029] The following description of exemplary embodiments provides non-limiting representative examples referencing numerals to particularly describe features and teachings of different exemplary aspects and exemplary embodiments of the present disclosure. The exemplary embodiments described should be recognized as capable of implementation separately, or in combination, with other exemplary embodiments from the description of the exemplary embodiments. A person of ordinary skill in the art reviewing the description of the exemplary embodiments should be able to learn and understand the different described aspects of the present disclosure. The description of the exemplary embodiments should facilitate understanding of the exemplary embodiments of the present disclosure to such an extent that other implementations, not specifically covered but within the knowledge of a person of skill in the art having read the description of embodiments, would be understood to be consistent with an application of the exemplary embodiments of the present disclosure.

[0030] The relay channel, that includes, e.g., a source-destination configuration / arrangement along with a relay, is an important component of cooperative communications. While the capacity of a general relay channel remains unknown, various relaying strategies, including compress-and-forward (CF), have been proposed. In CF, the relay forwards a quantized version of its received signal to the destination. Given the correlated signals at the relay and destination, distributed compression techniques, such as Wyner-Ziv coding, can be harnessed to utilize the relay-to-destination link more efficiently. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can generate and integrate a learned task-aware Wyner-Ziv compressor into a primitive relay channel with a finite-capacity out-of-band relay-to-destination link. TheP300735. W0.01 - 109197.0000195PATENT APPLICATIONresulting exemplary Al-based scheme demonstrates that a compressor according to the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can recover binning of the quantized indices at the relay, mimicking the optimal asymptotic CF strategy, although no structure exploiting the knowledge of source statistics is imposed into the design. The exemplary Al-based scheme of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure that employs finite order modulation, can operate closely to the rate achievable in a primitive relay channel with a Gaussian codebook. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can be used to exploit the correlated destination signal for relay compression through various Al-based architectures that involve end-to-end training of the compressor and the demodulator components. The learned task-oriented compressors of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can provide interpretable and practical Al-based relaying schemes.

[0031] To highlight the exemplary design for CF, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can focus on the primitive relay channel (PRC) 100 (see, e.g., Ref. 14), depicted in Fig. 1, where there is a source 105, a PRC 130, a relay 110, a destination 115, and an orthogonal (out-of-band) noiseless link 120 of rate R 122 connecting the relay 110 to the destination 115. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure contribute as follows:• The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can present learned CF relaying schemes for the Gaussian PRC that are based on task-aware neural distributed compressors, where the task is to maximize the source-to-destination communication rate. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can provide several architectures, differing in the way the distributed compression is carried out. Each of these schemes consists of a compressor at the relay and (soft) demodulator at the destination, both of which can be learned in an end-to-end fashion.P300735. W0.01 - 109197.0000195PATENT APPLICATION• The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can facilitate post-hoc interpretations of the resulting Al-based schemes on some representative modulation schemes. Through visualizations, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can show that the task- aware neural relay quantizer exhibits binning (grouping) in the source space, which is known to be information theoretically optimal. In addition, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can show explainable decision boundaries for the learned demodulator at the destination. These structures emerge from learning, not from design choices based on system parameters.• Using a comprehensive set of experimental results, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can evaluate the performance of the Al-based strategies both in terms of communication and error rates. Comparison with theoretical benchmarks suggests the effectiveness of the learning-based relaying frameworks of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure.• The systems, methods and computer accessible medium according to the exemplary embodiments of the present disclosure can provide a detailed analysis of robustness to varying signal-to-noise ratios (SNRs) both at the relay and the destination. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can empirically demonstrate that training over a range of SNRs enables the resulting CF strategy to maintain good performance across the range of interest.

[0032] Overall, the learned CF framework of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can provide the first practical and robust CF relaying, with the added benefit of yielding interpretable results.

[0033] The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure consider the PRC for a number of reasons.P300735. W0.01 - 109197.0000195PATENT APPLICATIONFirstly, the PRC offers a scenario where the compressed relay signal can be readily transmitted to the destination. Compared to the general relay channel, the PRC model can decouple the relay transmission from that of the source, facilitating a natural setting to study CF. For example, the PRC model can represent the simplest channel coding problem, viewed from the source’s perspective, with a rate constraint among the two receiving terminals (relay and destination). Simultaneously, it also encapsulates the simplest compression problem, viewed from the relay’s perspective, for facilitating channel coding between the source and the destination. Secondly, PRC can provide a good model for scenarios in which a different wireless or wired interface is used for relaying, such as base station cooperation. In addition, the relaying strategies developed for the PRC can be extended to a more general relay channel model by incorporating the multiaccess reception at the destination. Further, CF relaying can be optimal for the PRC if the relay is unaware of the source codebook, also known as oblivious relaying. (See, e.g., Ref. 15). The oblivious setting can be well- suited to the learning framework, in which the relay is not explicitly informed about the transmission strategy used by the source. Rather, a data-driven relay trains its compressor based on samples of its channel output.

[0034] There is limited literature addressing practical CF designs. (See, e.g., Refs. 16 and 17). Such publications proposed entropy- constrained scalar quantizer designs with binary phase shift keying (BPSK) modulation for the half-duplex Gaussian relay channel, with (see, e.g., Ref. 16) considering lossless Slepian-Wolf (SW) coded nested quantization as a practical form of WZ compression (following the WZ compressor proposed in e.g., Refs. 12 and 17), and (e.g., Ref. 17) not taking into account the side information at the destination while quantizing at the relay. In addition, these works relied on handcrafted and analytical solutions, thereby constraining their generalization to more complex communication settings. Unlike some of the previous distributed compression work (see, e.g., Refs. 18 and 19) or the aforementioned relay quantizer designs, the CF strategies of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure neither enforce any specific structure onto the model nor assume prior knowledge about the source-to-destination communication strategies or link qualities.

[0035] Prior recent learning approaches for the relay channel (see, e.g., Refs. 20-22) considered a joint source-channel setting, where the first two focused on image transmission via joint source- channel coding, while the last one targeted text communication utilizing attention-P300735. W0.01 - 109197.0000195PATENT APPLICATIONbased transformer architectures. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure, in contrast, can concentrate only on the channel part and can address an important open problem in the cooperative communications literature, namely, how to make CF practical. While the learned CF framework of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can be built upon (e.g., Refs. 12, 23, and 23), an important distinction can be that in CF, the goal is to facilitate source-to-destination communication, and not to reconstruct the relay signal per se. In fact, it is demonstrated in e.g., Ref. 17 that relay compression that minimizes mean squared error distortion can be significantly suboptimal. See (e.g., Ref. 13) for an overview of distributed compression and practical designs, including those based on neural networks, that focus on signal reconstruction.(I) EXEMPLARY SYSTEM MODELA. Exemplary Primitive Relay Channel (PRC)

[0036] The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider the PRC setup 100 (e.g., Ref.14), illustrated in Fig. 1, which shows an exemplary block functional diagram of an exemplary primitive relay channel (PRC) under consideration according to an exemplary embodiment of the present disclosure. The Gaussian PRC can be provided as:YR = hRX + NR,(1) YD = ho X + ND,where X denotes the signal transmitted by the source, YR and YD denote the received signals at the relay and the destination, and hR and ho are the corresponding channel gains, respectively. The noise components, NR and ND, are independent of one another and of X.

[0037] The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider both real and complex-valued channels. For the real-valued channel, without loss of generality, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider X, hR, ho G R, NR ~ 7\f(0, 1) and ND ~ J\f(O, 1). For the complex-valued channel, the exemplary systems, methods, and computer accessible mediumP300735. W0.01 - 109197.0000195PATENT APPLICATIONaccording to the exemplary embodiments of the present disclosure can assume X, hR, hD ∈ ℂ, NR ~ 풞풩(0, 1) and ND ~ 풞풩(0, 1). By allowing for arbitrary (HR, ho, one can incorporate the effect of different SNRs for the source-to-relay and source-to-destination links. As customary, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider communication over a block length of n, with n asymptotically large, and i.i.d. noise. For brevity, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can omit the time index in (1). The out-of- band relay-to-destination channel is represented by a link 120 with relay rate R bits / channel use 122.

[0038] For a general PRC p(yD, yR|x) 130 with an oblivious relay, where the relay is agnostic to the codebook shared by source and destination, it was shown that the capacity can be attained by the CF strategy with time sharing. (See, e.g., Ref. 15). Without time-sharing, the following rate C is achievable (see, e.g., Ref. 15):C = max I( X; YD, U), (2) s.t. R > 1(YR U | YD), (3) where maximization is with respect to the distribution p (x) p (u|yR). Here, U corresponds to the relay’s compressed description of YR, and the rate constraint in (3) coincides with the one that emerges in WZ rate-distortion function. (See, e.g., Ref. 10). Recall that in CF, the relay regards its received signal YR as an unstructured random process jointly distributed with the signal received at the destination YD. This enables the relay to exploit WZ compression (see, e.g., Ref.10), to efficiently describe its received signal. It should be noted that the capacity of the PRC without oblivious relaying constraint is still not fully characterized. (See, e.g., Ref. 15).

[0039] For the real-valued Gaussian PRC in (1), the following CF rate is achieved with Gaussian input under power constraint E[|X |2] < P (see, e.g., Ref. 15):CCF= ½log2( 1 + γD + γR / (1 + (1+γD+γR) / ((22R-1)(γD+1))) ),\ (22R-i) yD+i) / where γD= |hD|2P and γR= |hR|2P are SNRs at the destination and at the relay, respectively. Note that, in the case of a complex -valued PRC, the factor of 1 / 2 in equation (4) is removed. It is shown in e.g., Ref. 15 that while the Gaussian input is not necessarily optimal, the rate in equation (4) is at most 1 / 2 bit away from the capacity of the Gaussian PRC, even if the relay isP300735. W0.01 - 109197.0000195PATENT APPLICATIONnot oblivious. Hence, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can use (4) as a benchmark for the learned CF communication rates.B. Exemplary Performance Criterion

[0040] For the learning-based CF frameworks, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can assume a finite order modulation such that an index W E { 1,..., |X| }, which represents the output of the channel encoder, is mapped to a symbol X E X, where X c IR (or, X c C for complex-valued signals) is a constellation of cardinality |X|. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider a fixed modulation scheme with equally likely symbols, and not optimize over the constellation X or over the distribution p (x). As shown in Fig. 1, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can jointly learn the encoder 112 at the relay, which can output a compressed description U 121, and the (soft) demodulator 125 at the destination 115, which can output a probability distribution on W (Fig. 1) that maximize the mutual information I(X; YD, U) subject to the relay rate constraint R 122, as in equations (2) and (3). Exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can assume the availability of good channel codes to be used in conjunction with the modulation scheme, and as such the mutual information I( X; YD, U) can be viewed as a CF achievable rate. Discussion of how this performance criterion is incorporated into the objective function used in the learning process is described herein.(II) EXEMPLARY NEURAL COMPRESS-AND-FORWARD (CF) SCHEMES

[0041] By leveraging universal function approximation capability of artificial neural networks (ANNs) (see, e.g., Refs. 26 and 27), the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can propose three Al-based schemes to be employed in the PRC shown in Fig. 1. These schemes and design insights are described in detail below, as well as objective function and implementation details. As detailed above, the modulation scheme remains fixed throughout. On the other hand, the encoder 112 of the relay 110, employing CF strategy, and the destination’s demodulator 125P300735. W0.01 - 109197.0000195PATENT APPLICATIONcan be parameterized using ANNs, which can undergo joint optimization in an end-to-end manner.A. Exemplary Al-based Architectures

[0042] Building onto neural distributed compressors proposed in e.g., Ref. 12, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can provide learning-based CF schemes that include neural one-shot WZ compressors (with side information YD at the destination), paired with either a classic entropy coder (EC) or a SW coder, at the relay. These two variants are named as marginal (marg.) and conditional (cond.) formulations, respectively. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can also provide a neural one-shot point-to-point (p2p) compressor coupled with a classic EC. All of these learned compressors can be combined with a neural demodulator available at the destination, which has access to the side information yD.

[0043] The overall learned CF relaying architectures of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure are illustrated in Figs. 2(a)-2(c). Figs. 2(a) and 2(b) illustrate diagrams which are based on marginal (marg.) 205 and conditional (cond.) 250 formulations, (coupled with classic either entropy 210 or Slepian-Wolf (SW) 255 coder) respectively. Fig. 2(c) shows a diagram providing an exemplary point-to-point (p2p) 275 scheme, eθ 215, 260, and 280 respectively, qζ 220, 265, and 285 respectively, and pφ 225, 270, and 290 respectively are learned parameters. Schemes 205 and 250 in Figs. 2(a) and 2(b) operationally correspond to task-aware neural Wyner-Ziv compressors, since the encoder can exploit the side information YD 230 and 272 respectively at the receiver side. In (c), neither parameters of eθ 280 and qζ 285 are updated during the fine- tuning step (only pφ 290 is learned). In the split I-Q variants of each scheme (not depicted), it is possible to provide two separate encoders that compress in-phase and quadrature components of the complex -valued signal independently. Wherever certain exemplary relevant experiments are presented, it is possible to label the depicted respective scheme illustrated in these figures as joint I-Q, indicating a single encoder for both in-phase and quadrature components.

[0044] The encoder’s ANN at the relay is denoted by ee(-) 215, 260, and 280 respectively, with 9 representing its parameters; the probability distribution of the relayP300735. W0.01 - 109197.0000195PATENT APPLICATIONencoder’s output 216, 261, and 281 respectively (which is then used by the EC 210 or SW 255 coder) is modeled with q,-, 220, 265, and 285 respectively parameterized by the demodulator’s ANN is P (W|J / D, ee (y / ?)) 225, 270, and 290 respectively, where < > denotes its parameters. The mapping defined by the demodulator p<> 225, 270, 290, respectively, represents the posterior probability over the alphabet {1,..., |X| } (soft decision), which serves as an approximation of the true posterior distribution p (w|yD, eθ (yR)).

[0045] In the learning process of a point-to-point compressor, as shown in Fig. 2(c), the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can initially train a demodulator pζ (w|eθ (yR)) 286 to prevent this neural compressor from utilizing the side information YD 295 during training. The pre-trained point-to-point neural compressor 276 as such can then be used as input for finetuning the demodulator p< / > (w|yo, ee (yR)) 277, which can incorporate side information.

[0046] The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can set the relay encoder’s 112 output as U = ee YR), as shown in Fig. 1. Envisioning a practical scheme, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can have U as discrete. Specifically, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can have that eθ(YR) ∈ {1,..., K}, where K is a model parameter. This parameter K can be chosen large enough to guarantee sufficient support for the encoder output. To facilitate the learning process of the encoder, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can use a probabilistic model for eθ (YR) during training. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can set the encoder output in a deterministic way, as in e.g., Ref. 12, that is u = arg maxk∈{1,...,K} eθ (yR) for a given YR = y. Note that the encoder ee operates in an unordered categorical space, outputting one of the categories of the quantization index k G { 1,..., K] for each input realization.

[0047] Similar to the description of, e.g., Ref. 12, without loss of generality, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can define the probabilistic models eθ (YR) (during training) and qζ as discrete distributions with probabilities as follows:P300735. W0.01 - 109197.0000195PATENT APPLICATIONPk= exp αk / ΣKi=1exp αifor k E { 1,..., K}. The unnormalized log-probabilities (logits) αiare either directly treated as learnable parameters or computed by ANNs as functions of the conditioning variable. The lossless compression rates induced by the models qζ are attainable with high-order classic EC (see, e.g., Ref. 28) or SW coder (see, e.g., Ref. 29), operating on discrete values.

[0048] For implementations involving complex-valued modulation schemes, the CF architectures depicted in Figs. 2(a)-2(c) compress the in-phase (i.e., real) and quadrature (i.e., imaginary) components of YR jointly. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can also explore the variants of the architectures illustrated in Figs. 2(a)-2(c) (not shown therein), where the in- phase and quadrature components can be given as input to two separate encoders, each of which has parameters of its own. The compression rate in this case is computed as the sum of the rates achieved by the in-phase and the quadrature entropy coding schemes (involving either classic EC or SW coders for both). Similar to the architectures outlined in Figs. 2(a)-2(c), the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can still employ a single demodulator p<j& for all these variants, which can take as input the two indices coming from the compressed representations of the in-phase and the quadrature components, along with the side information YD. These architectural configurations can be referred to as the split I-Q variants, whereas the original architectures shown in Figs. 2(a)-2(c) can be named the joint I-Q versions.

[0049] While joint compression of in-phase and quadrature components using schemes illustrated in Figs. 2(a)-2(c) should, in principle, outperform independent processing as in the split I-Q variant, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can show that incorporating domain knowledge into the design, especially when training learning-based schemes, can sometimes facilitate finding the optimal solution for the algorithm.B. Exemplary Rationale Behind Design Choices

[0050] While the popular class of neural image compressors (see, e.g., Refs. 30-32) seems well-suited for distributed compression, and more specifically for the WZ problem, analysis in e.g.. Ref. 24 indicates that it fails to learn efficient many-to-one mappings exploitingP300735. W0.01 - 109197.0000195PATENT APPLICATIONthe side information. Consequently, these popular schemes do not recover proper binning schemes, which are known to be optimal in the asymptotic setting (see, e.g., Ref. 10), for abstract exemplary sources (such as the quadratic-Gaussian case), severely limiting their compression efficiency. In Ref. 24, it is hypothesized that this limitation stems from the inherent spectral bias (see, e.g., Ref. 33) of the popular class of neural compressors. This spectral bias arises because the encoder outputs operate on the real line. This inherently favors learning smooth functions, consequently hindering these neural compressors from capturing highly discontinuous functions and many-to-one mappings such as binning.

[0051] Based on this, the learning-based CF schemes of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure, as in the case of the learned WZ compressors (e.g., Refs. 12 and 24), can operate directly within an unordered categorical space, similar to traditional vector quantization. Neural relay compressors of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can be, therefore, in the form of entropy-constrained vector quantizers that can more easily leverage correlated signal available at the destination. This is in contrast to the popular class of neural compressors (e.g., Ref. 30-32), where each of the dimensions at the encoder output is subjected to entropy- constrained scalar quantization in an ordered transform space operating on real line.

[0052] The design choices described herein can maintain the parametric families in their most general form, avoiding any unnecessary imposition of structure. In particular, these can facilitate the model eg to recover, when necessary, quantization schemes featuring discontiguous quantization bins, reminiscent of the random binning operation in the achievability of the WZ theorem (see, e.g., Ref. 10), which also appears in the CF relaying strategy (see, e.g., Refs. 9 and 15).C. Exemplary Objective Function

[0053] In contrast to prior works on neural distributed compression (see, e.g., Ref. 12), which focus on minimizing the distortion in the reconstruction of the input source in tandem with variable rate entropy coding, the exemplary goal of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can be to optimize the operational trade-off between relay -to-destination compression rate and source-to-destination communication rate in the PRC setup, underscoring the task-aware natureP300735. W0.01 - 109197.0000195PATENT APPLICATIONof the relay compressor design.

[0054] For the objective function of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure, building onto the relay rate in equation (3), the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can first consider the following upper bound:I(YR; U|YD) ≤ H(U|YD),, (6)≤ 피 [- log2qζ(eθ(yR))] ≜ R̃, (7) where R represents an operational upper bound on the relay’s compression rate, which is limited by R. The inequality in equation (7) is due to the fact that the cross-entropy is larger or equal to entropy (see, e.g., Ref. 34, Theorem 5.4.3). In the present exemplary case, R encapsulates the compression rate of a relay quantizer having a one-shot encoder coupled with high-order entropy coder over large blocks of the quantized source.

[0055] Similarly, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can also establish a lower bound based on the achievable rate in equation (2), as follows:I(X; YD, U) = H(W) - H(W|YD, U), (8)≥ log(|X|) - D̃, (9) where D̃ ≜ 피 [- log(pφ(x|yD, eθ(yR)))], and (9) is a lower bound on the source-to-destination communication rate C from equation (2). In the present exemplary case, equation (8) follows from X being a one-to-one deterministic function of W, and (9) is again due to cross-entropy being larger or equal to entropy. Since exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can have a fixed modulation scheme and may not perform any probabilistic shaping, in equation (9) there is H(W) = H(X) = log(|X|).

[0056] For a demodulator making hard decisions as:Ŵ = arg max pφ(w|yD,eθ(yR)), (10)the corresponding symbol error rate (SER) is defined as:SER - P(VF A W). (11) Since minimizing the cross-entropy D is known to be a surrogate for maximizing the accuracy ofP300735. W0.01 - 109197.0000195PATENT APPLICATIONclassification (that is symbol detection) (see, e.g., Ref. 35), minimizing D also operationally corresponds to minimizing SER.

[0057] Building onto the such bounds, the training objective of some or all the Al-based relaying schemes of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure, as depicted in Figs. 2(a)-2(c), can be described by the following exemplary loss function:L(θ, φ, ζ) = R̃ + λD̃, (12) where R and D are from (7) and (9) respectively, and A > 0 controls the trade-off. The optimized ee, qr and p< / > models, parameterized by 0, C, and, yield the ANN-based encoder, EC or SW coder, and demodulator component, respectively. The upper bound in equation (7) corresponds to the compression rate achievable by a CF relaying scheme employing a one-shot task-aware encoder eθ and demodulator pφ, both coupled with an entropy code based on qζ (either classic EC or SW coder). This asymptotic compression rate can be equivalent to the cross-entropyE [ — log2Q^eCy / ?))] Similarly, the lower bound in equation (9) corresponds to the overall communication rate achieved by a capacity achieving channel code, operating over large block lengths, used in conjunction with the (soft) demodulator p<>. Therefore, minimizing the loss function in equation (12) facilitates the end-to-end optimization of this operational relaying scheme.

[0058] Consistent with findings in e.g., Refs. 16 and 17, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can empirically confirm that minimizing mean squared error distortion metric at the quantizers may not always maximize the source-to-destination communication rate. The intuition for this exemplary configuration can be as follows: A distortion-minimizing quantizer aims to preserve the relay ’s received signal, whereas the relay quantizer should instead retain the source information as the relay’s end goal is to facilitate the communication in the source-to- destination link, highlighting the task-aware nature of the compressor design objective at hand. Grounded in information theoretical principles following e.g., Ref. 15), this key insight underlies the objective function (see equation (12)) for the Al-based relaying schemes of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure.P300735. W0.01 - 109197.0000195PATENT APPLICATION

[0059] Adjusting the trade-off parameter A in equation (12) can result in using different points within the achievable region. The learnable parameters are amenable to joint optimization using stochastic gradient descent (SGD) since the loss function is differentiable with respect to them. The gradients can be computed using automatic differentiation methods, as implemented in deep learning frameworks such as JAX. (See, e.g., Ref. 36).

[0060] As in the popular class of neural compressors e.g., Ref. 32), the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can use SGD to optimize all learnable parameters jointly, which relies on Monte Carlo approximation for the expectations in the loss function. In SGD, the expectations in the loss functions are replaced by averages over batches of samples B, and the order of differentiation and summation is exchanged due to linearity. For a given generic pair of X = x and Y = y, let € e (x, y) denote the sample loss with parameters 6 (represented as one of the sample loss functions inside the brackets in equation (12)). In this case, Monte Carlo approximation yields:

[0061] This can provide that the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure draw some samples from the model ee throughout training. The Gumbel-max trick, initially proposed in e.g., Ref. 37, provides a method to draw samples from any discrete distribution. It does so by drawing samples from a distribution of K states (as in equation (5)) as follows:arg max {αk+ Gk},(14) where Gk are i.i.d. samples from a standard Gumbel distribution.

[0062] Recognizing that the derivative of the arg max operator in equation (14) is zero everywhere except at the boundaries of state changes, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can opt for a continuous relaxation of this operator during training to carry out SGD. Such a relaxation is provided by the Concrete distribution, introduced in e.g., Ref. 38. Rather than obtaining discrete (hard) samples, this method produces soft samples, forming a vector of length K where the mass is distributed across multiple states instead of being concentrated in one. TheP300735. W0.01 - 109197.0000195PATENT APPLICATIONindex k E { 1,..., K} of such a soft sample is determined using a softmax function:Uk... ■'Gk) / 0 / t) ’( | S )where t is a temperature parameter that controls the amount of relaxation. As t — > 0+, the soft samples converge to their hard counterparts, indicating that the Concrete distribution converges to a discrete one. Throughout the exemplary training, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can also choose the Concrete distribution for the models qζ to match the distribution of samples from eθ.

[0063] During the exemplary evaluation, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can transition from Concrete distributions back to their discrete counterparts. As explained above, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can also use a deterministic encoding function equivalent to the mode of ee, instead of sampling from it, by setting encoder output as u = arg maxk∈{1,...,K}eθ(yR)

[0064] In spite of considering specific modulation schemes in training, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure may not assume a priori knowledge of the modulation scheme by the relay in the Al-based schemes. The parameters {θ,can be learned solely in a data-driven fashion from samples, through the proposed loss function in equation (12). Similarly, the relay also may have no prior information on the channel gains hR and hD (see equation (1)). Further improvement in the performance may be obtained by also learning an optimized probabilistic shaping (p(x) in optimization equations (2)-(3)) and a geometric shaping (constellation X) of the modulation. (See, e.g., Ref. 25).(Ill) EXEMPLARY RESULTS AND DISCUSSION

[0065] The framework according to the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can be adapted to different modulation schemes and PRC setups, however, the exemplary systems,P300735. W0.01 - 109197.0000195PATENT APPLICATIONmethods, and computer accessible medium according to the exemplary embodiments of the present disclosure of the present disclosure can utilize the following exemplary system configuration to showcase numerical results. As stated above, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can assume equally likely symbols, i.e., p (x) = 1 / |X|. The average power constraint on the transmitted signal is 피[|X|2] = P. For real-valued channels, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider BPSK, 4-PAM, and 8-PAM modulations, having constellations X = {±4}, X = {±4, ±34}, and A = {±4, ±34, ±54, ±74}, respectively, where 4 is chosen to satisfy the power constraint P. For complex-valued channels, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider 4-QAM and 16-QAM modulations with power constraint P. The SNR at the destination and at the relay can be defined as γD= |hD|2P and γR= |hR|2P, respectively.[00661 For the parametrization of eθand pφ, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can use ANNs of three dense layers, with 100 units each, except the last one, and leaky rectified linear unit can be the activation function. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can show that increasing the size of the networks or employing different activation functions may not lead to improved results. The demodulator pφreceives a concatenated vector comprising both its inputs, eθ(YR) and YD.

[0067] The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can use the JAX framework (see, e.g.. Ref.36) and employ Adam (see, e.g., Ref. 39), a widely used variant of SGD. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can use a learning rate of 10−4, which can be selected by monitoring the convergence of the loss function in the high-rate regime, reducing it by a constant factor of 10 each time the loss visibly plateaus. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can show that convergence of the high-rate models can take longer than low-rate models, so exemplary embodiments can simply carry over the schedule to the lower-rate cases. Most or all exemplaryP300735. W0.01 - 109197.0000195PATENT APPLICATIONAl-based schemes can be trained for 500 epochs with randomly initialized network weights. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can use a batch size of B = 1024 (as in equation (13)) and set the model parameter K = 32. The output dimension of pφcan be set to be |X|, since this probabilistic model represents the posterior over the transmitted constellation.

[0068] The exemplary learned CF relaying schemes of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can be evaluated in terms of the trade-off between the relay rate R (using the proxy R in (7)), and two metrics: (i) the communication rate I( X, YD, U), for which it is possible to utilize the lower bound (hence, a pessimistic estimate) in (9), and (ii) the SER = P(W ≠ Ŵ) (see (11)). All empirical estimates of compression rates, communication rates, and bit error rates can be obtained by averaging over at least 106source realizations.

[0069] Exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can be organized as follows. Baseline references for R = 0 and R → ∞ can be presented in Section A below. The performance of various learned CF relay schemes can be analyzed in Section B below, while an interpretation of the corresponding relay’s encoder and destination’s demodulator can be provided in Section C below. Further, exemplary results for robustness against different SNRs can be shown in Section D below.A. Exemplary Baselines

[0070] The exemplary regimes where R = 0 and R → ∞ are referred to as without relay and perfect relay scenario, respectively. When R = 0, the destination has only access to YD, having an effective SNR of yo. In the perfect relay regime (R → ∞), however, the destination has full access to both YD and YR, and it optimally combines them. This effectively results in an increased SNR of γD+ γRcompared to the scenario without a relay. In these two regimes, mutual information and SER can be numerically computed for the considered modulations as a function of (γD, γR). (See, e.g., Ref. 40).

[0071] When 0 < R < co, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider CCF from equation (4) (or its complex channel equivalent) as a benchmark for the achievableP300735. W0.01 - 109197.0000195PATENT APPLICATIONcommunication rate of the learned CF schemes of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure with discrete modulations. Increasing the modulation order, |A|, gives more degrees of freedom for the end-to-end learned communication system to approach the rate of a PRC that assumes Gaussian inputs, as represented by CCF in (4).B. Exemplary Performance of the Learned CF Relaying Schemes

[0072] For example, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can assume that the SNR can be the same for both the destination and the relay, i.e., γD= γR.

[0073] Fig. 3 shows exemplary graphs of the symbol error rate (SER) and mutual information as a function of the relay-to-destination rate R, for the 4-PAM modulation when γD= γR= 13 dB. Each line represents the performance of one of the neural CF relay architectures shown in Figs. 2(a)-2(c) (205, 250, and 275), where each marker corresponds to a unique model trained for a particular value of A in (2). The horizontal black lines provide baseline results without relaying (R = 0) and with perfect relaying (R — > oo). In this exemplary case, YR and YD, are highly correlated. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure show that the three models exhibit different trade-offs. Recall that, in the point-to-point variant depicted in Fig. 2(c), ee is not able to use YD as side information in compression. As shown in Fig. 3, the conditional model yields, e.g., the best performance as the side information is also exploited within the SW coder. The marginal model of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure surpasses the point-to-point model mainly due to exploiting the side information during compression see herein for more details), yielding rate reduction.

[0074] Similarly, Fig. 4 shows exemplary graphs providing the SER and the mutual information for 16-QAM modulation when γD= γR= 7 dB. In this exemplary case, each line shows performance of one of the neural CF relay architectures depicted in Figs. 2(a)-2(c) (205, 250, and 275 as well as results where two separate encoders compress the in-phase and quadrature part of YR independently - these models are annotated as split I-Q variants. Each marker corresponds to a unique model trained for a specific value of A in (12). The horizontalP300735. W0.01 - 109197.0000195PATENT APPLICATIONblack lines indicate baseline results without relaying (R = 0) and with perfect relaying (R → ∞).

[0075] The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure show that at lower rates, the architectures depicted in Figs. 2(a)-2(c), which correspond to joint I-Q compression, can perform best across three different schemes (conditional, marginal and point-to-point). In these models, both the in-phase and quadrature components can be fed into a single encoder ee, facilitating a joint compression of real and imaginary parts of the complex-valued input signal. This can allow these compressors to learn more flexible quantization boundaries (not depicted), making them more efficient in the low-rate regime. However, at higher rates, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can show that the split I-Q variants outperform their joint counterparts.

[0076] Since “grid-like” quantization boundaries for QAM modulations can be expected, imposing separate processing on real and imaginary parts in the split I-Q models, effectively leverages this domain knowledge, facilitating them to approach capacity at high rates. In contrast, all of the joint I-Q architectures for conditional, marginal and point-to-point variants saturate around a capacity value of 3. These results suggest that as the modulation order and relay rate increase, incorporating domain knowledge into the compressor design could be beneficial. Imposing such well-informed design structures in this case can further enhance the efficiency of learned CF relaying schemes according to the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure, particularly at high rates, where training neural compressors becomes relatively more challenging compared to the low rate regime.

[0077] Fig. 5 shows an exemplary graph which compares CF from (4) with the mutual information obtained with the marginal formulation (Fig. 2(a) 205) for the BPSK, 4-PAM and 8-PAM modulations. For example, the SNR for all the considered schemes is γD= γR= 3 dB, suggesting a lower correlation between YR and YD compared to the graph illustrated in Fig. 3. As expected, increasing the modulation order narrows the gap to the bound in (4). Notably, the marginal variant meets the performance of the corresponding perfect relay (R → ∞) baseline at higher rates (represented by dotted lines).

[0078] Similarly, Fig. 6 shows an exemplary graph which compares CCF from equation (4) for the same modulation schemes considered as shown in Fig. 5, although now at higher SNRP300735. W0.01 - 109197.0000195PATENT APPLICATION YR = YD = 13 dB, suggesting a stronger correlation between YR and YD. At higher SNR, as theory suggests, the rate allowed by higher-order modulation is greater and the performance gap between different modulation schemes is larger. At high rates, for each of the modulation schemes considered, the Al-based schemes of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure once again match the communication rate bound for perfect relay (R → ∞) as represented by the dotted lines, mirroring the trend observed in the graph of Fig. 5.

[0079] Further, considering a complex-valued communication scenario, the results obtained on exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure with 4-QAM and 16-QAM modulations is shown in the exemplary graph of Fig. 7, where γR= γD= 7 dB is set. For this exemplary case, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can use an adapted version of CCF from (4) that considers instead a complex-valued PRC. For the 16-QAM results depicted in Fig. 7, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can select the best performing variant for the marginal model (either the joint I-Q scheme shown in Fig. 2(a) or the split I-Q version, both of which are described herein).

[0080] Consistent with the trends observed in the exemplary graphs of Figs. 5 and 6, the Al-based scheme of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can again meet the respective perfect relay baselines (R → ∞). These empirical results further confirm that the learning-based relay compression schemes of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can be easily adapted to any chosen fixed modulation, scoring higher communication throughput as the order of modulation increases.C. Exemplary Interpretability of the Learned CF Relaying Schemes

[0081] For example, the maximum posteriori (MAP) estimator for W in the PRC of Fig.1 can be as follows:ŵ = arg max p(w|yD, u), (16) wP300735. W0.01 - 109197.0000195PATENT APPLICATION= arg max p(yD|w) p(u|w) p(w), (17) wwhere exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure use the independence of yo and u given w. For equally likely symbols, p (w) is a constant and therefore, can be removed from equation (17). Note that the term p (u|w) represents the likelihood of w based on the relay’s quantized observation u, and it updates the destination’s likelihood p (yD|w) in equation (17). For reference, without the relay, the optimal decision thresholds on YD for the maximum likelihood estimator for a PAM (QAM) modulation under Gaussian noise would be the intersection between adjacent likelihoods, that is the middle point (line) between adjacent symbols. (See, e.g., Ref. 40).

[0082] As indicated herein, for the learned CF schemes of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure introduced above, u = eθ(yR), and the posterior estimated by the neural demodulator is pφ(w|yD, eθ(yR)). Results that help to visualize and interpret the quantization boundaries recovered by the neural encoder eθand learned MAP (10) decision thresholds adopted by the demodulator are provided. First, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can show that the marginal CF variant (see Fig. 2(a)) groups the quantized indices at the relay, by assigning the same quantization index to discontiguous intervals in the source space. This empirical evidence suggests that the scheme effectively uses the side information YD during compression. Next, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can show how the relay’s likelihood p (eθ(yR)|w) operationally shifts the decision thresholds.

[0083] Fig. 8 illustrates an exemplary visualization providing the marginal CF scheme and the demodulation’s hard decision regions (see (10)) for 4-PAM with γD= γD= 13 dB and relay rate of R ~ 1. The vertical axis and horizontal axis show YR and YD, respectively. The colors represent the transmitted indices eθ(YR) by the relay, and the horizontal lines are the corresponding quantization boundaries. This Al-based architecture exhibits binning (e.g., grouping) since non-adjacent intervals are assigned to the same index (same color). It is worth noting that this recovered grouping behavior is similar to the random binning operation in theP300735. W0.01 - 109197.0000195PATENT APPLICATIONachievability proof of the WZ theorem (see, e.g., Ref. 10), and also in the achievability of CF (see, e.g., Ref. 9). This emergence of learned one-shot binning behavior also explains the further reduction in relay rate compared to the point-to-point model, as illustrated in the experimental results shown in the exemplary graphs of Figs. 3 and 4. Unlike the marginal scheme, the point-to-point model (see Fig. 2(c)), however, lacks access to the side information signal YD, which is available at the decoder, during compression. Therefore, this latter model cannot learn a binning behavior in the relay compressor (not depicted). In contrast, the conditional variant (see Fig. 2(b)) leverages the side information not only during compression but also within the entropy coding stage. This can facilitate the conditional scheme to execute binning over long sequences i.e., in a multi-shot fashion. Such a high-order binning scheme, facilitated by the SW coder, can be more efficient than the one-shot binning achievable by an encoder at the relay. As the model eθcompresses each source realization one at a time, e.g., it can only bin the quantized indices at the relay in a one-shot fashion.

[0084] The vertical lines shown in Fig. 8 denote the hard decision boundaries for the demodulator, where the markers denote the decisions Ŵ. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can show that the decision boundaries are shifted with respect to the midpoints between transmitted symbols (optimal boundaries without relaying). This highlights the interpretability of the Al-based relaying scheme of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure. For example, when cross or star are transmitted, the index blue will be the (e.g., most likely) relayed index. In this case, the decision regions for cross and star at the destination are larger than the other symbols.

[0085] Figs. 9(a)-9(c) show exemplary graphs providing the learned marginal CF strategy for the complex-valued 4-QAM modulation when γD= γR= 7 dB and relay rate of R ~ 1. The vertical and horizontal axis of each figure represent real and imaginary parts of YR and YD. Fig. 9(a) illustrates a graph providing the output of the relay’s encoder showing exemplary quantization boundaries on YR (on the complex plane), where the color represents ee (YR). One can note that the regions surrounding the farthest symbols are paired with the same encoding (color) eθ(YR). Similar to the exemplary graphs of Fig. 8, it is possible to state that this is yet another instance of binning in the relay compressor. Fig. 9(b) shows an exemplary graph providing the exemplary hard decision boundaries on YD when eθ(YR) corresponds to the blueP300735. W0.01 - 109197.0000195PATENT APPLICATIONindex from Fig. 9(a) (the lighter shading). Meanwhile, Fig. 9(c) illustrates an exemplary graph providing the exemplary hard decision boundaries on YD when ee (YR) corresponds to the red index from Fig. 9(a) (the darker shading). The decision boundaries are shifted to favor the symbols that were most likely to be received at the relay.

[0086] In practice, the exemplary graphs of Figs. 8 and 9(a)-9(c) can be used as, e.g., look-up tables for direct deployment of the resulting CF relaying strategies, including both the relay’s encoder and the destination’s demodulator. Although ANN-based architectures (see Figs.2(a)-2(c)) were used to minimize the loss function in (12), the actual CF scheme and the hard demodulator implementation at test time rely only on the learned quantization boundaries and threshold values shown in Figs. 8 and 9.D. Exemplary Robustness to Signal-to-Noise Ratio (SNR) Variations

[0087] The discussion above includes performance evaluation at the same SNRs used for training. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can also show robustness with respect to the training SNR. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider 4-PAM modulation for the source X, and a range of test SNRs γD, γR∈ {0, 1,…, 6} dB. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider models that satisfy the relay rate constraint of R ≲ 1. For this SNR range, it can be known that the 4-PAM capacity is superior to the Binary Phase Shift Keying (BPSK) modulation, and almost equivalent to those achieved by higher order PAM modulations. (See, e.g., Ref. 40). This is also evident in the exemplary graph shown in Fig. 5 at γD= γR= 3 dB. Adapting the modulation order to the SNR is a key component of modern communication systems relying on link adaption (see, e.g., Ref. 41), and as such, it is assumed that 4-PAM modulation is only used in the above SNR range.

[0088] The following exemplary scenarios are considered:1) Same SNR at both the relay and the destination, i.e.,γD= γR= γ ∈ {0, 1,…, 6} dB;2) Relay SNR fixed at γR= 3 dB, and variable destination SNRγD∈ {0, 1,…, 6} dB;P300735. W0.01 - 109197.0000195PATENT APPLICATION3) Destination SNR fixed at YD = 3 dB, variable relay SNRγR∈ {0, 1,…, 6} dB.For all of the above scenarios, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can consider baseline models that are trained at a single SNR γD= γR= γ, where γ ∈ {0, 1,…, 6} dB, The performance of the baselines on the abovementioned scenarios can be analyzed, and alternative learning strategies can be proposed based on robust training.

[0089] 1) The same SNR at both the relay and the destination: Fig. 10 shows an exemplary graph providing the exemplary mutual information when the same SNR is experienced at both the destination and the relay, i.e., γD= γR= γ. The rate constraint is satisfied for all the models R ~ 1 (not shown here). The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can also include a robust model trained on a range of SNRs γD= γR= γ ~ Unif.{0, 1,…, 6} dB. The baseline models trained at a single SNR perform well for adjacent SNRs too. The robust model trained on the range γ ∈ {0, 1,…, 6} dB exhibits a good compromise, offering performance similar to the model trained for the SNR in the middle of the range, and minimal performance degradation in the lower and higher end of the SNR range. Another observation is that models trained for lower SNRs exhibit less degradation at higher SNRs compared to the opposite case; in fact, the models trained at high SNRs fail at lower SNRs.

[0090] 2) A range of SNRs at the destination, fixing the SNR at the relay: Fig. 11 shows an exemplary graph providing the exemplary mutual information achieved as a function of the SNR at the destination γD∈ {0, 1,…, 6} dB, when the SNR at the relay is fixed as γR= 3 dB. In other words, the statistics of the relay’s received signal do not change, while the received signal YD at the destination has variable SNR levels. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can also include two robust models, one trained for a single yR = 3 dB, and a range of yo ~ Unif {0, 1,..., 6} dB, and another trained for SNRs γD= γR= γ ~ Unif.{0, 1,..., 6} dB. Note that the performance of the model trained on a range (with the same SNR on both γD= γR= γ) is equivalent to the performance of the robust model trained for [γR= 3 dB, γD∈ {0, 1,…, 6} dB],

[0091] 3) A range of SNRs at the relay, fixing the SNR at the destination: Fig. 12P300735. W0.01 - 109197.0000195PATENT APPLICATIONillustrates an exemplary graph providing the exemplary mutual information as a function of the SNR at the relay γR∈ {0, 1,…, 6} dB, when the SNR at the destination is fixed as γD= 3 dB. In this case, the received signal YD at the destination has fixed statistics, while the relay’s received signal is subjected to different SNR levels. As above, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can include two robust models, one trained for a single γD= 3 dB, and a range of γR~ Unif.{0, 1,…, 6} dB, and another one trained for SNRs γD= γR= γ ~ Unif.{0, 1,…, 6} dB. Similar to the previous scenario, the performance of the model trained on a range (with the same SNR on both γD= γR= γ) is equivalent to the performance of the robust model trained for [γD= 3 dB, γR∈ {0, 1,…, 6} dB], Also note that, in this scenario, the baseline models trained at an SNR in the vicinity of γD= γR= γ = 3 dB perform well.

[0092] In summary, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure show that training on a range of equal SNRs for both at the relay and the destination provides a good compromise in performance. This suggests good generalization capabilities for both the compressor and the demodulator, eliminating the need for ad-hoc SNR choices during training. Experimental results suggest that knowing the SNR at the destination is generally more important in order to achieve good performance. In principle, the destination could have a fine-tuned model for each SNR (or SNR range) it experiences. Concurrently, the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure demonstrate that training robust relay nodes only requires a rough estimate of the SNR range at the relay.(IV) EXEMPLARY CONCLUSION

[0093] Exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure revisit CF relaying in the context of learned distributed compression and can incorporate a task- oriented neural WZ compressor into a PRC setup as a practical form of CF relaying mechanism. The exemplary framework of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure represents an exemplary functional interpretable learned CF relaying scheme, where both the compressor and the demodulator components areP300735. W0.01 - 109197.0000195PATENT APPLICATIONparameterized with lightweight ANNs. Such exemplary configuration also facilitates the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure to provide post-hoc explanations of these learned components by explicitly visualizing their behaviors. These exemplary results demonstrate that the learned CF schemes of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure can exhibit characteristics of the optimal asymptotic CF, such as binning of the quantized indices at the relay. The performance of these exemplary schemes according to the exemplary embodiments, across various modulation schemes (both real and complex-valued), meets the communication rate of perfect or near perfect relay (R → ∞) with minimal relay rate R. The exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure also demonstrate that training over a range of SNRs, both at the destination and the relay, can provide good generalization over the range of interest, with minimal performance degradation compared to models trained for a specific SNR.

[0094] Extending the exemplary framework of the exemplary systems, methods, and computer accessible medium according to the exemplary embodiments of the present disclosure to a general relay channel, in which the destination does successive decoding of the compressed relay index and the source information, can be made.(IV) EXEMPLARY SYSTEM

[0095] Fig. 13 shows a block diagram of an exemplary embodiment of a system according to the present disclosure. For example, exemplary procedures in accordance with the present disclosure described herein can be performed by a processing arrangement and / or a computing arrangement (e.g., computer hardware arrangement) 1305. Such processing / computing arrangement 1305 can be, for example entirely or a part of, or include, but not limited to, a computer / processor 1310 that can include, for example one or more microprocessors, and use instructions stored on a computer-accessible medium (e.g., RAM, ROM, hard drive, or other storage device).

[0096] As shown in Fig. 13, for example a computer-accessible medium 1315 (e.g., as described herein above, a storage device such as a hard disk, floppy disk, memory stick, CD-ROM, RAM, ROM, etc., or a collection thereof) can be provided (e.g., in communication withP300735. W0.01 - 109197.0000195PATENT APPLICATIONthe processing arrangement 1305). The computer-accessible medium 1315 can contain executable instructions 1320 thereon. In addition, or alternatively, a storage arrangement 1325 can be provided separately from the computer-accessible medium 1315, which can provide the instructions to the processing arrangement 1305 so as to configure the processing arrangement to execute certain exemplary procedures, processes, and methods, as described herein above, for example. Further, the exemplary processing arrangement 1305 can be provided with or include an input / output ports 1335, which can include, for example a wired network, a wireless network, the internet, an intranet, a data collection probe, a sensor, etc. As shown in Fig. 13, the exemplary processing arrangement 1305 can be in communication with an exemplary display arrangement 1330, which, according to certain exemplary embodiments of the present disclosure, can be a touch-screen configured for inputting information to the processing arrangement in addition to outputting information from the processing arrangement, for example. Further, the exemplary display arrangement 1330 and / or a storage arrangement 1325 can be used to display and / or store data in a user-accessible format and / or user-readable format.

[0097] According to the exemplary embodiments of the present disclosure, numerous specific details have been set forth. It is to be understood, however, that implementations of the disclosed technology can be practiced without these specific details. In other instances, well-known methods, structures and techniques have not been shown in detail in order not to obscure an understanding of this description. References to “some examples,” “other examples,” “one example,” “an example,” “various examples,” “one embodiment,” “an embodiment,” “some embodiments,” “example embodiment,” “various embodiments,” “one implementation,” “an implementation,” “example implementation,” “various implementations,” “some implementations,” etc., indicate that the implementation(s) of the disclosed technology so described may include a particular feature, structure, or characteristic, but not every implementation necessarily includes the particular feature, structure, or characteristic. Further, repeated use of the phrases “in one example,” “in one exemplary embodiment,” or “in one implementation” does not necessarily refer to the same example, exemplary embodiment, or implementation, although it may.

[0098] As used herein, unless otherwise specified the use of the ordinal adjectives “first,” “second,” “third,” etc., to describe a common object, merely indicate that different instances of like objects are being referred to, and are not intended to imply that the objects so described mustP300735. W0.01 - 109197.0000195PATENT APPLICATIONbe in a given sequence, either temporally, spatially, in ranking, or in any other manner.

[0099] While certain implementations of the disclosed technology have been described in connection with what is presently considered to be the most practical and various implementations, it is to be understood that the disclosed technology is not to be limited to the disclosed implementations, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

[0100] The foregoing merely illustrates the principles of the disclosure. Various modifications and alterations to the described embodiments will be apparent to those skilled in the art in view of the teachings herein. It will thus be appreciated that those skilled in the art will be able to devise numerous systems, arrangements, and procedures which, although not explicitly shown or described herein, embody the principles of the disclosure and can be thus within the spirit and scope of the disclosure. Various different exemplary embodiments can be used together with one another, as well as interchangeably therewith, as should be understood by those having ordinary skill in the art. In addition, certain terms used in the present disclosure, including the specification and drawings, can be used synonymously in certain instances, including, but not limited to, for example, data and information. It should be understood that, while these words, and / or other words that can be synonymous to one another, can be used synonymously herein, that there can be instances when such words can be intended to not be used synonymously. Further, to the extent that the prior art knowledge has not been explicitly incorporated by reference herein above, it is explicitly incorporated herein in its entirety. All publications referenced are incorporated herein by reference in their entireties.

[0101] Throughout the disclosure, the following terms take at least the meanings explicitly associated herein, unless the context clearly dictates otherwise. The term “or” is intended to mean an inclusive “or.” Further, the terms “a,” “an,” and “the” are intended to mean one or more unless specified otherwise or clear from the context to be directed to a singular form.

[0102] This written description uses examples to disclose certain implementations of the disclosed technology, including the best mode, and also to enable any person skilled in the art to practice certain implementations of the disclosed technology, including making and using anyP300735. W0.01 - 109197.0000195PATENT APPLICATIONdevices or systems and performing any incorporated methods. The patentable scope of certain implementations of the disclosed technology is defined in the appended claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the appended claims if they have structural elements that do not differ from the literal language of the appended claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the appended claims.P300735. W0.01 - 109197.0000195PATENT APPLICATION EXEMPLARY REFERENCES

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Claims

P300735. W0.01 - 109197.0000195PATENT APPLICATION WHAT IS CLAIMED IS:

1. A method for facilitating a compress-and-forward communication format, comprising:observing a signal transmitted by a source configuration at a relay configuration and a destination configuration;compressing the signal observed by the relay configuration using an artificial intelligence (Al) model based on a correlation of the relay to the destination configuration, wherein the AI-based model determines the correlation without visibility of the signal observed by either the relay configuration or the destination configuration;with the relay configuration, forwarding the compressed signal to the destination configuration; andwith the destination configuration, demodulating the compressed signal, and determining information associated with the transmitted signal based on a combination of the signal observed by the destination configuration and the demodulated compressed signal.

2. The method of claim 1, wherein the destination configuration determines the transmitted signal by minimizing or reducing at least one error between the transmitted signal and the determined transmitted signal.

3. The method of claim 1, wherein the AI-based model the AI-based model determines the correlation further based on delivering a maximum number of bits per second to the destination.

4. The method of claim 1, wherein the AI-based model (i) is linked to the relay and destination configurations, and (ii) further performs the demodulation of the compressed signal at the destination.

5. The method of claim 1, wherein the amount of compression performed by the AI-basedmodel is adjusted based on the correlation of the relay configuration to the destinationconfiguration.P300735. W0.01 - 109197.0000195PATENT APPLICATION6. The method of claim 1, wherein the amount of compression performed by the AI-basedmodel is further based on a determined trade-off between a probability of error and anavailable bandwidth.

7. A system for facilitating a compress-and-forward communication format, comprising:a relay configuration configured to:observe a signal transmitted by a source configuration, andcompress the signal observed by the relay configuration using an artificial intelligence (Al) model based on a correlation of the relay to the destination, and wherein the Al-based model determines the correlation without visibility of the signal observed by either the relay configuration or the destination configuration; anda destination configuration configured to:observe the signal transmitted by the source configuration;receive and demodulate the compressed signal, anddetermine information associated with the transmitted signal based on a combination of the signal observed by the destination configuration and the demodulated compressed signal.

8. The system of claim 7, wherein the destination configuration determines the transmitted signal by minimizing or reducing at least one error between the transmitted signal and the determined transmitted signal.

9. The system of claim 7, wherein the AI-based model the AI-based model determines the correlation further based on delivering a maximum number of bits per second to the destination.

10. The system of claim 7, wherein the AI-based model (i) is linked to the relay and destination configurations, and (ii) further performs the demodulation of the compressed signal at the destination.P300735. W0.01 - 109197.0000195PATENT APPLICATION11. The system of claim 7, wherein the amount of compression performed by the AI-basedmodel is adjusted based on the correlation of the relay configuration to the destinationconfiguration.

12. The system of claim 7, wherein the amount of compression performed by the AI-basedmodel is further based on a determined trade-off between a probability of error and anavailable bandwidth.

13. A non-transitory computer-accessible medium having stored thereon computer-executable instructions for facilitating a compress-and-forward communication format, which when executed by a computer arrangement, configure the computer arrangement to perform procedures comprisingobserving a signal transmitted by a source configuration at a relay configuration and a destination configuration;compressing the signal observed by the relay configuration using an artificial intelligence (AI) model based on a correlation of the relay to the destination configuration, wherein the AI-based model determines the correlation without visibility of the signal observed by either the relay configuration or the destination configuration;with the relay configuration, forwarding the compressed signal to the destination configuration; andwith the destination configuration, demodulating the compressed signal, and determining information associated with the transmitted signal based on a combination of the signal observed by the destination configuration and the demodulated compressed signal.

14. The non-transitory computer-accessible medium of claim 13, wherein the destination configuration determines the transmitted signal by minimizing or reducing at least one error between the transmitted signal and the determined transmitted signal.

15. The non-transitory computer-accessible medium of claim 13, wherein the AI-based model the AI-based model determines the correlation further based on delivering a maximum number of bits per second to the destination.P300735. W0.01 - 109197.0000195PATENT APPLICATION16. The non-transitory computer-accessible medium of claim 13, wherein the AI-based model (i) is linked to the relay and destination configurations, and (ii) further performs the demodulation of the compressed signal at the destination.

17. The non-transitory computer-accessible medium of claim 13, wherein the amount of compression performed by the AI-basedmodel is adjusted based on the correlation of the relay configuration to the destinationconfiguration.

18. The non-transitory computer-accessible medium of claim 13, wherein the amount of compression performed by the AI-basedmodel is further based on a determined trade-off between a probability of error and anavailable bandwidth.

19. A method for facilitating a compress-and-forward communication format, comprising:generating an artificial intelligence (AI) model so as to:(i) compress a signal observed by a relay configuration based on a correlation of the relay configuration to a destination configuration and without visibility to the signal observed by either the relay configuration or the destination configuration, and(ii) demodulate the compressed signal at the destination configuration.

20. The method of claim 19, wherein the AI-based model is trained on synthetic data comprising Binary Phase Shift Keying (BPSK) and Pulse Amplitude Modulation 4-level (4-PAM) modulations, having constellations X = {±1} and X = {±1, ±3}, respectively.

21. The method of claim 20, wherein the synthetic data further comprises 8-PAM, with constellation X = {±1, ±3, ±5, ±7}, and Pulse Amplitude Modulation 4-level (4-PAM) 4-QAM and Pulse Amplitude Modulation 16-level (16-QAM) modulations with a predetermined power constraint.P300735. W0.01 - 109197.0000195PATENT APPLICATION22. The method of claim 19, wherein the AI-based model is trained on synthetic data comprising a plurality of additive white Gaussian channels, where one or more input signals are provided from a finite order fixed modulation scheme.

23. A method for facilitating a compress-and-forward communication format, comprising:integrating a task-aware entropy-constrained vector quantization (ECVQ) with a side information so as to the compress-and-forward communication format, wherein a compressor that generates information associated with the compress-and-forward communication format is integrated in a relay, and wherein a demodulator receiving and demodulating the information is integrated in a destination configuration.

24. The method of claim 23, wherein the ECVQ is implemented with a hand-design technique.

25. The method of claim 23, wherein the ECVQ is implemented with an end-to-end learning-based technique.

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