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The surge in demand for efficient radio resource management has necessitated the development of sophisticated yet compact neural network architectures. In this paper, we introduce a novel approach to Graph Neural Networks (GNNs) tailored for radio resource management by presenting a new architecture: the Low Rank Message Passing Graph Neural Network (LR-MPGNN). The cornerstone of LR-MPGNN is the implementation of a low-rank approximation technique that substitutes the conventional linear layers with their low-rank counterparts. This innovative design significantly reduces the model size and the number of parameters. We evaluate the performance of the proposed LR-MPGNN model based on several key metrics: model size, number of parameters, weighted sum rate of the communication system, and the distribution of eigenvalues of weight matrices. Our extensive evaluations demonstrate that the LR-MPGNN model achieves a sixtyfold decrease in model size, and the number of model parameters can be reduced by up to 98%. Performance-wise, the LR-MPGNN demonstrates robustness with a marginal 2% reduction in the best-case scenario in the normalized weighted sum rate compared to the original MPGNN model. Additionally, the distribution of eigenvalues of the weight matrices in the LR-MPGNN model is more uniform and spans a wider range, suggesting a strategic redistribution of weights., Comment: Accepted as a full paper by the tinyML Research Symposium 2024

Utilizing autonomous drones or unmanned aerial vehicles (UAVs) has shown great advantages over preceding methods in support of urgent scenarios such as search and rescue (SAR) and wildfire detection. In these operations, search efficiency in terms of the amount of time spent to find the target is crucial since with the passing of time the survivability of the missing person decreases or wildfire management becomes more difficult with disastrous consequences. In this work, it is considered a scenario where a drone is intended to search and detect a missing person (e.g., a hiker or a mountaineer) or a potential fire spot in a given area. In order to obtain the shortest path to the target, a general framework is provided to model the problem of target detection when the target's location is probabilistically known. To this end, two algorithms are proposed: Path planning and target detection. The path planning algorithm is based on Bayesian inference and the target detection is accomplished by means of a residual neural network (ResNet) trained on the image dataset captured by the drone as well as existing pictures and datasets on the web. Through simulation and experiment, the proposed path planning algorithm is compared with two benchmark algorithms. It is shown that the proposed algorithm significantly decreases the average time of the mission.

User privacy can be compromised by matching user data traces to records of their previous behavior. The matching of the statistical characteristics of traces to prior user behavior has been widely studied. However, an adversary can also identify a user deterministically by searching data traces for a pattern that is unique to that user. Our goal is to thwart such an adversary by applying small artificial distortions to data traces such that each potentially identifying pattern is shared by a large number of users. Importantly, in contrast to statistical approaches, we develop data-independent algorithms that require no assumptions on the model by which the traces are generated. By relating the problem to a set of combinatorial questions on sequence construction, we are able to provide provable guarantees for our proposed constructions. We also introduce data-dependent approaches for the same problem. The algorithms are evaluated on synthetic data traces and on the Reality Mining Dataset to demonstrate their utility.

The Internet of Things (IoT) promises to improve user utility by tuning applications to user behavior, but revealing the characteristics of a user's behavior presents a significant privacy risk. Our previous work has established the challenging requirements for anonymization to protect users' privacy in a Bayesian setting in which we assume a powerful adversary who has perfect knowledge of the prior distribution for each user's behavior. However, even sophisticated adversaries do not often have such perfect knowledge; hence, in this paper, we turn our attention to an adversary who must learn user behavior from past data traces of limited length. We also assume there exists dependency between data traces of different users, and the data points of each user are drawn from a normal distribution. Results on the lengths of training sequences and data sequences that result in a loss of user privacy are presented.

The prevalence of mobile devices and Location-Based Services (LBS) necessitate the study of Location Privacy-Preserving Mechanisms (LPPM). However, LPPMs reduce the utility of LBS due to the noise they add to users' locations. Here, we consider the remapping technique, which presumes the adversary has a perfect statistical model for the user location. We consider this assumption and show that under practical assumptions on the adversary's knowledge, the remapping technique leaks privacy not only about the true location data, but also about the statistical model. Finally, we introduce a novel solution called "Randomized Remapping" as a countermeasure., Comment: Submitted to IEEE Wireless Communications Letters

Unmanned aerial vehicles (UAVs) have become important in many applications including last-mile deliveries, surveillance and monitoring, and wireless networks. This paper aims to design UAV trajectories that simultaneously perform multiple tasks. We aim to design UAV trajectories that minimize package delivery time, and at the same time provide uniform coverage over a neighborhood area which is needed for applications such as network coverage or surveillance. We first consider multi-task UAVs for a simplified scenario where the neighborhood area is a circular region with the post office located at its center and the houses are assumed to be uniformly distributed on the circle boundary. We propose a trajectory process such that if according to which the drones move, a uniform coverage can be achieved while the delivery efficiency is still preserved. We then consider a more practical scenario in which the delivery destinations are arbitrarily distributed in an arbitrarily-shaped region. We also do not assume any restrictions on the package arrivals. We show that simultaneous uniform coverage and efficient package delivery is possible for such realistic scenarios. This is shown using both rigorous analyses as well as simulations.

The rapid growth of computer systems which generate graph data necessitates employing privacy-preserving mechanisms to protect users' identity. Since structure-based de-anonymization attacks can reveal users' identity's even when the graph is simply anonymized by employing naive ID removal, recently, $k-$anonymity is proposed to secure users' privacy against the structure-based attack. Most of the work ensured graph privacy using fake edges, however, in some applications, edge addition or deletion might cause a significant change to the key property of the graph. Motivated by this fact, in this paper, we introduce a novel method which ensures privacy by adding fake nodes to the graph. First, we present a novel model which provides $k-$anonymity against one of the strongest attacks: seed-based attack. In this attack, the adversary knows the partial mapping between the main graph and the graph which is generated using the privacy-preserving mechanisms. We show that even if the adversary knows the mapping of all of the nodes except one, the last node can still have $k-$anonymity privacy. Then, we turn our attention to the privacy of the graphs generated by inter-domain routing against degree attacks in which the degree sequence of the graph is known to the adversary. To ensure the privacy of networks against this attack, we propose a novel method which tries to add fake nodes in a way that the degree of all nodes have the same expected value., Comment: Graph Privacy

In this paper, we propose a new practical power allocation technique based on bit error probability (BEP) for physical layer security systems. It is shown that the secrecy rate that is the most commonly used in physical layer security systems, cannot be a suitable criterion lonely. Large positive values are suitable for the secrecy rate in physical layer security, but it does not consider the performance of the legitimate and adversary users. In this paper, we consider and analyze BEP for physical layer security systems because based on it, the performance of the legitimate and adversary users are guaranteed and it is needed to use lower power. BEP is calculated for the legitimate and adversary users and it is shown that BEP can be better criterion for performance evaluation of the physical layer security systems. Based on BEP, the optimum transmit power is obtained and a new definition for outage probability is proposed and obtained theoretically. Also, the proposed approach is applied for adversary users with unknown mode and the cooperative adversary users. Simulation results show that the proposed method needs more than 5dB lower power for different scenarios., Comment: 11 pages, 9 figures

In this paper, a new queuing model for the Tactile Internet (TI) is proposed for the cloud radio access network (C-RAN) architecture of the next generation wireless networks, e.g., 5G, assisted via orthogonal frequency division multiple access (OFDMA) technology. This model includes both the radio remote head (RRH) and baseband processing unit (BBU) queuing delays and reliability for each end to end (E2E) connection between each pair of tactile users. For this setup, with the aim to minimize the transmit power of users subject to guaranteeing tolerable delay of users, and fronthaul and access limitations, we formulate a resource allocation problem. Since the proposed optimization problem is highly non-convex, to solve it in an efficient manner, we utilize diverse transformation techniques such as successive convex approximation (SCA) and difference of two convex functions (DC). In addition, we propose an admission control (AC) algorithm to make problem feasible. In our proposed system model, we dynamically adjust the fronthaul and access links to minimize the transmit power. Simulation results reveal that by dynamic adjustment of the access and fronthaul delays, transmit power can be saved compared to the case of fixed approach per each transmission session. Moreover, the number of rejected users in the network is significantly reduced and more users are accepted., Comment: arXiv admin note: substantial text overlap with arXiv:1901.09389

Various modern and highly popular applications make use of user data traces in order to offer specific services, often for the purpose of improving the user's experience while using such applications. However, even when user data is privatized by employing privacy-preserving mechanisms (PPM), users' privacy may still be compromised by an external party who leverages statistical matching methods to match users' traces with their previous activities. In this paper, we obtain the theoretical bounds on user privacy for situations in which user traces are matchable to sequences of prior behavior, despite anonymization of data time series. We provide both achievability and converse results for the case where the data trace of each user consists of independent and identically distributed (i.i.d.) random samples drawn from a multinomial distribution, as well as the case that the users' data points are dependent over time and the data trace of each user is governed by a Markov chain model., Comment: The 53rd Annual Conference on Information Sciences and Systems

Ultra-low latency is the most important requirement of the Tactile Internet (TI), which is one of the proposed services for the next-generation wireless network (NGWN), e.g., fifth generation (5G) network. In this paper, a new queuing model for the TI is proposed for the cloud radio access network (CRAN) architecture of the NGWN by applying power domain non-orthogonal multiple access (PD-NOMA) technology. In this model, we consider both the radio remote head (RRH) and baseband processing unit (BBU) queuing delays for each end-to-end (E2E) connection between a pair of tactile users. In our setup, to minimize the transmit power of users subject to guaranteeing an acceptable delay of users, and fronthaul and access constraints, we formulate a resource allocation (RA) problem. Furthermore, we dynamically set the fronthaul and access links to minimize the total transmit power. Given that the proposed RA problem is highly non-convex, in order to solve it, we utilize diverse transformation techniques such as successive convex approximation (SCA) and difference of two convex functions (DC). Numerical results show that by dynamic adjustment of the access and fronthaul delays, transmit power reduces in comparison with the fixed approach per each connection. Also, energy efficiency of orthogonal frequency division multiple access (OFDMA) and PD-NOMA are compared for our setup.

The rapid growth of the Internet of Things (IoT) necessitates employing privacy-preserving techniques to protect users' sensitive information. Even when user traces are anonymized, statistical matching can be employed to infer sensitive information. In our previous work, we have established the privacy requirements for the case that the user traces are instantiations of discrete random variables and the adversary knows only the structure of the dependency graph, i.e., whether each pair of users is connected. In this paper, we consider the case where data traces are instantiations of Gaussian random variables and the adversary knows not only the structure of the graph but also the pairwise correlation coefficients. We establish the requirements on anonymization to thwart such statistical matching, which demonstrate the significant degree to which knowledge of the pairwise correlation coefficients further significantly aids the adversary in breaking user anonymity., Comment: IEEE Wireless Communications and Networking Conference

Modern applications significantly enhance user experience by adapting to each user's individual condition and/or preferences. While this adaptation can greatly improve a user's experience or be essential for the application to work, the exposure of user data to the application presents a significant privacy threat to the users\textemdash even when the traces are anonymized\textemdash since the statistical matching of an anonymized trace to prior user behavior can identify a user and their habits. Because of the current and growing algorithmic and computational capabilities of adversaries, provable privacy guarantees as a function of the degree of anonymization and obfuscation of the traces are necessary. Our previous work has established the requirements on anonymization and obfuscation in the case that data traces are independent between users. However, the data traces of different users will be dependent in many applications, and an adversary can potentially exploit such. In this paper, we consider the impact of dependency between user traces on their privacy. First, we demonstrate that the adversary can readily identify the association graph of the obfuscated and anonymized version of the data, revealing which user data traces are dependent. Next, we demonstrate that the adversary can use this association graph to break user privacy with significantly shorter traces than in the case of independent users, and that obfuscating data traces independently across users is often insufficient to remedy such leakage. Finally, we discuss how users can improve privacy by employing joint obfuscation that removes or reduces the data dependency., Comment: Submitted to IEEE Transaction on Information Theory

Modern applications significantly enhance user experience by adapting to each user's individual condition and/or preferences. While this adaptation can greatly improve utility or be essential for the application to work (e.g., for ride-sharing applications), the exposure of user data to the application presents a significant privacy threat to the users, even when the traces are anonymized, since the statistical matching of an anonymized trace to prior user behavior can identify a user and their habits. Because of the current and growing algorithmic and computational capabilities of adversaries, provable privacy guarantees as a function of the degree of anonymization and obfuscation of the traces are necessary. Our previous work has established the requirements on anonymization and obfuscation in the case that data traces are independent between users. However, the data traces of different users will be dependent in many applications, and an adversary can potentially exploit such. In this paper, we consider the impact of correlation between user traces on their privacy. First, we demonstrate that the adversary can readily identify the association graph, revealing which user data traces are correlated. Next, we demonstrate that the adversary can use this association graph to break user privacy with significantly shorter traces than in the case when traces are independent between users, and that independent obfuscation of the data traces is often insufficient to remedy such. Finally, we discuss how the users can employ dependency in their obfuscation to improve their privacy., Comment: arXiv admin note: text overlap with arXiv:1702.02701 and arXiv:1710.00197

Many popular applications use traces of user data to offer various services to their users. However, even if user data is anonymized and obfuscated, a user's privacy can be compromised through the use of statistical matching techniques that match a user trace to prior user behavior. In this work, we derive the theoretical bounds on the privacy of users in such a scenario. We build on our recent study in the area of location privacy, in which we introduced formal notions of location privacy for anonymization-based location privacy-protection mechanisms. Here we derive the fundamental limits of user privacy when both anonymization and obfuscation-based protection mechanisms are applied to users' time series of data. We investigate the impact of such mechanisms on the trade-off between privacy protection and user utility. We first study achievability results for the case where the time-series of users are governed by an i.i.d. process. The converse results are proved both for the i.i.d. case as well as the more general Markov chain model. We demonstrate that as the number of users in the network grows, the obfuscation-anonymization plane can be divided into two regions: in the first region, all users have perfect privacy; and, in the second region, no user has privacy., Comment: 48 pages, 12 figures, Submitted to IEEE Transactions on Information Theory

In this paper, a new approach for multiple access (MA) in fifth generation (5G) of cellular networks called power domain sparse code multiple access (PSMA) is proposed. In PSMA, we adopt both the power domain and the code domain to transmit multiple users' signals over a subcarrier simultaneously. In such a model, the same SCMA codebook can be used by multiple users where, for these users, power domain non-orthogonal multiple access (PD-NOMA) technique is used to send signals non-orthogonally. Although different SCMA codebooks are orthogonal and produce no interference over each other, the same codebook used by multiple users produces interference over these users. We investigate the signal model as well as the receiver and transmitter of the PSMA method. To evaluate the performance of PSMA, we consider a heterogeneous cellular network (HetNet). In this case our design objective is to maximize the system sum rate of the network subject to some system level and QoS constraints such as transmit power constraints. We formulate the proposed resource allocation problem as an optimization problem and solve it by successive convex approximation (SCA) techniques. Moreover, we compare PSMA with sparse code multiple access (SCMA) and PD-NOMA from the performance and computational complexity perspective. Finally, the effectiveness of the proposed approach is investigated using numerical results. We show that by a reasonable increase in complexity, PSMA can improve the spectral efficiency about 50\% compared to SCMA and PD-NOMA., Comment: 11 pages, 8 figures, journal

This paper considers secure energy-efficient routing in the presence of multiple passive eavesdroppers. Previous work in this area has considered secure routing assuming probabilistic or exact knowledge of the location and channel-state-information (CSI) of each eavesdropper. In wireless networks, however, the locations and CSIs of passive eavesdroppers are not known, making it challenging to guarantee secrecy for any routing algorithm. We develop an efficient (in terms of energy consumption and computational complexity) routing algorithm that does not rely on any information about the locations and CSIs of the eavesdroppers. Our algorithm guarantees secrecy even in disadvantaged wireless environments, where multiple eavesdroppers try to eavesdrop each message, are equipped with directional antennas, or can get arbitrarily close to the transmitter. The key is to employ additive random jamming to exploit inherent non-idealities of the eavesdropper's receiver, which makes the eavesdroppers incapable of recording the messages. We have simulated our proposed algorithm and compared it with existing secrecy routing algorithms in both single-hop and multi-hop networks. Our results indicate that when the uncertainty in the locations of eavesdroppers is high and/or in disadvantaged wireless environments, our algorithm outperforms existing algorithms in terms of energy consumption and secrecy.

The popularity of mobile devices and location-based services (LBS) has created great concern regarding the location privacy of their users. Anonymization is a common technique that is often used to protect the location privacy of LBS users. Here, we present an information-theoretic approach to define the notion of perfect location privacy. We show how LBS's should use the anonymization method to ensure that their users can achieve perfect location privacy. First, we assume that a user's current location is independent from her past locations. Using this i.i.d model, we show that if the pseudonym of the user is changed before $O(n^{\frac{2}{r-1}})$ observations are made by the adversary for that user, then the user has perfect location privacy. Here, n is the number of the users in the network and r is the number of all possible locations that users can go to. Next, we model users' movements using Markov chains to better model real-world movement patterns. We show that perfect location privacy is achievable for a user if the user's pseudonym is changed before $O(n^{\frac{2}{|E|-r}})$ observations are collected by the adversary for the user, where |E| is the number of edges in the user's Markov chain model., Comment: 12 pages, 3 figures

This paper studies the need for individualizing vehicular communications in order to improve collision warning systems for an N-lane highway scenario. By relating the traffic-based and communications studies, we aim at reducing highway traffic accidents. To the best of our knowledge, this is the first paper that shows how to customize vehicular communications to driver's characteristics and traffic information. We propose to develop VANET protocols that selectively identify crash relevant information and customize the communications of that information based on each driver's assigned safety score. In this paper, first, we derive the packet success probability by accounting for multi-user interference, path loss, and fading. Then, by Monte carlo simulations, we demonstrate how appropriate channel access probabilities that satisfy the delay requirements of the safety application result in noticeable performance enhancement., Comment: A major reason: Since now CV2X has considerable advantages over 802.11p and it can be the next specification used for V2X communication, I'd like to withdraw this paper in order to make it easier for the readers to find the best papers in the area. See: https://www.qualcomm.com/news/onq/2018/04/25/lets-set-record-straight-c-v2x

Secure communication over a wiretap channel is considered in the disadvantaged wireless environment, where the eavesdropper channel is (possibly much) better than the main channel. We present a method to exploit inherent vulnerabilities of the eavesdropper's receiver to obtain everlasting secrecy. Based on an ephemeral cryptographic key pre-shared between the transmitter Alice and the intended recipient Bob, a random jamming signal is added to each symbol. Bob can subtract the jamming signal before recording the signal, while the eavesdropper Eve is forced to perform these non-commutative operations in the opposite order. Thus, information-theoretic secrecy can be obtained, hence achieving the goal of converting the vulnerable "cheap" cryptographic secret key bits into "valuable" information-theoretic (i.e. everlasting) secure bits. We evaluate the achievable secrecy rates for different settings, and show that, even when the eavesdropper has perfect access to the output of the transmitter (albeit through an imperfect analog-to-digital converter), the method can still achieve a positive secrecy rate. Next we consider a wideband system, where Alice and Bob perform frequency hopping in addition to adding the random jamming to the signal, and we show the utility of such an approach even in the face of substantial eavesdropper hardware capabilities.

The effectiveness and simple implementation of physical layer jammers make them an essential threat for wireless networks. In a multihop wireless network, where jammers can interfere with the transmission of user messages at intermediate nodes along the path, one can employ jamming oblivious routing and then employ physical-layer techniques (e.g. spread spectrum) to suppress jamming. However, whereas these approaches can provide significant gains, the residual jamming can still severely limit system performance. This motivates the consideration of routing approaches that account for the differences in the jamming environment between different paths. First, we take a straightforward approach where an equal outage probability is allocated to each link along a path and develop a minimum energy routing solution. Next, we demonstrate the shortcomings of this approach and then consider the joint problem of outage allocation and routing by employing an approximation to the link outage probability. This yields an efficient and effective routing algorithm that only requires knowledge of the measured jamming at each node. Numerical results demonstrate that the amount of energy saved by the proposed methods with respect to a standard minimum energy routing algorithm, especially for parameters appropriate for terrestrial wireless networks, is substantial.

This paper discusses the need for individualizing safety systems and proposes an approach including the Real-Time estimation of the distribution of brake response times for an individual driver. While maintaining high level of safety, the collision warning system should send "tailored" responses to the driver. This method could be the first step to show that safety applications would potentially benefit from customizing to individual drivers' characteristics using VANET. Our simulation results show that, as one of the imminent and preliminary outcomes of the new improved system, the number of false alarms will be reduced by more than 40%. We think this tactic can reach to even beyond the safety applications for designing the future innovative systems.

Adapting the functioning of the collision warning systems to the specific drivers' characteristics is of great benefit to drivers. For example, by customizing collision warning algorithms we can minimize false alarms, thereby reducing injuries and deaths in highway traffic accidents. In order to take the behaviors of individual drivers into account, the system needs to have a Real-Time estimation of the distribution of brake response times for an individual driver. In this paper, we propose a method for doing this estimation which is not computationally intensive and can take advantage of the information contained in all data points.

Every year, many people are killed and injured in highway traffic accidents. In order to reduce such casualties, collisions warning systems has been studied extensively. These systems are built by taking the driver reaction times into account. However, most of the existing literature focuses on characterizing how driver reaction times vary across an entire population. Therefore, many of the warnings that are given turn out to be false alarms. A false alarm occurs whenever a warning is sent, but it is not needed. This would nagate any safety benefit of the system, and could even reduce the overall safety if warnings become a distraction. In this paper, we propose our solution to address the described problem; First, we briefly describe our method for estimating the distribution of brake response times for a particular driver using data from a Vehicular Ad-Hoc Network (VANET) system. Then, we investigate how brake response times of individual drivers can be used in collision warning algorithms to reduce false alarm rates while still maintaining a high level of safety. This will yield a system that is overall more reliable and trustworthy for drivers, which could lead to wider adoption and applicability for V2V/V2I communication systems. Moreover, we show how false alarm rate varies with respect to probability of accident. Our simulation results show that by individualizing collision warnings the number of false alarms can be reduced more than $50\%$. Then, we conclude safety applications could potentially take full advantage of being customized to an individual's characteristics., Comment: A major reason: Since now CV2X has considerable advantages over 802.11p and it can be the next specification used for V2X communication, I'd like to withdraw this paper in order to make it easier for the readers to find the best papers in the area. See: https://www.qualcomm.com/news/onq/2018/04/25/lets-set-record-straight-c-v2x

Many analytic results for the connectivity, coverage, and capacity of wireless networks have been reported for the case where the number of nodes, $n$, tends to infinity (large-scale networks). The majority of these results have not been extended for small or moderate values of $n$; whereas in many practical networks, $n$ is not very large. In this paper, we consider finite (small-scale) wireless sensor networks. We first show that previous asymptotic results provide poor approximations for such networks. We provide a set of differences between small-scale and large-scale analysis and propose a methodology for analysis of finite sensor networks. Furthermore, we consider two models for such networks: unreliable sensor grids, and sensor networks with random node deployment. We provide easily computable expressions for bounds on the coverage and connectivity of these networks. With validation from simulations, we show that the derived analytic expressions give very good estimates of such quantities for finite sensor networks. Our investigation confirms the fact that small-scale networks possesses unique characteristics different from the large-scale counterparts, necessitating the development of a new framework for their analysis and design.

Secure communication over a memoryless wiretap channel in the presence of a passive eavesdropper is considered. Traditional information-theoretic security methods require an advantage for the main channel over the eavesdropper channel to achieve a positive secrecy rate, which in general cannot be guaranteed in wireless systems. Here, we exploit the non-linear conversion operation in the eavesdropper's receiver to obtain the desired advantage - even when the eavesdropper has perfect access to the transmitted signal at the input to their receiver. The basic idea is to employ an ephemeral cryptographic key to force the eavesdropper to conduct two operations, at least one of which is non-linear, in a different order than the desired recipient. Since non-linear operations are not necessarily commutative, the desired advantage can be obtained and information-theoretic secrecy achieved even if the eavesdropper is given the cryptographic key immediately upon transmission completion. In essence, the lack of knowledge of the key during the short transmission time inhibits the recording of the signal in such a way that the secret information can never be extracted from it. The achievable secrecy rates for different countermeasures that the eavesdropper might employ are evaluated. It is shown that even in the case of an eavesdropper with uniformly better conditions (channel and receiver quality) than the intended recipient, a positive secure rate can be achieved.

In this paper, we study polar codes from a practical point of view. In particular, we study concatenated polar codes and rate-compatible polar codes. First, we propose a concatenation scheme including polar codes and Low-Density Parity-Check (LDPC) codes. We will show that our proposed scheme outperforms conventional concatenation schemes formed by LDPC and Reed-Solomon (RS) codes. We then study two rate-compatible coding schemes using polar codes. We will see that polar codes can be designed as universally capacity achieving rate-compatible codes over a set of physically degraded channels. We also study the effect of puncturing on polar codes to design rate-compatible codes.