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This paper considers the achievability and converse bounds on the maximal channel coding rate at a given blocklength and error probability over AWGN channels. The problem stems from covert communication with Gaussian codewords. By re-visiting [18], we first present new and more general achievability bounds for random coding schemes under maximal or average probability of error requirements. Such general bounds are then applied to covert communication in AWGN channels where codewords are generated from Gaussian distribution while meeting the maximal power constraint. Further comparison is made between the new achievability bounds and existing one with deterministic codebooks., 18 pages

In this paper, we consider the problem of partitioning active users in a manner that facilitates multi-access without collision. The setting is of a noisy, synchronous, Boolean, multi-access channel where $K$ active users (out of a total of $N$ users) seek to access. A solution to the partition problem places each of the $N$ users in one of $K$ groups (or blocks) such that no two active nodes are in the same block. We consider a simple, but non-trivial and illustrative case of $K=2$ active users and study the number of steps $T$ used to solve the partition problem. By random coding and a suboptimal decoding scheme, we show that for any $T\geq (C_1 +\xi_1)\log N$, where $C_1$ and $\xi_1$ are positive constants (independent of $N$), and $\xi_1$ can be arbitrary small, the partition problem can be solved with error probability $P_e^{(N)} \to 0$, for large $N$. Under the same scheme, we also bound $T$ from the other direction, establishing that, for any $T \leq (C_2 - \xi_2) \log N$, the error probability $P_e^{(N)} \to 1$ for large $N$; again $C_2$ and $\xi_2$ are constants and $\xi_2$ can be arbitrarily small. These bounds on the number of steps are lower than the tight achievable lower-bound in terms of $T \geq (C_g +\xi)\log N $ for group testing (in which all active users are identified, rather than just partitioned). Thus, partitioning may prove to be a more efficient approach for multi-access than group testing., Comment: This paper was submitted in June 2014 to IEEE Transactions on Information Theory, and is under review now

We propose a mixture-Gaussian model for a cognitive radio channel to analyze the interplay between the interference in the system and the degrees-of-freedom (DOF), i.e., the average number of channel uses per transmission frame, used by the secondary user (SU) for communications in the long run. In contrast to the conventional studies, we assume that the SU receiver (SU-RX) does not precisely know whether the primary-user (PU) transmitter is on or off. Due to this assumption the resulting interference channel is mixture-Gaussian. Our objective is to find the optimal sensing threshold and sensing time for the signal detector used by the SU transmitter (SU-TX). Our formulation of the optimization problem reflects the trade-off between SU-TX’s DOF for communications and that for detection. Both the DOFs affect PU’s interference to SU, and SU’s interference to PU. The latter interference causes PU performance degradation, which is kept within tolerable range as a constraint. As a further contribution, we define interference regimes for SU performance on the basis of PU transmission power level. We also address the scenario when PU receiver uses the nearest neighbor decoding while wrongly anticipating that the channel is Gaussian. Finally, we demonstrate that even if SU-TX’s signal detector performs suboptimally, SU can still achieve the optimal detector’s performance in the high interference regime by adjusting the sensing parameters.

In this paper, we propose a novel partition reservation system to study the partition information and its transmission over a noise-free Boolean multi-access channel. The objective of transmission is not message restoration, but to partition active users into distinct groups so that they can, subsequently, transmit their messages without collision. We first calculate (by mutual information) the amount of information needed for the partitioning without channel effects, and then propose two different coding schemes to obtain achievable transmission rates over the channel. The first one is the brute force method, where the codebook design is based on centralized source coding; the second method uses random coding where the codebook is generated randomly and optimal Bayesian decoding is employed to reconstruct the partition. Both methods shed light on the internal structure of the partition problem. A novel hypergraph formulation is proposed for the random coding scheme, which intuitively describes the information in terms of a strong coloring of a hypergraph induced by a sequence of channel operations and interactions between active users. An extended Fibonacci structure is found for a simple, but non-trivial, case with two active users. A comparison between these methods and group testing is conducted to demonstrate the uniqueness of our problem., Comment: Submitted to IEEE Transactions on Information Theory, major revision

This paper focuses on the problem of sharing secret keys using Automatic Repeat reQuest (ARQ) protocol. We consider cases where forward and feedback channels are erasure channels for a legitimate receiver (Bob) and an eavesdropper (Eve). In prior works, the wiretap channel is modeled as statistically independent packet erasure channels for Bob and Eve. In this paper, we go beyond the state-of-the-art by addressing correlated erasure events across the wiretap channel. The created randomness is shared between two legitimate parties through ARQ transmissions that is mapped into a destination set using a first-order digital filter with feedback. Then, we characterize Eve's information loss about this shared destination set, due to inevitable transmission errors. This set is then transformed into a highly secure key using privacy amplification in order to intensify and exploit Eve's lack of knowledge. We adopt two criteria for analysis and design of the system: secrecy outage probability as a measure of the secrecy quality, and secret key rate as a metric for efficiency. The resulting secrecy improvement is presented as a function of the correlation coefficients and the erasure probabilities for both channels. It is shown that secrecy improvement is achievable even when Eve has a better channel than legitimate receivers, and her channel conditions are unknown to legitimate users.

In this paper, we propose a feedback scheme for transmitting secret messages between two legitimate parties, over an eavesdropped communication link. Relative to Wyner's traditional encoding scheme, our feedback-based encoding often yields larger rate-equivocation regions and achievable secrecy rates. More importantly, by exploiting the channel randomness inherent in the feedback channels, our scheme achieves a strictly positive secrecy rate even when the eavesdropper's channel is less noisy than the legitimate receiver's channel. All channels are modeled as binary and symmetric. We demonstrate the versatility of our feedback-based encoding method by using it in three different configurations: the stand-alone configuration, the mixed configuration (when it combines with Wyner's scheme), and the reversed configuration. Depending on the channel conditions, significant improvements over Wyner's secrecy capacity can be observed in all configurations.

In this paper, we study the problem of half-duplex active eavesdropping in fast-fading channels. The active eavesdropper is a more powerful adversary than the classical eavesdropper. It can choose between two functional modes: eavesdropping the transmission between the legitimate parties (Ex mode), and jamming it (Jx mode)-the active eavesdropper cannot function in full duplex mode. We consider a conservative scenario, when the active eavesdropper can choose its strategy based on the legitimate transmitter-receiver pair's strategy, and thus, the transmitter and legitimate receiver have to plan for the worst. We show that conventional physical-layer secrecy approaches perform poorly (if at all), and we introduce a novel encoding scheme, based on very limited and unsecured feedback-the Block-Markov Wyner encoding scheme-which outperforms any schemes currently available.

We consider a constrained energy optimization called minimum energy scheduling problem (MESP) for a wireless network of N users transmitting over M time slots, where the constraints arise because of interference between wireless nodes that limits their transmission rates along with load and duty-cycle (on-off) restrictions. Since traditional optimization methods using Lagrange multipliers do not work well and are computationally expensive given the nonconvex constraints, we consider approximation schemes for finding the optimal (minimum energy) transmission schedule by discretizing power levels over the interference channel. First, we show the toughness of approximating MESP for an arbitrary number of users N even with a fixed M. For any r > 0, we demonstrate that there does not exist any (r, r)-bicriteria approximation for this MESP, unless P = NP . Conversely, we show that there exist good approximations for MESP with given N users transmitting over an arbitrary number of M time slots by developing fully polynomial (1,1+?) approximation schemes (FPAS). For any ? > 0, we develop an algorithm for computing the optimal number of discrete power levels per time slot (O(1/?)), and use this to design a (1, 1+?)-FPAS that consumes no more energy than the optimal while violating each rate constraint by at most a 1+?-factor. For wireless networks with low-cost transmitters, where nodes are restricted to transmitting at a fixed power over active time slots, we develop a two-factor approximation for finding the optimal fixed transmission power value P opt that results in the minimum energy schedule.

Wireless links form a critical component of communication systems that aim to provide ubiquitous access to information. However, the time-varying characteristics (or "state") of wireless channels caused by the mobility of transmitters, receivers, and objects in the environment make it difficult to achieve reliable communication. Adaptive signaling exploits any channel state information (CSI) available at the transmitter to provide the potential to significantly increase the throughput of wireless links and/or greatly reduce the receiver complexity. As such, adaptive signaling has attracted significant research interest in the last decade and has found application in numerous commercial wireless systems, ranging from cellular data systems to wireless local area networks (WLANs). However, one of the great challenges of wireless communications is that it is difficult to obtain perfect CSI due to the inherently noisy and outdated nature of CSI available at the transmitter. Over the last decade, we have championed the idea of choosing the appropriate transmitted signal based on statistical models for the current channel state conditioned on the channel measurements. In this semi-tutorial paper, we first review how this class of methods has been developed for single-antenna systems, and then present novel recent designs for multiple-antenna systems. Key to the development in each case is the development of the error characterization given the outdated estimates and the use of such to allocate data rate and power over time and possibly space. In general, the focus is on rate allocation, while power allocation is done through a pruning method. Numerical results will demonstrate in both the single-antenna and multiple-antenna cases that such an approach provides a robust method for improving system data rate versus the standard practice of employing link margin to compensate for such uncertainties.

Synchronization of relay nodes is an important and critical issue in exploiting cooperative diversity in wireless networks. In this paper, two asynchronous cooperative diversity schemes are proposed, namely, distributed delay diversity and asynchronous space-time coded cooperative diversity schemes. In terms of the overall diversity-multiplexing (DM) tradeoff function, we show that the proposed independent coding based distributed delay diversity and asynchronous space-time coded cooperative diversity schemes achieve the same performance as the synchronous space-time coded approach which requires an accurate symbol-level timing synchronization to ensure signals arriving at the destination from different relay nodes are perfectly synchronized. This demonstrates diversity order is maintained even at the presence of asynchronism between relay node. Moreover, when all relay nodes succeed in decoding the source information, the asynchronous space-time coded approach is capable of achieving better DM tradeoff than synchronous schemes and performs equivalently to transmitting information through a parallel fading channel as far as the DM tradeoff is concerned. Our results suggest the benefits of fully exploiting the space-time degrees of freedom in multiple antenna systems by employing asynchronous space-time codes even in a frequency-flat-fading channel. In addition, it is shown asynchronous space-time coded systems are able to achieve higher mutual information than synchronous space-time coded systems for any finite signal-to-noise ratio (SNR) when properly selected baseband waveforms are employed.

Cooperative diversity, which employs multiple nodes for the simultaneous relaying of a given packet in wireless ad hoc networks, has been shown to be an effective means of improving diversity, and, hence, mitigating the detrimental effects of multipath fading. However, in previously proposed cooperative diversity schemes, it has been assumed that coordination among the relays allows for accurate symbol-level timing synchronization at the destination and orthogonal channel allocation, which can be quite costly in terms of signaling overhead in mobile ad hoc networks, which are often defined by their lack of a fixed infrastructure and the difficulty of centralized control. In this paper, cooperative diversity schemes are considered that do not require symbol-level timing synchronization or orthogonal channelization between the relays employed. In the process, a novel minimum mean-squared error (MMSE) receiver is designed for combining disparate inputs in the multiple-relay channel. Outage probability calculations and simulation results demonstrate the not unexpected significant performance gains of the proposed schemes over single-hop transmission, and, more importantly, demonstrate performance comparable to schemes requiring accurate symbol-level synchronization and orthogonal channelization

Impulsive ultra-wideband (UWB) radio provides many promising features for wireless communications in a dense multipath environment. However, these features are largely the result of the enormous effective processing gain, which can make acquisition difficult at the receiver. In this paper, a recently developed theory of minimum complexity sequential detection is applied to the hybrid acquisition problem. As in previous hybrid schemes, a number of potential timing phases are checked as a group; however, a phase is disregarded as soon as it appears unlikely rather than waiting for a "winner" to be chosen from the group. Another phase then replaces the disregarded one. Analysis and simulation results indicate that the proposed scheme can improve average acquisition times for highly spread systems operating over either additive white Gaussian noise (AWGN) or multipath fading channels.

The measurement of the average received power is essential for power control and dynamic channel allocation in wireless communication systems. However, due to the effects of multipath fading and additive noise inherent to the wireless channel, there can be significant errors in such measurements. In this paper, the error statistics for average power measurements are considered; in particular, the probability distribution of the value of the average received power at the time of interest conditioned on an outdated measurement is obtained. The resulting expression should have high utility in the analysis of wireless communication systems. However, in this paper, the design of power control algorithms that minimize the average transmitted power required to achieve a desired outage probability for the link is considered. A number of novel power control algorithms based on various models for the error in the average power measurement are derived. Numerical results indicate that power control algorithms based on the accurate expression derived in this paper can demonstrate significant gains over those based on previous approximate models.

We explore the degrees-of-freedom and interference tradeoff for a simple cognitive radio system under an assumption that the secondary-user (SU) receiver operates incoherently with the primary-user (PU) transmitter. This assumption makes our system model practically more rigorous, as compared to the conventional studies where a coherent operation is assumed. Due to the incoherent operation of SU receiver, the resulting interference channel is mixture-Gaussian. Our objective is to find the optimal sensing threshold and sensing time, for the signal detector that is used by the SU, such that the SU performance is maximized while the PU performance degradation, caused by the interference due to SU, remains within a tolerable range. Also, we define the interference regimes for SU performances on the basis of PU transmission power level.

In this paper we propose an encoding-encryption approach to take advantage of intentional noise introduced in ciphertexts for a block cipher working in CFB or CBC mode. First of all, we provide a rigorous analysis of the impacts of channel degradation on block ciphered systems. We show that the overall channel can be modeled as a Finite State Markov Chain (FSMC) with symmetric channels associated in each state, whose underlying non-coherent Shannon capacity is derived and computed. Despite Eve's efforts in modifying her linear crytanalysis given the intercepted noisy ciphertexts, there is still a non-negligible probability of having possible failures in her attack. We essentially create a wiretap channel in application layer that is a degraded version of the main channel and measure security of the system in terms of secrecy capacity and show that it depends on the deliberately introduced bit error rate. In addition, Alice can accordingly adjust cross over probability of the channel to maximize secrecy rate. This secrecy rate can be achieved by wiretap channel coding over multiple frames in application layer if the delay in system is bearable.

This paper focuses on the problem of sharing secret keys using the Automatic Repeat reQuest (ARQ) protocol. We first model the forward and feedback channels as erasure channels for both legitimate receiver (Bob) and an eavesdropper (Eve). In prior works, wiretap channel is modeled as statistically independent packet erasure channels for Bob and Eve. In this paper, we go beyond the state-of-the-art by addressing correlated erasure events across the wiretap channel. The created randomness is shared between two legitimate parties through ARQ transmission that will be mapped into a destination set using the first order digital filter with feedback. Then, we characterize Eve's information loss about this shared destination set, due to inevitable transmission errors that will be manipulated by privacy amplification to generate a series of secret keys about which Eve's knowledge remains negligible. We define two metrics to measure secrecy enhancement: outage probability and secret key rate. The resulting secrecy improvement is presented as a function of the correlation coefficients and the erasure probabilities for both channels. It is shown that secrecy improvement is achievable even when Eve has a better channel than the legitimate receiver, and her channel condition is unknown.

In this paper we propose an encoding-encryption approach to take advantage of intentional noise introduced in ciphertexts for DES based block ciphers working in CFB mode. Despite Eve's efforts in modifying her linear crytanalysis given the intercepted noisy ciphertexts, there is still a non-negligible probability of having either a crypto-analysis failure or a misdetected key under her limited resources. Consequently, we essentially create a wiretap channel in application layer that is a degraded version of the main channel, whose secrecy rate depends on the deliberately introduced bit error rate. In addition, Alice can accordingly adjust that cross over probability of the channel to maximize the secrecy rate. This secrecy rate can be achieved by wiretap channel coding over multiple frames in application layer if the delay in system is bearable.

In this paper, we provide a fundamental channel model to characterize the interference effect inherent in cognitive radio systems. Mutual information rates of our proposed probabilistic block interference channels for both primary and secondary users are derived without assuming that receivers have knowledge on channel interference states. Novel constrained optimization problems are then put forward with a constraint on the performance loss margin tolerated by the primary user. Furthermore, we investigate some special cases where conditions are provided to justify the optimality of adopting Neyman-Pearson rule. Also presented are some scenarios in which randomized decision without using sensing measurement is needed to balance the rateloss for PU and throughput gain for SD.

In the presence of channel errors, the error pattern in decrypted plaintexts in block-ciphered systems demonstrates certain burst features. In this paper, we provide a rigorous study of error properties of block-ciphered cryptosystems operating in either ECB or CFB mode. By analyzing the relationship between bits within and across adjacent output blocks, we obtain the resulting equivalent channel transitional probabilities for each case. Our statistical characterization of the underlying burst patterns is of great importance to designing powerful error correcting codes that can enhance a legitimate system's throughput under channel distortions.

In this paper, we study the effects of channel errors on security and decoding error probability of three encryption systems where encrypted message is sent and eavesdropped over binary symmetric channels (BSC). The three systems are all based on Data Encryption Standard (DES) in cipher feedback (CFB) mode. They are DES only (DC), DES concatenated with Reed Solomon encoding (DCRS), and DES concatenated with RS coding and S-box diffusion (DCRSS). We adopt linear crypt-analysis to quantitatively measure the effects of channel errors on the security of these systems. We have found the required known cipher-plain text pairs in each system for linear attack launched by Eve, an eavesdropper. In addition, performance analysis in terms of decoded information bit error probability (IBER) for Bob, the legitimate receiver, has been conducted for each system, whose accuracy is later verified by simulation results. Our results suggest there exists tradeoff between communication reliability and security. More security level can be attained by sacrificing the accuracy at the legitimate receiver end, which can be captured by the relationship between IBER and our proposed novel metric, security improvement factor (SIF).

In this paper we study the problem of active eavesdropping in fast fading channels. The active eavesdropper is a more powerful adversary than the classical eavesdropper. It can choose between two functional modes: eavesdropping the transmission between the legitimate parties (Ex mode), and jamming it (Jx mode) - the active eavesdropper cannot function in full duplex mode. In this paper we only consider the best-case scenario, when the transmitter knows the eavesdropper's strategy in advance - and hence can adaptively choose an encoding strategy. We show that, even under these most optimistic assumptions, an active eavesdropper can induce moderate to severe degradation of the achievable secrecy rate.

We study the problem of jamming in a fixed-rate wireless system over fast fading channels. Both transmitter and jammer are subject to long term (average) power constraints. Our jamming problem is formulated as a zero-sum game, with the probability of outage as pay-off function and power control functions as strategies. We consider both the case with full channel state information (CSI) at all parties (available from a training and feedback protocol), and the case when no CSI is fed back from the receiver. Nash equilibria of mixed strategies are found by solving the generalized form of an older problem dated back to Bell and Cover [1].

We consider the problem of a transmitter transmitting to its receiver over a wireless link subject to jamming and develop two online power control algorithms for maximizing wireless link quality (transmission rate). We assume that the transmitter transmits and the jammer interferes over a period of M time slots. The impact of the jammer is to deteriorate the quality of the wireless channel during time slots in which it is present. We assume a powerful random jammer with the ability to arbitrarily decrease the channel quality and affect any (unknown) number of time slots. Since the presence of the jammer is arbitrary, the complete jamming pattern (channel quality) over the given time period is unknown apriori. The current channel quality is revealed to the transmitter at the start of the current time slot while future channel quality remains unknown. The transmitter must then allocate power optimally to maximize the total transmission rate over M slots given only its knowledge of the current channel quality, thus giving rise to an online power control problem. We develop two online power control algorithms for maximizing the wireless link quality (transmission rate). The first algorithm is based on constant power scaling and has O(1) competitive ratio when the average received power quality over M time slots (ĥh g P T /M) is either very small or very large. However when ĥh g P T = O(M), this algorithm has an upper bound on its competitive ratio of O(logM/log logM}. This upper bound is tight. The second online algorithm based on constant rate scaling has a worst case competitive ratio of given equation. By judiciously choosing which algorithm to use based on the offline available parameter of average received power, we can assure an almost constant competitive ratio for maximizing link quality under all cases.

It has been shown lately the optimality of uncoded transmission in estimating Gaussian sources over homogeneous/symmetric Gaussian multiple access channels (MAC) using multiple sensors. It remains, however, unclear whether it still holds for any arbitrary networks and/or with high channel signal-to-noise ratio (SNR) and high signal-to-measurement-noise ratio (SMNR). In this paper, we first provide a joint source and channel coding approach in estimating Gaussian sources over Gaussian MAC channels, as well as its sufficient and necessary condition in restoring Gaussian sources with a prescribed distortion value. An interesting relationship between our proposed joint approach with a more straightforward separate source and channel coding scheme is then established. We then formulate constrained power minimization problems and transform them to relaxed convex geometric programming problems, whose numerical results exhibit that either separate or uncoded scheme becomes dominant over a linear topology network. In addition, we prove that the optimal decoding order to minimize the total transmission powers for both source and channel coding parts is solely subject to the ranking of MAC channel qualities, and has nothing to do with the ranking of measurement qualities. Finally, asymptotic results for homogeneous networks are obtained which not only confirm the existing optimality of the uncoded approach, but also show that the asymptotic SNR exponents of these three approaches are all the same. Moreover, the proposed joint approach share the same asymptotic ratio with respect to high SNR and high SMNR as the uncoded scheme.

Consider a parallel Gaussian channel with M subchannels each of which experiences independent flat fading. There exists a smart jammer which is capable of intercepting the feedback channel message such that channel state information (CSI) measured and sent back by a receiver can be perfectly known to the jammer, as well. We formulate a novel two-layer two-person zero-sum game. Under this zero-sum game framework, the following three fundamental questions are addressed. The first one is about whether to hop or to spread power over M frequency bands given the full CSI at both transmitter and jammer sides. We prove that spreading versus spreading is the Nash equilibrium point. The second question is about the impact of sending back CSI on the overall throughput, to feedback or not to feedback, considering the presence of a smart jammer capable to exploit CSI for its malicious purpose. We show that possessing the full CSI enables a better means to defend against the jammerpsilas attacks. The last question is about whether the amount of feedback information can be reduced given the mutual restrictions between transmitter and jammer. We prove that the receiver should also get involved by adaptively sending CSI without compromising the sum rate at the equilibrium point.

In this paper, we propose a feedback scheme to achieve a strictly positive secrecy rate over an eavesdropped communication link when the eavesdropper's channel is less noisy than the legitimate receiver's channel. All channels are assumed binary and symmetric (BSC). The proposed scheme exploits the channel randomness inherent in feedback channels. We show that our feedback scheme can further increase the secrecy rate achievable by the Wyner's method when the eaves-dropper's channel is worse. Some pre-/post-processing schemes to intentionally improve and degrade the equivalent wiretapper channels, respectively, are also proposed to further enhance the overall secrecy rate.

In the existing works on distributed detection in sensor networks, local sensor nodes either quantize the observation or directly scale the analog observation and then transmit the processed information independently over wireless channels to a fusion center. In this paper, we exploit the advantages of both of these two approaches by constructing an equivalent Sigma-Delta ADC across space over wireless sensor networks. Sensors are arranged in a mixing of parallel and serial topologies, enabling each sensor to transmit binary information to the fusion center, while in the meantime preserving the analog information through collaborative processing. Comparison with existing approaches demonstrates the superiority of our proposed scheme in both AWGN and fading channels in terms of the resulting detection error probability.

To address the coordination issue of sensors communicating with a fusion center, we propose a spreading sequence based non-coherent detection scheme for sensor networks to reduce the coordination between sensors to the largest extent. In this scheme, sensors employ independent spreading sequences to transmit their measurements. Non-coherent detection is conducted at the fusion center where only statistics regarding channel gains and sensor measurement uncertainties are needed. To evaluate the detector's performance, we first derive the large deviation exponents of detection error probabilities and then compare them with the approaches assuming orthogonal channel allocation (e.g. TDMA/FDMA). Numerical and simulation results demonstrate the dependence of large deviation exponent on the asymptotic number of sensors per chip (defined as c), as well as the better performance of our proposed scheme than the one using non-coherent detection with orthogonal link, for some c.

Relaying is often advocated for improving system performance by enhancing spatial diversity in wireless networks. In this paper, we address the issue of energy tradeoff made by relay nodes between transmitting their own data and forwarding other nodes' information in fading channels. First, assuming perfect channel state information (CSI), we propose a power control policy in a two-node relay network under which total energy consumption across both nodes is minimized while meeting both outage probability requirements. However perfect CSI at each node is not possible in general due to bandwidth limitations that prevent the full exchange of precise channel information. Thus in this paper, we develop power control algorithms for relaying under bandwidth constraints, via quantization. Specifically, we develop a quantization protocol that accounts for the asymmetric nature of uplink/downlink communication bandwidths and develop an optimal polynomial time algorithm for channel quantization using this protocol. The quantization algorithm minimizes the sum of expected transmission powers at the source and relay, required for collaborative relaying to satisfy the given outage probability.

Relaying is often advocated for improving system performance by enhancing spatial diversity in wireless networks. Relay nodes make contributions to improving the source-destination link quality by sacrificing their own energy. In this paper, we address the issue of energy tradeoff made by relay nodes between transmitting their own data and forwarding other nodes' information in fading channels. Assuming channel state information (CSI) on fading amplitudes is perfectly known to both transmitters and receivers, we propose two power control and relaying policies. One is based on a strategic motivation, where each node functions as a relay and minimizes its own energy expenditure while meeting the outage probability requirement of all nodes. The second approach is based on complete collaboration, where the total energy consumption across all nodes is minimized. Numerical results demonstrate a significant impact of CSI on energy saving in relaying as compared with the relaying scheme without power control. In most cases, collaborative relaying dominates over the non-cooperative strategic one in the sense that the former not only minimizes total energy but also reduces individual energy expenditure of all nodes. This implies once forwarding and relaying is adopted across various nodes, exchanging of CSI becomes crucial, and collaborative energy minimization rather than the non-cooperative strategic approach should be pursued.

We propose two-level superposition coding based relaying schemes in which optimal power and rate allocations are investigated. Instead of confining us with fixed decoding order, two-levels of signals are considered as virtual users in a two-user multiple access channel and we prove that in certain cases the optimal joint multiuser decoding is equivalent to an approach using successive interference cancellation in a fixed order. Numerical results are provided to show the improvements in power savings using our proposed strategies compared with fixed rate and single level coding approach. I. INTRODUCTION Channel quality plays an important role in determining the average throughput of wireless systems. If channel quality is too bad, transmitted signals will be corrupted and the receiver terminal will not be able to decode the data. Hence we need to have an adaptive transmitter which reduces the rate when the channel quality is bad. This cannot be accomplished in compound channels where channel state information is not available to transmitters. Shamai (1) and Liu (2) investigated employing superposition coding in compound channels to enhance average throughput. The message to be transmitted is encoded using multi-level superposition coding (3) and all layers of messages are transmitted over the channel simul- taneously. In this approach, they treated channel states as the virtual users of a broadcast channel, which means that the decoding order has been fixed for the destination, i.e. successive interference cancellation is assumed at the receiver end.

This paper studies the capacity, as well as the performance of dirty paper coding (DPC) for a point to point power constrained fading channel given two-sided mixed state information on additive and multiplicative interferences. We show the optimality of DPC when perfect channel state information about fading variable is available to both transmitter and receiver, and provide multiplexing/demultiplexing based strategies to achieve capacity. By employing an adaptation of Heegard's algorithm to this channel model, we also evaluate numerically both the achievable rate of the modified DPC strategy, as well as the actual channel capacity when transmitter has imperfect side information. Numerical results demonstrate significant improvements on channel capacity, as well as increased disparity between the achievable rate using DPC and channel capacity when only one-bit feedback on channel sate information of fading variable is available to encoder. The futility of knowing the additive interference at transmitter, when the multiplicative interference is only available to the receiver, is also shown numerically.

In this article, we adopt outage probability (λ-capacity) in fast-fading channels as a pay-off function in a zero-sum game between a legitimate transceiver pair and an uncorrelated Gaussian jammer. The transmitter aims at minimising the outage probability, while the jammer attempts to maximise the outage probability. We consider both peak (over each codeword) and average (over all codewords) power constraints. For peak power constraints, a transmission rate is either supported by the system, or if too large, causes the whole transmission to fail. By imposing average power constraints, large rates can be supported at the cost of positive probability of codeword error. Maxmin (where the jammer is assumed to play first) and minimax (where the transmitter is assumed to play first) power control strategies are developed under each power constraint, which show that no Nash equilibrium of pure strategies exists under the average power constraint when the follower has perfect knowledge about the randomisation outcome of the first player.