Rate Splitting Research Articles

On the achievable rates of a secondary link coexisting with a primary multiple access network

An achievable rate region for a primary multiple access network coexisting with a secondary link of one transmitter and a corresponding receiver is analyzed. The rate region depicts the sum primary rate versus the secondary rate and is established assuming that the secondary link performs rate splitting. The achievable rate region is the union of two types of rate regions. The first type is a rate region established assuming that the secondary receiver cannot decode any primary signal, whereas the second is established assuming that the secondary receiver can decode the signal of one primary link. The achievable rate region is determined first assuming discrete memoryless channel (DMC), then the results are applied to a Gaussian channel. In the Gaussian channel, the performance of rate splitting is characterized for the two types of rate regions. Moreover, a necessary and sufficient condition to determine which primary signal the secondary receiver can decode without degrading the range of primary achievable sum rates is provided. When this condition is satisfied by a certain primary user, the secondary receiver can decode its signal and achieve larger rates without reducing the sum of the primary achievable rates as compared to the case in which it does not decode any primary signal. It is also shown that the probability of having at least one primary user satisfying this condition grows with the primary signal-to-noise ratio.

Communication With Disturbance Constraints

Motivated by the broadcast view of the interference channel, the new problem of communication with disturbance constraints is formulated. The rate-disturbance region is established for the single constraint case and the optimal encoding scheme turns out to be the same as the Han-Kobayashi scheme for the two user-pair interference channel. This result is extended to the Gaussian vector (multiple-input and multiple-output) case. For the case of communication with two disturbance constraints, inner and outer bounds on the rate-disturbance region for a deterministic model are established. The inner bound is achieved by an encoding scheme that involves rate splitting, Marton coding, and superposition coding, and is shown to be optimal in several nontrivial cases. This encoding scheme can be readily applied to discrete memoryless interference channels and motivates a natural extension of the Han-Kobayashi scheme to more than two user pairs.

Tradeoff between energy-efficiency and spectral-efficiency by cooperative rate splitting

The trend of an increasing demand for a high-quality user experience, coupled with a shortage of radio resources, has necessitated more advanced wireless techniques to cooperatively achieve the required quality-of-experience enhancement. In this study, we investigate the critical problem of rate splitting in heterogeneous cellular networks, where concurrent transmission, for instance, the coordinated multipoint transmission and reception of LTE-A systems, shows promise for improvement of network-wide capacity and the user experience. Unlike most current studies, which only deal with spectral efficiency enhancement, we implement an optimal rate splitting strategy to improve both spectral efficiency and energy efficiency by exploring and exploiting cooperation diversity. First, we introduce the motivation for our proposed algorithm, and then employ the typical cooperative bargaining game to formulate the problem. Next, we derive the best response function by analyzing the dual problem of the defined primal problem. The existence and uniqueness of the proposed cooperative bargaining equilibrium are proved, and more importantly, a distributed algorithm is designed to approach the optimal unique solution under mild conditions. Finally, numerical results show a performance improvement for our proposed distributed cooperative rate splitting algorithm.

Three‐user interference channel with common information: a rate splitting‐based achievability scheme

In this study, the three-user interference channel (IFC) with common information is considered, where each receiver decode not only the private message from the intended transmitter but also the common messages from the non-intended transmitters by applying a simultaneous decoding scheme. An achievable rate region is presented using rate splitting and superposition encoding at the transmitters and simultaneous joint decoding at the receivers in which the transmitters cooperatively send the split messages which allows the interference cancellation at the receivers. The implicit form of the achievable rate region is also extended to K-user IFC with common information. Finally the inner bound derived for the three-user discrete memoryless IFC with common information is generalised to the Gaussian case and is evaluated in a numerical example.

Rate Maximization for Half-Duplex Multiple Access with Cooperating Transmitters

We derive the optimal resource allocation of a practical half-duplex scheme for the Gaussian multiple access channel with transmitter cooperation (MAC-TC). Based on rate splitting and superposition coding, two users transmit information to a destination over 3 phases, such that the users partially exchange their information during the first 2 phases and cooperatively transmit to the destination during the last one. This scheme is near capacity-achieving when the inter-user links are stronger than each user-destination link; it also includes partial decode-forward relaying as a special case. We propose efficient algorithms to find the optimal resource allocation for maximizing either the individual or the sum rate and identify the corresponding optimal scheme for each channel configuration. For fixed phase durations, the power allocation problem is convex and can be solved analytically based on the KKT conditions. The optimal phase durations can then be obtained numerically using simple search methods. Results show that as the inter-user link qualities increase, the optimal scheme moves from no cooperation to partial then to full cooperation, in which the users fully exchange their information and cooperatively send it to the destination. Therefore, in practical systems with strong inter-user links, simple decode-forward relaying at both users is rate-optimal.

Error Exponent for Gaussian Channels With Partial Sequential Feedback

This paper studies the error exponent of block coding over an additive white Gaussian noise channel where a fraction ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$f$</tex></formula> ) of the channel output symbols are revealed to the transmitter through noiseless feedback. If the code rate exceeds <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$fC$</tex></formula> , where <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$C$</tex> </formula> is the channel capacity, then the probability of decoding error cannot decay faster than exponentially with block length. However, if the code rate is below <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$fC$</tex></formula> , the error probability can decrease faster than exponentially with the block length, as with full feedback ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$f=1$</tex></formula> ). This is achieved by combining a feedback code and a forward error control code, and jointly decoding them at the receiver. This scheme can attain higher reliability than rate splitting in which feedback and forward codes independently encode separate source messages.

Multi-antenna transmission for underlay and overlay cognitive radio with explicit message-learning phase

We consider the coexistence of a multiple-input multiple-output secondary system with a multiple-input single-output primary link with different degrees of coordination between the systems. First, for the uncoordinated underlay cognitive radio scenario, we fully characterize the optimal parameters that maximize the secondary rate subject to a primary rate constraint for a transmission strategy that combines rate splitting and interference cancellation. Second, we establish a model for the coordinated overlay cognitive radio scenario that consists of a message-learning phase followed by a communication phase. We then propose a transmission strategy that combines techniques for cooperative communication and for the classical cognitive radio channel. We optimize our system to maximize the rate of communication for the secondary users under a primary-user rate constraint and find efficient algorithms to compute the optimal system parameters. Finally, we compare both cognitive radio strategies to assess their relative merits and to evaluate the effect of the message-learning phase. We observe that for closely located transmitters, the overlay strategy outperforms the underlay strategy. In this situation, learning the primary message is very beneficial for the secondary systems, especially if they are interference-limited rather than power-limited. The situation is reversed when the distance between the transmitters is large. In either case, we observe that there is room for significant improvement if the transmitter implements both strategies and decides adaptively which one to use according to the channel conditions. We conclude our work with a discussion on the extension to the coexistence with multiple-input multiple-output primaries.

Wiretap Channels: Implications of the More Capable Condition and Cyclic Shift Symmetry

Characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables: <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</i> , for rate splitting and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> , for channel prefixing. In this paper, we explore specific classes of wiretap channels for which the evaluation of the rate-equivocation region is simpler. We show that if the wiretap channel is more capable, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> = <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> is optimal and the boundary of the rate-equivocation region is achieved by varying rate splitting <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</i> alone. Conversely, we show under a mild condition that if the wiretap channel is not more capable, then <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> = <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> is strictly suboptimal. Next, we focus on the class of cyclic shift symmetric wiretap channels. We show that optimal rate splitting <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</i> that achieves the boundary of the rate-equivocation region is uniform with cardinality | <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> | and the prefix channel between optimal <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</i> is expressed as cyclic shifts of the solution of an auxiliary optimization problem over a single variable. We provide a special class of cyclic shift symmetric wiretap channels for which <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</i> =φ is optimal. We apply our results to the binary-input cyclic shift symmetric wiretap channels and thoroughly characterize the rate-equivocation regions of the BSC-BEC and BEC-BSC wiretap channels.

Multi-Receiver Wiretap Channel With Public and Confidential Messages

We study the multi-receiver wiretap channel (MR-WC) with public and confidential messages. In this channel, there is a transmitter that wishes to communicate with two legitimate users in the presence of an external eavesdropper. The transmitter sends a pair of public and confidential messages to each legitimate user. While there are no secrecy constraints on the public messages, confidential messages need to be transmitted in perfect secrecy. We study the discrete memoryless MR-WC as well as its Gaussian multi-input multi-output (MIMO) counterpart. First, we propose an inner bound for the general, not necessarily degraded, discrete memoryless MR-WC by using Marton's inner bound and rate splitting in conjunction with superposition coding and binning. Second, we specialize this inner bound for the degraded discrete memoryless case. This specialized form of the inner bound can be obtained by using superposition coding and binning only. Next, we obtain an outer bound for the capacity region of the degraded channel, which matches the inner bound for some special cases. Third, we consider the degraded Gaussian MIMO channel, and show that, to evaluate both the inner and outer bounds, considering only jointly Gaussian auxiliary random variables and channel input is sufficient. Similar to the discrete memoryless case, for the Gaussian MIMO case as well, these bounds match for some special cases.

Wiretap Channel with Action-Dependent States and Rate-Limited Feedback

We introduce the wiretap channel with action-dependent states and rate-limited feedback. In the new model, the state sequence is dependent on the action sequence which is selected according to the message, and a secure rate-limited feedback link is shared between the transmitter and the receiver. We obtain the capacity-equivocation region and secrecy capacity of such a channel both for the case where the channel inputs depend noncausally on the state sequence and the case where they are restricted to causal dependence. We construct the capacity-achieving coding schemes utilizing Wyner's random binning, Gel'fand and Pinsker’s coding technique, and rate splitting. Furthermore, we compare our results with the existing approaches without feedback, with noiseless feedback, and without action-dependent states. The simulation results show that the secrecy capacity of our model is bigger than that of the first two existed approaches. Besides, it is also shown that, by taking actions to affect the channel states, we guarantee the data integrity of the message transmitted in the two-stage communication systems although the tolerable overhead of transmission time is brought.

Power Minimization of Cooperative Relay Transmission with Relay's Private Information

Power minimization of a cooperative decode-and-forward (DF) half-duplex relaying, where two users communicate with one destination node (D), is studied in this paper. Recognizing the difference in link qualities, one user not only transmits its own message to D but also acts as a relay node (R) for the other user. To achieve total network power minimization, we consider two strategies: (i) a rate splitting strategy (RSS) which splits the whole message into two sub-messages with one being transmitted via R and the other directly to D, (ii) a transmission power boosting strategy (TPBS) in the broadcast phase that allocates more power than needed to ensure correct decoding of the message at R. We first consider joint optimization of rate splitting, a time sharing factor (between the broadcast phase and cooperation phase), and transmission powers. We then consider the second scenario where the time sharing factor is fixed. We prove that TPBS is not required for the first scenario, but is necessary for the second scenario to minimize the total network power. We also obtain channel conditions for which the optimal solution is to employ a multiple access channel (MAC) strategy, i.e., without relaying. Finally we show through numerical results that significant power saving is achieved by our proposed strategies.

Achievable rate for three-node discrete memoryless relay channel with generalized feedbacks

This paper studies the achievable rate for three-node discrete memoryless relay channel. Specifically in this mode, we explore two generalized feedbacks simultaneously: the source node actively collects feedback signals from the channel; and at the same time, the destination node actively transmits feedback signals to the relay node. These two feedback signals, which are called generalized feedback overheard from the channel that is likely to be noisy, induce that all the three nodes are in full duplex mode. The basic coding strategies of Cover and El Gamal are applied to the relay-source feedback transmission by the source forwarding the compressions of the channel output sequences at the relay node to the destination, and are also applied to the destination-relay feedback transmission to improve the decoding ability at the relay. Based on Cover and El Gamal coding, a new coding scheme adopting rate splitting and four-block Markov superposition encoding is proposed and the corresponding achievable rate is achieved. The proposed scheme is able to exploit two feedbacks simultaneously which can effectively eliminate underlying transmission bottlenecks for the channels. The derived achievable rate result generalizes several previously known results by including them as special cases.

Paranoid Secondary: Waterfilling in a Cognitive Interference Channel with Partial Knowledge

We study a two-user cognitive channel, where the primary flow is sporadic, cannot be re-designed and operating below its link capacity. To study the impact of primary traffic uncertainty, we propose a block activity model that captures the random on-off periods of primary's transmissions. Each block in the model can be split into parallel Gaussian-mixture channels, such that each channel resembles a multiple user channel (MAC) from the point of view of the secondary user. The secondary senses the current state of the primary at the start of each block. We show that the optimal power transmitted depends on the sensed state and the optimal power profile is paranoid, i.e. either growing or decaying in power as a function of time. We show that such a scheme achieves capacity when there is no noise in the sensing. The optimal transmission for the secondary performs rate splitting and follows a layered water-filling power allocation for each parallel channel to achieve capacity. The secondary rate approaches a genie-aided scheme for large block-lengths. Additionally, if the fraction of time primary uses the channel tends to one, the paranoid scheme and the genie-aided upper bound get arbitrarily close to a no-sensing scheme.

Security Embedding Codes

This paper considers the problem of simultaneously communicating two messages, a high-security message and a low-security message, to a legitimate receiver, referred to as the security embedding problem. An information-theoretic formulation of the problem is presented. A coding scheme that combines rate splitting, superposition coding, nested binning, and channel prefixing is considered and is shown to achieve the secrecy capacity region of the channel in several scenarios. Specifying these results to both scalar and independent parallel Gaussian channels (under an average individual per-subchannel power constraint), it is shown that the high-security message can be embedded into the low-security message at full rate (as if the low-security message does not exist) without incurring any loss on the overall rate of communication (as if both messages are low-security messages). Extensions to the wiretap channel II setting of Ozarow and Wyner are also considered, where it is shown that "perfect" security embedding can be achieved by an encoder that uses a two-level coset code.

IEEE 802.11 medium access control enhancements based on simultaneous multiple‐input multiple‐output bandwidth sharing

ABSTRACTThe demand for higher data rate has spurred the adoption of multiple‐input multiple‐output (MIMO) transmission techniques in IEEE 802.11 products. MIMO techniques provide an additional spatial dimension that can significantly increase the channel capacity. A number of multiuser MIMO system have been proposed, where the multiple antenna at the physical layer are employed for multiuser access, allowing multiple users to share the same bandwidth. As these MIMO physical layer technologies further evolve, the usable bandwidth per application increases; hence, the average service time per application decreases. However, in the IEEE 802.11 distributed coordination function‐based systems, a considerable amount of bandwidth is wasted during the medium access and coordination process. Therefore, as the usable bandwidth is enhanced using MIMO technology, the bandwidth wastage of medium access and coordination becomes a significant performance bottleneck. Hence, there is a fundamental need for bandwidth sharing schemes at the medium access control (MAC) layer where multiple connections can concurrently use the increased bandwidth provided by the physical layer MIMO technologies. In this paper, we propose the MIMO‐aware rate splitting (MRS) MAC protocol and examine its behavior under different scenarios. MRS is a distributed MAC protocol where nodes locally cooperate with one another to share bandwidth via splitting the spatial channels of MIMO systems. Simulation results of MRS protocol are obtained and compared with those of IEEE 802.11n protocol. We show that our proposed MRS scheme can significantly outperform the IEEE 802.11n in medium access delay and throughput. Copyright © 2012 John Wiley &amp; Sons, Ltd.

Outage Analysis of Block-Fading Gaussian Interference Channels

This paper considers the asymptotic behavior of the outage probability of a two-source block-fading single-antenna Gaussian interference channel in the high-SNR regime by means of the diversity-multiplexing tradeoff. A general setting where the user rates and the average channel gains are not restricted to be symmetric is investigated. This asymmetric scenario allows to analyze networks with “mixed” interference, i.e., when different sources are at different distance from their intended destination, that are not possible under the commonly used symmetric assumption. Inner and outer bounds for the diversity are derived. The outer bound is based on the recent “to within one bit” capacity result of Etkin for the unfaded Gaussian channel and is a re-derivation of a known bound for which an error is pointed out. The inner bound is based on the Han and Kobayashi achievable region both without rate splitting and with a rate spitting inspired by the “to within one bit” capacity result. An analytical comparison of the diversity upper and lower bounds for a general channel seems difficult; by numerical evaluations, the two bounds are shown to coincide for a fairly large set of channel parameters.

Multicell Interference Mitigation with Joint Beamforming and Common Message Decoding

Conventional wireless cellular systems treat out-of-cell interference as noise. This paper proposes methods and examines the benefit of designing decodable interference signals, whereby a transmitter may split its message into a common and a private part, and the common message may be decoded and subtracted by users in adjacent cells. This paper considers a downlink scenario, where the base-stations are equipped with multiple antennas, the mobile users are equipped with a single antenna, and multiple users are active simultaneously via spatial multiplexing. The network optimization problem consists of jointly determining the appropriate users in adjacent cells for rate splitting, the optimal transmit beamformers for common and private messages, and the optimal common-private rates to maximize the minimum achievable rate across the users. This paper shows that for fixed user selection and fixed common-private rate splitting, the optimization of transmit beamformers can be solved using a semidefinite programming (SDP) relaxation approach. Further, it is shown that for the case where the network consists of two message-splitting pairs, SDP relaxation is tight, i.e., beamforming is optimal. Finally, this paper proposes a heuristic user-selection and rate splitting strategy to characterize the performance improvement for cell-edge users due to common-message decoding.

New Inner and Outer Bounds for the Memoryless Cognitive Interference Channel and Some New Capacity Results

The cognitive interference channel is a two-user interference channel in which one transmitter is non-causally provided with the message of the other transmitter. This channel model has been extensively studied in the past years and capacity results have been proved for certain classes of channels. This paper presents new inner and outer bounds for the capacity region of the cognitive interference channel, as well as new capacity results. Previously proposed outer bounds are expressed in terms of auxiliary random variables for which no cardinality constraint of their alphabet is known. Consequently, it is not possible to evaluate such outer bounds explicitly for a given channel. The outer bound derived in this work is based on an idea originally devised by Sato for channels without receiver cooperation and results in an outer bound that does not contain auxiliary random variables, thus allowing it to be more easily evaluated. The inner bound presented in this work-which includes rate splitting, superposition coding, a broadcast channel-like binning scheme and Gel'fand Pinsker coding-is the largest known to date and is explicitly shown to include all previously proposed achievable rate regions. The novel inner and outer bounds are shown to coincide in certain cases. In particular, capacity is proved for a class of channels in the so-called “better cognitive decoding” regime, which includes the regimes in which capacity was known. Finally, the capacity region of the semi-deterministic cognitive interference channel, in which the signal at the cognitive receiver is an arbitrary deterministic function of the channel inputs, is established.

The Capacity Region of Multiway Relay Channels Over Finite Fields With Full Data Exchange

The multi-way relay channel is a multicast network where L users exchange data through a relay. In this paper, the capacity region of a class of multi-way relay channels is derived, where the channel inputs and outputs take values over finite fields. The cut-set upper bound to the capacity region is derived and is shown to be achievable by our proposed functional-decode-forward coding strategy. More specifically, for the general case where the users can transmit at possibly different rates, functional-decode-forward, combined with rate splitting and joint source-channel decoding, is proved to achieve the capacity region; while for the case where all users transmit at a common rate, rate splitting and joint source-channel decoding are not required to achieve the capacity. That the capacity-achieving coding strategies do not utilize the users' received signals in the users' encoding functions implies that feedback does not increase the capacity region of this class of multi-way relay channels.

Ergodic Fading Interference Channels: Sum-Capacity and Separability

The sum-capacity for specific sub-classes of ergodic fading Gaussian two-user interference channels (IFCs) is developed under the assumption of perfect channel state information at all transmitters and receivers. For the sub-classes of uniformly strong (every fading state is strong) and ergodic very strong two-sided IFCs (a mix of strong and weak fading states satisfying specific fading averaged conditions) the optimality of completely decoding the interference, i.e., converting the IFC to a compound multiple access channel (C-MAC), is proved. It is also shown that this capacity-achieving scheme requires encoding and decoding jointly across all fading states. As an achievable scheme and also as a topic of independent interest, the capacity region and the corresponding optimal power policies for an ergodic fading C-MAC are developed. For the sub-class of uniformly weak IFCs (every fading state is weak), genie-aided outer bounds are developed. The bounds are shown to be achieved by treating interference as noise and by separable coding for one-sided fading IFCs. Finally, for the sub-class of one-sided hybrid IFCs (a mix of weak and strong states that do not satisfy ergodic very strong conditions), an achievable scheme involving rate splitting and joint coding across all fading states is developed and is shown to perform at least as well as a separable coding scheme.