Gaussian Two-way Relay Channel Research Articles

Asymmetric Successive Compute-and-Forward and the Capacity Gap for the Gaussian Two-way Relay Channel

Background: The compute-and-forward strategy is one of the outstanding methods which is used for interference management in wireless relay networks where decoding linear combinations of code words is required. Recently, many efforts have been made for decoding integer and noninteger combinations. The difference between the methods is the manner of handling different conditions of networks, such as equal or unequal power constraints and equal or unequal channel gains. Objective: In this work, we present a modified n-step asymmetric successive compute-and-forward strategy for the communication network where we have both unequal power constraints and unequal channel gains conditions. Methods: In the proposed method, we scale channel gains and coefficients with the square root of power constraints. In this way, despite previous methods, without the need for scaling factors in our formulation, it is still able to solve the problem of general Gaussian relay networks with unequal power constraints and unequal channel gains. We also use scaling factors in our method in order to have the ability to divide the rates between users fairly. Results and Conclusion: We evaluate the ability of the modified strategy for the uplink communication of the two-way relay channel, where one relay can help communication between the two users. At the relay, we decode the linear combinations of the messages of the two users and obtain 1/2 bit/sec/Hz per user capacity gap from the cut-set bound. Through some theoretical and simulation results, we show that by appropriately adjusting parameters, different points and areas of rate regions are achievable.

Capacity of the Gaussian Two-Pair Two-Way Relay Channel to Within $\frac{1}{2}$ Bit

This paper studies the transceiver design of the Gaussian two-pair two-way relay channel (TWRC), where two pairs of users exchange information through a common relay in a pairwise manner. Our main contribution is to show that the capacity of the Gaussian two-pair TWRC is achievable to within $\frac{1}{ 2}$ bit for arbitrary channel conditions. For the outer bound, we derive a genie-aided bound of the Gaussian two-pair TWRC, which is tighter than the cut-set bound. For the inner bound, we develop a hybrid coding scheme involving Gaussian random coding, nested lattice coding, superposition coding, and network-coded decoding. We further present a message-reassembling strategy to decouple the coding design for the user-to-relay and relay-to-user links, so as to provide flexibility to fully exploit the channel randomness. We show that judicious power allocation at the users and at the relay is necessary to approach the channel capacity under various channel conditions.

Hybrid cognitive Gaussian two-way relay channel: Performance analysis and optimal resource allocation

Motivated by the deployment of hybrid cooperative cognitive radio (HCCR) based relays in cellular environments, this paper proposes the hybrid cognitive Gaussian two-way relay channel (HCGTWRC) model. Recently, the combination of licensed and cognitive radios with cooperative systems has gained popularity. These combined techniques have the potential to outperform primary network and pure cognitive network by utilizing the complementary nature of licensed and cognitive radios. In the proposed HCGTWRC model, a relay jointly utilizes both the licensed as well as the unlicensed/cognitive radio resources (RRs). Unlike conventional two-way relay channel, in this proposed model, source uses licensed resources for transmission and relay forwards this information using cognitive RRs. These licensed and unlicensed resources are not affected by total resource constraints of source and relay. Here, unlicensed RRs are not only described by bandwidth and power but also by reliability/availability parameter because of its opportunistic nature. In this paper, the proposed HCGTWRC model is studied by taking information theoretic aspect. In this respect, firstly, upper and lower bounds of performance metrics such as capacity, spectral efficiency (SE), and energy efficiency (EE) are analytically derived for the proposed HCGTWRC model. Then the optimal resource (such as power and bandwidth) allocation is derived with respect to upper and lower bounds of each performance metrics. Further, the performance comparison of the proposed HCGTWRC model is presented with the existing one. Numerical results are also presented for the optimal resource allocation to validate the analytical ones.

A Lattice-Based Compress-and-Forward Strategy for Gaussian Two-Way Relay Channel With Direct Links

In this letter, the Gaussian two-way relay channel with direct links is investigated in which two users aim at exchanging their messages with the help of a relay node. We propose a new lattice-based compress-and-forward strategy and obtain its achievable rate-region. We show that the proposed scheme is superior to all previously known achievable schemes for channel gains larger than one. In particular, under the symmetric case, the proposed scheme is able to achieve a capacity region within 0.5 bit or $ {({1}/{2})\log 3\cong 0.79}$ bit, depending on the power of the relay.

On the Capacity Region of Asymmetric Gaussian Two-Way Line Channel

Lattice codes are known to outperform random codes for certain networks, especially in the Gaussian two-way relay channels (GTWRCs) where lattice codes are able to exploit their linearity. As an extension of the GTWRC, in this paper, we consider the asymmetric Gaussian two-way line network where two nodes exchange their messages through multiple relays. We first investigate the capacity region of the full-duplex two-way two-relay line network. The results can be extended to an arbitrary number of relays and to half-duplex scenarios. This channel consists of four nodes: $1\leftrightarrow 2\leftrightarrow 3\leftrightarrow 4$ , where nodes 1 and 4 with the help of two full-duplex relays, i.e., nodes 2 and 3, exchange their messages with each other. Using lattice codes, we design a novel scheme that allows the relay nodes to send the data in both directions simultaneously under an asymmetric rate region. In the proposed scheme, each relay decodes the sum of lattice points and then re-encodes it into another lattice codeword (which satisfies the transmit power constraint at the relay). It is shown that the proposed scheme achieves the capacity region of asymmetric two-way line network within 0.5 bit independent of the number of relays.

Lattice-coded cooperation protocol for the half-duplex Gaussian two-way relay channel

This paper studies the Gaussian two-way relay channel (GTWRC), where two nodes exchange their messages with the help of a half-duplex relay. We investigate a cooperative transmission protocol, consisting of four phases: multiple access (MA) phase, broadcast (BC) phase, and two cooperative phases. For this setup, we propose a new transmission scheme based on superposition coding for nested lattice codes, random coding, and jointly typical decoding. This scheme divides the message of each node into two parts, referred to as satellite codeword and cloud center. Depending on the phase type, the encoder sends a linear combination of satellite codewords or cloud centers. For comparison, a rate region outer bound using a cut-set bound is provided. We show that the proposed scheme can achieve the capacity region in the high signal-to-noise ratio (SNR) regime. In addition, the achievable rate region is within 0.5 bit of the outer bound, regardless of all channel parameters. Using numerical examples, we show that our proposed scheme achieves a larger rate region than the best known 4-phase transmission strategy so far, called the Hybrid Broadcast (HBC) protocol by Kim et al. Our proposed scheme not only improves upon previous 2- and 3- and 4-phase protocols but also can perform superior at some cases to the introduced 6-phase protocol by Gong, Yue, and Wang (which has more complexity relative to our 4-phase protocol).

On the Capacity Regions of Two-Way Diamond Channels

In this paper, we study the capacity regions of two-way diamond channels. We show that for a linear deterministic model the capacity of the diamond channel in each direction can be simultaneously achieved for all values of channel parameters, where the forward and backward channel parameters are not necessarily the same. We divide the achievability scheme into three cases, depending on the forward and backward channel parameters. For the first case, we use a reverse amplify-and-forward strategy in the relays. For the second case, we use four relay strategies based on the reverse amplify-and-forward with some modifications in terms of replacement and repetition of some stream levels. For the third case, we use two relay strategies based on performing two rounds of repetitions in a relay. The proposed schemes for deterministic channels are used to find the capacity regions within constant gaps for two special cases of the Gaussian two-way diamond channel. First, for the general Gaussian two-way relay channel with a simple coding scheme the smallest gap is achieved compared to the prior works. Then, a special symmetric Gaussian two-way diamond model is considered and the capacity region is achieved within four bits.

Causal Relay Networks

In this paper, we study causal discrete memoryless relay networks. The network consists of multiple nodes, each of which can be a source, a relay, and/or a destination. In the network, there are two types of relays: 1) relays with one sample delay (strictly causal) and 2) relays without delay (causal) whose transmit signals depend not only on the past received symbols but also on the current received symbols. For this network, we derive two new cut-set bounds, one when every node has a message and the other when only the strictly causal relays have messages. Using the examples of a causal vector Gaussian two-way relay channel and a causal vector Gaussian relay channel, we show that the new cut-set bounds can be achieved by a simple amplify-and-forward type relaying. Our result for the causal relay channel strengthens the previously known capacity result for the same channel by El Gamal, Hassanpour, and Mammen.

A New Achievable Rate Region for the Gaussian Two-Way Relay Channel via Hybrid Broadcast Protocol

In this letter, we study the Gaussian two-way relay channel (GTWRC) with a direct link in which two nodes want to exchange information with each other with the help of a relay node in the presence of a direct link between two nodes. Specially, we focus on a protocol with four phases, which is called the hybrid broadcast (HBC) protocol. In the HBC protocol, sequential transmissions from both users are followed by a transmission from the relay. Using nested lattice codes, we obtain a new achievable rate region for this protocol. In fact, utilizing a four-stage lattice partition chain, we introduce an intermediate lattice in our lattice-based coding scheme, and by using it, we split the codebook of each node judiciously into two parts. This enables us to decode a linear combination of lattice codewords partially at the relay. Using our proposed strategy, we show that the achievable rate region is superior to the obtained achievable rate region by Kim, Mitran, and Tarokh.

Achievable Rate Regions for Two-Way Relay Channel Using Nested Lattice Coding

This paper studies a Gaussian two-way relay channel where two communication nodes exchange messages with each other via a relay. It is assumed that all nodes operate in half-duplex mode without any direct link between the communication nodes. A compress-and-forward relaying strategy using nested lattice codes is first proposed. Then, the proposed scheme is improved by performing layered coding: A common layer is decoded by both receivers, and a refinement layer is recovered only by the receiver that has the best channel conditions. The achievable rates of the new scheme are characterized and are shown to be higher than those provided by the decode-and-forward strategy in some regions.

Design and Analysis of Multi-Level Physical-Layer Network Coding for Gaussian Two-Way Relay Channels

In this paper, we propose a multi-level physical-layer network coding (MPLNC) scheme that optimizes the relay performance for both symmetric and asymmetric traffic in a Gaussian two-way relay channel. The proposed MPLNC scheme enables each source to employ multiple linear binary codes for encoding, one per modulation level, and the relay node to decode superimposed network codewords at each modulation level. We first derive the achievable rate for the transmission of arbitrary constellations and then prove that MPLNC with multistage decoding (MPLNC/MSD) can achieve the achievable rate if binary code rates are properly chosen for both sources. Furthermore, the design criteria for the proposed MPLNC scheme is investigated, which includes the rate design rule and the labeling strategy. Moreover, we derive the error exponent and an upper bound of the overall error probability for MPLNC. Our analysis and simulation results show that MPLNC/MSD has a significant performance advantage in comparison to the existing bit-interleaved coded modulation (BICM)-based PLNC scheme.

The Role of Feedback in Two-Way Secure Communications

Most practical communication links are bidirectional. In these models, since the source node also receives signals, its encoder has the option of computing its output based on the signals it received in the past. On the other hand, from a practical point of view, it would also be desirable to identify the cases where such an encoder design may not improve communication rates. This question is particularly interesting for the case where the transmitted messages and the feedback signals are subject to eavesdropping. In this paper, we investigate the question of how much impact the feedback has on the secrecy capacity by studying two fundamental models. First, we consider the Gaussian two-way wiretap channel and derive an outer bound for its secrecy capacity region. We show that the secrecy rate loss can be unbounded when feedback signals are not utilized except for a special case we identify, and thus conclude that utilizing feedback can be highly beneficial in general. Second, we consider a half-duplex Gaussian two-way relay channel where the relay node is also an eavesdropper, and find that the impact of feedback is less pronounced compared to the previous scenario. Specifically, the loss in secrecy rate, when ignoring the feedback, is quantified to be less than 0.5 bit per channel use when the relay power goes to infinity. This achievable rate region is obtained with simple time sharing along with cooperative jamming, which, with its simplicity and near optimum performance, is a viable alternative to an encoder that utilizes feedback signals.

Design of Irregular Repeat-Accumulate Coded Physical-Layer Network Coding for Gaussian Two-Way Relay Channels

This paper addresses the design of irregular repeat accumulate (IRA) codes for coded physical-layer network coding (PNC) for the binary-input Gaussian two-way relay channel, assuming perfect synchronization and equal received power at the relay. The design is based on a nontrivial extension of EXIT-chart based design. Specifically, we analyze the components of the IRA-PNC scheme and propose an approach to model the soft information exchanged between these components. Then, we develop upper and lower bounds on the extrinsic information transfer functions to characterize the iterative process of computing the network-coded information. Based on that, we construct optimized IRA codes to minimize the computation error at the relay. The optimized IRA-PNC has considerable performance improvement over the existing regular RA coded PNC. For a rate 3/4 code, as an example, we observed improvements of 2.6 dB, and the optimized IRA-PNC scheme is only about 1.7 dB away from the capacity upper bound of the Gaussian two-way relay channel.

Distance Spectrum and Performance of Channel-Coded Physical-Layer Network Coding for Binary-Input Gaussian Two-Way Relay Channels

We investigate a channel-coded physical-layer network coding (CPNC) scheme for binary-input Gaussian two-way relay channels. In this scheme, the codewords of the two users are transmitted simultaneously. The relay computes and forwards a network-coded (NC) codeword without complete decoding of the two users' individual messages. We propose a new punctured codebook method to explicitly find the distance spectrum of the CPNC scheme. Based on that, we derive an asymptotically tight performance bound for the error probability. Our analysis shows that, compared to the single-user scenario, the CPNC scheme exhibits the same minimum Euclidean distance but an increased multiplicity of error events with minimum distance. At a high SNR, this leads to an SNR penalty of at most ln2 (in linear scale), for long channel codes of various rates. Our analytical results match well with the simulated performance.

Distance Spectrum and Performance of Channel-Coded Physical-Layer Network Coding for Binary-Input Gaussian Two-Way Relay Channels

We investigate a channel-coded physical-layer network coding (CPNC) scheme for binary-input Gaussian two-way relay channels. In this scheme, the codewords of the two users are transmitted simultaneously. The relay computes and forwards a network-coded (NC) codeword without complete decoding of the two users' individual messages. We propose a new punctured codebook method to explicitly find the distance spectrum of the CPNC scheme. Based on that, we derive an asymptotically tight performance bound for the error probability. Our analysis shows that, compared to the single-user scenario, the CPNC scheme exhibits the same minimum Euclidean distance but an increased multiplicity of error events with minimum distance. At a high SNR, this leads to an SNR penalty of at most ln2 (in linear scale), for long channel codes of various rates. Our analytical results match well with the simulated performance.

Gaussian Two-Way Relay Channel with Private Information for the Relay

We introduce a generalized two-way relay channel where two sources exchange information (not necessarily of the same rate) with help from a relay, and each source additionally sends private information to the relay. We consider the Gaussian setting where all point-to-point links are Gaussian channels. For this channel, we consider a two-phase protocol consisting of a multiple access channel (MAC) phase and a broadcast channel (BC) phase. We propose a general decode-and-forward (DF) scheme where the MAC phase is related to computation over MAC, while the BC phase is related to BC with receiver side information. In the MAC phase, we time share a capacity-achieving code for the MAC and a superposition code with a lattice code as its component code. We show that the proposed DF scheme is near optimal for any channel conditions, in that it achieves rates within half bit of the capacity region of the two-phase protocol.

Capacity of the Gaussian Two-Way Relay Channel to Within ${1\over 2}$ Bit

In this paper, a Gaussian two-way relay channel, where two source nodes exchange messages with each other through a relay, is considered. We assume that all nodes operate in full-duplex mode and there is no direct channel between the source nodes. We propose an achievable scheme composed of nested lattice codes for the uplink and structured binning for the downlink. Unlike conventional nested lattice codes, our codes utilize two different shaping lattices for source nodes based on a three-stage lattice partition chain, which is a key ingredient for producing the best gap-to-capacity results to date. Specifically, for all channel parameters, the achievable rate region of our scheme is within <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> / <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> bit from the capacity region for each user and its sum rate is within log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> / <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> bit from the sum capacity.