Combined decode-forward and layered noisy network coding schemes for relay channels

This work proposes a new coding scheme for the discrete memoryless two-user interference channel whose receivers can cooperate to decode their desired messages. The coding scheme is built upon Han-Kobayashi rate splitting and superposition coding at the transmitters, noisy network coding, and non-unique joint decoding at the receivers. As a case study the general achievable region leads to an inner bound for the Gaussian interference channel whose receivers cooperate through rate-limited orthogonal channels. It is shown that this inner bound is equivalent to the one-round quantize-bin-and-forward inner bound established by Wang and Tse, thereby showing that noisy network coding achieves within 1 bit/s/Hz to the capacity region when the interference is strong, and achieves within 1 bit/s/Hz to the capacity region of the Gaussian compound multiple access channel with conferencing decoders regardless of channel parameters.

In this paper, we consider the design of a new secure transmission scheme for a four-node relay-eavesdropper channel, where user cooperation is used to facilitate secure communications. The key idea of the proposed achievable scheme is to apply the compression relaying concept of noisy network coding (NNC) to the secrecy communication scenario. But different from the original non-secrecy NNC, the compression rate at the relay is adaptively chosen according to the eavesdropping channel. Particularly, helping interference information is injected into the compression codebook at the relay by simply enlarging the compression rate, which is to effectively suppress the eavesdropping channel. Closed-form expressions of the secrecy rates achieved by the proposed NNC-based secure scheme are characterized for both the discrete memoryless and Gaussian relay-eavesdropper channels, where the optimal compression rate and the optimal transmit power at the relay are also determined. The proposed secure scheme can be viewed as a general framework, which naturally combines the NNC compression relaying scheme with the interference-assisted scheme. Analytical and numerical results demonstrate that the proposed secure scheme offers constant performance gains over typical existing cooperative secure schemes.

In this paper, we re-examine the relay channel under the decode-forward (DF) strategy. Contrary to the established belief that block Markov coding is always the rate-optimal DF strategy, under certain channel conditions (a link regime), independent signaling between the source and relay achieves the same transmission rate without requiring coherent channel phase information. Further, this independent signaling regime allows the relay to conserve power. As such, we design a composite DF relaying strategy that achieves the same rate as block Markov DF but with less required relay power. The finding is attractive from the link adaptation perspective to adapt relay coding and relay power according to the link state. We examine this link adaptation in fading under both perfect channel state information (CSI) and practical CSI, in which nodes have perfect receive and long-term transmit CSI, and derive the corresponding relay power savings in both cases. We also derive the outage probability of the composite relaying scheme which adapts the signaling to the link regime. Through simulation, we expose a novel trade-off for relay placement showing that the relay conserves the most power when closer to the destination but achieves the most rate gain when closer to the source.

In this paper cooperation among users at the physical layer level is studied for the downlink. Distributed space time linear dispersion codes are proposed for the cooperative strategies amplify and forward (AF) and decode forward (DF), assuming no channel state knowledge at the transmitter. Both AF and DF strategies are evaluated in a cellular multiuser realistic scenario based on TDMA access, considering cellular reuse of the relay slot. Different configurations regarding the number of antennas at the relay and destination nodes are considered. The maximum achievable rate of cooperative schemes implemented by means of space time linear dispersion codes is compared with the theoretical capacity of the cooperative channel. Finally an analysis in terms of BER is given for different schemes.

Coding scheme for discrete memoryless multicast networks with rate-limited feedback from the receivers and relays to the transmitter is proposed. The coding scheme is based on block-Markov coding, joint backward decoding and hybrid relaying strategy. In each block, the relays use partial decode-forward strategy to decode part of the source message. Meanwhile, the receivers and relays use compress-forward strategy to compress their channel outputs and send the compression indices to the transmitter through the feedback links. In the next block, after obtaining the compression indices, the transmitter sends them together with the source message. Each receiver uses backward decoding to jointly decode the source message and all compression indices. It is shown that our coding scheme generalizes Gabbai and Bross's results for the single relay channel with partial feedback, where they proposed coding schemes based on restricted decoding and deterministic partitioning. For the single relay channel with relay-transmitter feedback, our coding scheme can strictly improve on noisy network coding, distributed decode-forward coding and all known lower bounds on the achievable rate in the absence of feedback. Furthermore, motivated by the feedback coding scheme, we propose a new coding scheme for discrete memoryless multicast networks without feedback, which also improves noisy network coding and distributed decode-forward coding.

It has been conjectured that lattice codes are good for (almost) everything. As an additional bit of evidence for this claim, we offer a few results showing the utility of lattice codes for the AWGN relay channel. We show that the decode-and-forward rates of the relay channel can be achieved using lattice encoding and decoding. We present an encoding/decoding technique that uses a doubly-nested lattice code. Encoding is accomplished using a combination of superposition encoding and block Markov encoding, while decoding is accomplished using a strategy reminiscent of Cover and El Gamal's list decoding. Our technique can be extended to a wide variety of relay topologies, including the half-duplex relay channel and the cooperative multiple-access channel.

Amplify-forward (AF) and decode-forward (DF) continue to dominate the practical strategies for signal relaying. Amplify-forward is a way of forwarding soft reliability information that is extracted directly from the channel reception - without making use of the channel code that may well exist in the packet, whereas decode-forward exploits the coding gain, but forwards only the hard-decisions (provided that decoder succeeds). This paper joins the merits of AF and DF by exploiting “analog codes” - a special class of error correction codes that can directly encode and protect real-valued data. Exploiting useful ideas from the chaos theory and the parallel concatenation structure, we show that how chaos-based analog turbo-like codes can be designed and used in user cooperation. In the proposed “analog-encode-forward (AEF)” scheme, the relay node first soft-decodes the packet from the source, then re-encodes this soft decoder output using an appropriate analog code, and forwards it to the destination. A hybrid scheme that combines AEF and DF is further exploited to improve performance.

For noisy network with multiple relays, short message noisy network coding with rate splitting (SNNC-RS) scheme is presented. It has recently been shown by Hou and Kramer that mixed cooperative strategies in which relays in favorable positions decode-and-forward (DF) and the rest quantize via short message noisy network coding (SNNC) can outperform existing cooperative strategies (e.g., noisy network coding (NNC) and decode-and-forward). A drawback of such schemes is that forwarding of quantized signals at SNNC relays introduces interference to the rest of the relays. Our proposed relaying scheme has a capability to reduce such interference and thereby improve the rate performance. In the proposed scheme, superposition coding is incorporated into SNNC encoding to enable partial interference cancellation at DF relays. The achievable rate with proposed scheme is derived for the discrete two-relay network and evaluated in the Gaussian case where gains over the rate achievable without rate splitting are demonstrated.

Uplink and downlink cloud radio access networks are modeled as two-hop ${K}$ -user ${L}$ -relay networks, whereby small base-stations act as relays for end-to-end communications and are connected to a central processor via orthogonal fronthaul links of finite capacities. Simplified versions of network compress–forward (or noisy network coding) and distributed decode–forward are presented to establish inner bounds on the capacity region for uplink and downlink communications, that match the respective cutset bounds to within a finite gap independent of the channel gains and signal to noise ratios. These approximate capacity regions are then compared with the capacity regions for networks with no capacity limit on the fronthaul. Although it takes infinite fronthaul link capacities to achieve these “fronthaul-unlimited” capacity regions exactly, these capacity regions can be approached approximately with finite-capacity fronthaul. The total fronthaul link capacities required to approach the fronthaul-unlimited sum-rates (for uplink and downlink) are characterized. Based on these results, the capacity scaling law in the large network size limit is established under certain uplink and downlink network models, both theoretically and via simulations.

In this paper, we first study a two-user interference channel with generalized feedback. We establish an inner bound on its capacity region. The coding scheme that we employ for the inner bound is based on an appropriate combination of Han-Kobayash rate splitting and compress-and-forward at the senders. Each sender compresses the channel output that is observes using a compression scheme that is \`a-la Lim et al. noisy network coding and Avestimeher et al. quantize-map-and-forward. Next, we study an injective deterministic model in which the senders obtain output feedback only intermittently. Specializing the coding scheme of the model with generalized feedback to this scenario, we obtain useful insights onto effective ways of combining noisy network coding with interference alignment techniques. We also apply our results to linear deterministic interference channels with intermittent feedback.

We study a two-user state-dependent generalized multiple-access channel (GMAC) with correlated states. It is assumed that each encoder noncausally knows partial channel state information. We develop an achievable rate region by employing rate-splitting, block Markov encoding, Gelfand-Pinsker multicoding, superposition coding and jointly typical decoding. In the proposed scheme, the encoders use a partial decoding strategy to collaborate in the next block, and the receiver uses a backward decoding strategy with a joint unique decoding at each stage. Our achievable rate region includes several previously known rate regions proposed in the literature for different scenarios of multiple-access and relay channels. We finally consider a Gaussian GMAC with an additive interference which is known noncausally at both of the encoders and construct a multi-layer Costa precoding scheme that removes completely the effect of the interference.

This paper studies the achievable degrees of freedom (DoF) for multi-user multiple-input multiple-output (MIMO) two-way relay channels, where there are K source nodes, each equipped with M antennas, one relay node, equipped with N antennas, and each source node exchanges independent messages with an arbitrary set of other source nodes via the relay. By allowing an arbitrary information exchange pattern, the considered channel model is a unified one. It includes several existing channel models as special cases: 1) K-user MIMO Y channel; 2) multi-pair MIMO two-way relay channel; 3) generalized MIMO two-way X relay channel; and 4) L-cluster MIMO multiway relay channel. Previous studies mainly considered the achievability of the DoF cut-set bound 2N at the antenna configuration N <; 2M by applying signal alignment for network coding. This paper aims to investigate the achievability of the DoF cut-set bound K M for the case N 2M. To this end, we first derive tighter DoF upper bounds for three special cases of the considered channel model. Then, we propose a new transmission framework, generalized signal alignment (GSA), to approach these bounds. The notion of GSA is to form network-coded symbols by aligning every pair of signals to be exchanged in a compressed subspace at the relay. A necessary and sufficient condition to construct the relay compression matrix is given. We show that using GSA, the new DoF upper bound is achievable when: 1) N/m ∈ (0, 2+ 4/{K(K-1)}]∪[K-2, +∞) for the K-user MIMO Y channel; 2) N/M ∈ (0,2 +4/K]∪[K - 2, +∞) for the multi-pair MIMO two-way relay channel; and 3) N/M ∈ (0, 2+ 8/K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ]∪[K-2, +∞) for the generalized MIMO two-way X relay channel. We also provide the antenna configuration regions for the general multi-user MIMO two-way relay channel to achieve the total DoF KM.

We propose a class of practical efficient lattice codes for real-valued full-duplex one- and two-way relay channels. First, we investigate the problem from a theoretical perspective, proposing lattice-coding instantiations of superposition block Markov encoding. Our encoding/decoding strategies recover the well-known decode-and-foward rates for the one-way relay channel and a previously-proven rate region for the two-way relay channel. Then, we construct practical, low-complexity implementations of these schemes using low-density lattice codes. Simulations show that our schemes achieve performance as close as 2.5 dB away from theoretical limits. Finally, we show that, due to features inherent to full-duplex relaying and practical codes, the gap to theoretical limits depends on the channel gains and transmit power of the relay relative to the source(s). We characterize this gap analytically, providing insight into the design of practical full-duplex relay systems.

This paper investigates the problem of information transmission over the simultaneous relay channel with two users (or two possible channel outcomes) where for one of them the more suitable strategy is Decode-and-Forward (DF) while for the other one is Compress-and-Forward (CF). In this setting, it is assumed that the source wishes to send common and private informations to each of the users (or channel outcomes). This problem is relevant to: (i) the transmission of information over the broadcast relay channel (BRC) with different relaying strategies and (ii) the transmission of information over the conventional relay channel where the source is oblivious to the coding strategy of relay. A novel coding that integrates simultaneously DF and CF schemes is proposed and an inner bound on the capacity region is derived for the case of general memoryless BRCs. As special case, the Gaussian BRC is studied where it is shown that by means of the suggested broadcast coding the common rate can be improved compared to existing strategies. Applications of these results arise in broadcast scenarios with relays or in wireless scenarios where the source does not know whether the relay is collocated with the source or with the destination.

We demonstrate a decoding scheme for nested lattice codes which is able to decode a list of a particular size which contains the transmitted codeword with high probability. This list decoder is analogous to that used in random coding arguments in achievability schemes of relay channels, and allows for the effective combination of information from the relay and source node. Using this list decoding result, we demonstrate 1) that lattice codes may achieve the capacity of the physically degraded AWGN relay channel, 2) an achievable rate region for the two-way relay channel with direct links using lattice codes, and 3) that we may improve the constant gap to capacity for specific cases of the two-way relay channel with direct links.