Compute-and-forward Research Articles

Maximum Throughput Gain of Compute-and-Forward for Multiple Unicast

Compute-and-Forward (CF), also known as reliable physical layer network coding, is a technique that provides the possibility of exploiting the features of broadcast and superposition in wireless networks. It has been shown that the throughput for multiple unicast traffic can be significantly boosted by CF. In this letter, the limit of such improvement is investigated by comparing the performance of CF with the traditional routing-based transmission schemes. For networks characterized by local interference and half-duplex constraints, it is proven that the throughput gain of CF over traditional routing, expressed by an improvement factor, is upper bounded by 3K, where K is the number of unicast sessions. Furthermore, a class of networks is presented for which an improvement by a factor of K/2 is feasible by applying CF. Hence, the throughput gain of CF is at most on the order of K for any network, and a gain in that order is indeed achievable for some networks.

스몰셀 무선망 간섭 상쇄 기법 연구

최근 무선트래픽 수요가 폭발적으로 증가하면서 셀룰라 무선망에서 이를 효율적으로 지원하기 위한 스몰셀 연구가 활발히 수행중이다. 본 논문은 스몰셀 구현의 가장 큰 걸림돌인 다중셀 간섭을 효율적으로 해결하기 위한 간섭상쇄 기법에 대해 연구하였다. 각 사용자의 메시지가 기지국 혹은 릴레이를 통하여 전달되는 경우, 무선채널의 시변특성을 이용한 간섭상쇄 기법을 제안하였다. Amplify-and-forward (AF) 에 기반한 기존 접근방식은 잡음증폭 특성으로 인하여 신호대잡음비가 낮은 영역에서는 심한 성능열화를 보였다. 본 논문은 최근 개발된 compute-and-forward (CF) 에 기반한 간섭상쇄를 제안하여 이러한 문제를 해결하고 신호대잡음비가 작은 영역에서 전송율을 크게 개선하였다. As the recently soaring wireless traffic, small-cell techniques have been actively studied in order to support such a wireless demand for cellular wireless networks. This paper focuses on the inter-cell interference neutralization to resolve the main barrier for implementing small-cell cellular networks. Assuming that each message is delivered to the final destination by the help of base stations or relays, ergodic interference neutralization is proposed, which exploits the time-varying nature of wireless channels. The previous approach based on amplify-and-forward (AF) suffers from severe performance degradation in the low signal-to-noise (SNR) regime due to noise amplification. On the other hand, the proposed interference neutralization based on recently developed compute-and-forward (CF) fixes such a problem and improves the performance in the low SNR regime.

Simplified compute‐and‐forward and its performance analysis

The compute-and-forward (CMF) method has shown a great promise as an innovative approach to exploit interference towards achieving higher network throughput. The CMF was primarily introduced by means of information theory tools. Although there have been some recent works discussing different aspects of efficient and practical implementation of CMF, there are still some issues that are not covered. In this study, the authors first introduce a method to decrease the implementation complexity of the CMF method. They then evaluate the exact outage probability of the authors proposed simplified CMF scheme, and hereby provide an upper bound on the outage probability of the optimum CMF in all signal-to-noise ratio (SNR) values, and a close approximation of its outage probability in low SNR regimes. They also evaluate the effect of the channel estimation error (CEE) on the performance of both optimum and their proposed simplified CMF by simulations. Their simulation results indicate that the proposed method is more robust against CEE than the optimum CMF method for the examples considered.

Physical Layer Network Coding Based on Integer Forcing Precoded Compute and Forward

In this paper, we address the implementation of physical layer network coding (PNC) based on compute and forward (CF) in relay networks. It is known that the maximum achievable rates in CF-based transmission is limited due to the channel approximations at the relay. In this work, we propose the integer forcing precoder (IFP), which bypasses this maximum rate achievability limitation. Our precoder requires channel state information (CSI) at the transmitter, but only that of the channel between the transmitter and the relay, which is a feasible assumption. The overall contributions of this paper are three-fold. Firstly, we propose an implementation of CF using IFP and prove that this implementation achieves higher rates as compared to traditional relaying schemes. Further, the probability of error from the proposed scheme is shown to have up to 2 dB of gain over the existent lattice network coding-based implementation of CF. Secondly, we analyze the two phases of transmission in the CF scheme, thereby characterizing the end-to-end behavior of the CF and not only one-phase behavior, as in previous proposals. Finally, we develop decoders for both the relay and the destination. We use a generalization of Bezout’s theorem to justify the construction of these decoders. Further, we make an analytical derivation of the end-to-end probability of error for cubic lattices using the proposed scheme.

Integer-Forcing Linear Receiver Design with Slowest Descent Method

Compute-and-forward (CPF) strategy is one category of network coding in which a relay will compute and forward a linear combination of source messages according to the observed channel coefficients, based on the algebraic structure of lattice codes. Recently, based on the idea of CPF, integer forcing (IF) linear receiver architecture for MIMO system has been proposed to recover different integer combinations of lattice codewords for further original message detection. In this paper, we consider the problem of IF linear receiver design with respect to the channel conditions. Instead of exhaustive search, we present practical and efficient suboptimal algorithms to design the IF coefficient matrix with full rank such that the total achievable rate is maximized, based on the slowest descent method. Numerical results demonstrate the effectiveness of our proposed algorithms.

Multihop compute‐and‐forward for generalised two‐way relay channels

AbstractThe compute‐and‐forward (CaF) relaying strategy recently proposed by Nazer and Gastpar has been proven to achieve significant improvements in ‘computation rate’ than conventional relaying strategies in the multiple‐access channel. Although there have been some recent efforts on the implementations of CaF, to the best of our knowledge, there has been no published work that analyses the outage performance of CaF in the multihop two‐way relay channel (MH‐TRC). In this paper, we extend the original CaF strategy to multihop CaF (MH‐CaF) and investigate the outage performance of the proposed MH‐CaF in the generalised MH‐TRC. The transmission strategy of MH‐CaF for the L‐node K‐message MH‐TRC is generalised. The network throughput of MH‐CaF is proven to be significantly better than the non‐network coding (Non‐NC) scheme for the MH‐TRC with a large number of messages. The outage probabilities for both Non‐NC and MH‐CaF schemes are derived for comparison. Numerical results show that for a five‐node MH‐TRC, MH‐CaF can achieve a better outage performance than Non‐NC when the number of messages is less than 12. Furthermore, it is also demonstrated that MH‐CaF is always superior to Non‐NC in outage performance when the number of nodes of the MH‐TRC is relatively large. Copyright © 2013 John Wiley & Sons, Ltd.

Outage Performance for Compute-and-Forward in Generalized Multi-Way Relay Channels

The compute-and-forward (CPF) relaying strategy proposed by Nazer and Gastpar has been proven to achieve a significant improvement in "computation rate" than conventional relaying strategies in the multiple-access channel (MAC). Although there has been some recent work on the implementations of CPF, to our best knowledge, there is no published work that has analysed the outage performance of CPF for the multi-way relay channel (MWRC). In this paper, we apply the CPF strategy in generalized MWRCs. Outage probabilities for both non-network coding (Non-NC) and CPF are derived. The numerical results show that CPF can achieve a 7 dB gain in comparison with Non-NC at the outage probability of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> in the canonical two-way relay channel. It is also demonstrated that CPF is superior to Non-NC in outage performance in the MWRCs with relatively small number of users.