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Asynchronous physical-layer network coding,” technical report. Available: http://arxiv.org/abs/1105.3144
"... Abstract—A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmit-ted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrier-phase offset. ..."
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Cited by 100 (11 self)
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Abstract—A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmit-ted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalignment as well as relative carrier-phase offset. A second important issue is how to integrate channel coding with PNC to achieve reliable communication. This paper investigates these two issues and makes the following contributions: 1) We propose and investigate a general framework for decoding at the receiver based on belief propagation (BP). The framework can effectively deal with symbol and phase asynchronies while incorporating channel coding at the same time. 2) For unchannel-coded PNC, we show that for BPSK and QPSK modulations, our BP method can significantly reduce the asynchrony penalties compared with prior methods. 3) For QPSK unchannel-coded PNC, with a half symbol offset between the transmitters, our BP method can drastically reduce the performance penalty due to phase asynchrony, from more than 6 dB to no more than 1 dB. 4) For channel-coded PNC, with our BP method, both symbol and phase asynchronies actually improve the system performance compared with the perfectly synchronous case. Furthermore, the performance spread due to different combinations of symbol and phase offsets between the transmitters in channel-coded PNC is only around 1 dB. The implication of 3) is that if we could control the symbol arrival times at the receiver, it would be advantageous to deliberately introduce a half symbol offset in unchannel-coded PNC. The implication of 4) is that when channel coding is used, symbol and phase asynchronies are not major performance concerns in PNC. Index Terms—Physical-layer network coding, network coding, synchronization. I.
Reliable physical layer network coding
- PROCEEDINGS OF THE IEEE
, 2011
"... When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typicall ..."
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Cited by 54 (5 self)
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When two or more users in a wireless network transmit simultaneously, their electromagnetic signals are linearly superimposed on the channel. As a result, a receiver that is interested in one of these signals sees the others as unwanted interference. This property of the wireless medium is typically viewed as a hindrance to reliable communication over a network. However, using a recently developed coding strategy, interference can in fact be harnessed for network coding. In a wired network, (linear) network coding refers to each intermediate node taking its received packets, computing a linear combination over a finite field, and forwarding the outcome towards the destinations. Then, given an appropriate set of linear combinations, a destination can solve for its desired packets. For certain topologies, this strategy can attain significantly higher throughputs over routing-based strategies. Reliable physical layer network coding takes this idea one step further: using judiciously chosen linear error-correcting codes, intermediate nodes in a wireless network can directly recover linear combinations of the packets from the observed noisy superpositions of transmitted signals. Starting with some simple examples, this survey explores the core ideas behind this new technique and the possibilities it offers for communication over interference-limited wireless networks.
An Algebraic Approach to Physical-Layer Network Coding
- IEEE TRANS. INFORM. THEORY
, 2010
"... The problem of designing new physical-layer net-work coding (PNC) schemes via lattice partitions is considered. Building on recent work by Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, we take an algebraic approach to show its potential in non-asymptotic ..."
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Cited by 41 (4 self)
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The problem of designing new physical-layer net-work coding (PNC) schemes via lattice partitions is considered. Building on recent work by Nazer and Gastpar, who demonstrated its asymptotic gain using information-theoretic tools, we take an algebraic approach to show its potential in non-asymptotic settings. We first relate Nazer-Gastpar’s approach to the fundamental theorem of finitely generated modules over a principle ideal domain. Based on this connection, we generalize their code construction and simplify their encoding and decoding methods. This not only provides a transparent understanding of their approach, but more importantly, it opens up the opportunity to design efficient and practical PNC schemes. Finally, we apply our framework to the Gaussian relay network and demonstrate its advantage over conventional PNC schemes.
Multilevel coding schemes for computeand-forward,” see http://arxiv.org/abs/1010.1016
"... Abstract—We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that permits the recovery of a class of functions at the ..."
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Cited by 22 (3 self)
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Abstract—We consider the design of coding schemes for the wireless two-way relaying channel when there is no channel state information at the transmitter. In the spirit of the compute and forward paradigm, we present a multilevel coding scheme that permits the recovery of a class of functions at the relay. We define such a class of functions and derive rates that are universally achievable over a set of channel gains when this class of functions is used at the relay. We develop our framework with general modulation formats in mind, but numerical results are presented for the case where each node transmits using the QPSK constellation. Numerical results with QPSK show that substantially higher rates are achievable with our proposed approach than those achievable by always using a fixed function or adapting the function at the relay but coding over GF(4). Index Terms—Network coding, multilevel coding, two-way relaying, compute-and-forward I.
Joint relay selection and analog network coding using differential modulation in two-way relay channels
- IEEE Transactions on Vehicular Technology
, 2010
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Optimal decoding algorithm for asynchronous physical-layer network coding
- In Proc. IEEE Int. Conf. on Comm. (ICC
, 2011
"... Abstract—A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalign-ment as well as relative carrier-phase offset. ..."
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Cited by 10 (3 self)
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Abstract—A key issue in physical-layer network coding (PNC) is how to deal with the asynchrony between signals transmitted by multiple transmitters. That is, symbols transmitted by different transmitters could arrive at the receiver with symbol misalign-ment as well as relative carrier-phase offset. In this paper, 1) we propose and investigate a general framework based on belief propagation (BP) that can effectively deal with symbol and phase asynchronies; 2) we show that for BPSK and QPSK modulations, our BP method can significantly reduce the SNR penalty due to asynchrony compared with prior methods; 3) we find that symbol misalignment makes the system performance less sensitive and more robust against carrier-phase offset. Observation 3) has the following practical implication. It is relatively easier to control symbol timing than carrier-phase offset. Our results indicate that if we could control the symbol offset in PNC, it would actually be advantageous to deliberately introduce symbol misalignment to desensitize the system to phase offset. Index Terms—physical-layer network coding, network coding, symbol synchronization, phase synchronization I.
Channel quantization for physical layer network-coded two-way relaying
- in Proc. IEEE WCNC
, 2012
"... Abstract—The design of modulation schemes for the physical layer network-coded two way relaying scenario is considered with the protocol which employs two phases: Multiple access (MA) Phase and Broadcast (BC) phase. It was observed by Koike-Akino et al. that adaptively changing the network coding ma ..."
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Cited by 9 (7 self)
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Abstract—The design of modulation schemes for the physical layer network-coded two way relaying scenario is considered with the protocol which employs two phases: Multiple access (MA) Phase and Broadcast (BC) phase. It was observed by Koike-Akino et al. that adaptively changing the network coding map used at the relay according to the channel conditions greatly reduces the impact of multiple access interference which occurs at the relay during the MA phase. In other words, the set of all possible channel realizations (the complex plane) is quantized into a finite number of regions, with a specific network coding map giving the best performance in a particular region. We highlight the issues associated with the scheme proposed by Koike-Akino et al. and propose a scheme which solves these issues. We obtain a quantization of the set of all possible channel realizations analytically for the case when M-PSK (for M any
Phase-level synchronization for physical-layer network coding,” to appear at
- IEEE GLOBECOM
, 2012
"... Abstract—Physical-layer network coding (PNC) brings throughput improvement for wireless networks. However, its synchronization requirement is widely recognized as an obstacle to its implementation. In this paper, we focus on phase-level synchronization and propose a time-slotted carrier synchronizat ..."
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Cited by 6 (4 self)
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Abstract—Physical-layer network coding (PNC) brings throughput improvement for wireless networks. However, its synchronization requirement is widely recognized as an obstacle to its implementation. In this paper, we focus on phase-level synchronization and propose a time-slotted carrier synchronization scheme for PNC. We then analyze the phase error tolerance of PNC under different bit error rate (BER) requirements, and the synchronization overhead for obtaining synchronous signals below the phase error margin. We also consider the impact of different hardware (in particular, the phase-locked loop) parameters on the overhead in our analysis. Afterwards, we evaluate the performance of the proposed synchronization scheme with simulations. The results show that the proposed scheme is feasible with some typical hardware parameters. The throughput gain of PNC when using the proposed scheme is only slightly lower than the theoretical gain. Index Terms—Bit error rate (BER) analysis; phase error; physical-layer network coding (PNC); synchronization; wireless networks. I.
Cellular multiuser two-way MIMO AF relaying via signal space alignment: Minimum weighted SINR maximization
- IEEE Trans. Signal Process
, 2012
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1Layered Design of Hierarchical Exclusive Codebook and Its Capacity Regions for HDF Strategy in Parametric Wireless 2-WRC
"... Forward (HDF) strategy in the wireless 2-Way Relay Channel (2-WRC). This strategy uses a Hierarchical eXclusive Code (HXC) that allows full decoding of the hierarchical symbols at the relay. The HXC represents two data sources only through the exclusive law and requires side information on the compl ..."
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Cited by 6 (5 self)
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Forward (HDF) strategy in the wireless 2-Way Relay Channel (2-WRC). This strategy uses a Hierarchical eXclusive Code (HXC) that allows full decoding of the hierarchical symbols at the relay. The HXC represents two data sources only through the exclusive law and requires side information on the complementary data at the destination (which naturally holds for the 2-WRC). The HDF strategy has the advantage over classical MAC stage relaying with joint decoding that its rate region extends beyond the classical MAC region. We present a layered design of the HXC codebook which uses an arbitrary outer state-of-the-art capacity approaching code (e.g. LDPC) and an inner layer with an exclusive symbol alphabet. We provide basic theorems showing that this scheme forms an HXC and we also evaluate its alphabet constrained rate regions. The rate regions depend on the relative channel phase parameters. Some channel rotation leads to catastrophic violation of the exclusive law. However these values appear only in a limited range of phases and have only mild impact on the mean capacity for some component symbol constellations.
