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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.
Achievable rate regions and performance comparison of half duplex bi-directional relaying protocols
- IEEE Trans. Inf. Theory
, 2011
"... Abstract—In a bi-directional relay channel, two nodes wish to ex-change independent messages over a shared wireless half-duplex channel with the help of a relay. In this paper, we derive achiev-able rate regions for four new half-duplex protocols and compare these to four existing half-duplex protoc ..."
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Cited by 29 (1 self)
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Abstract—In a bi-directional relay channel, two nodes wish to ex-change independent messages over a shared wireless half-duplex channel with the help of a relay. In this paper, we derive achiev-able rate regions for four new half-duplex protocols and compare these to four existing half-duplex protocols and outer bounds. In time, our protocols consist of either two or three phases. In the two phase protocols, both users simultaneously transmit during the first phase and the relay alone transmits during the second phase, while in the three phase protocol the two users sequentially transmit followed by a transmission from the relay. The relay may forward information in one of four manners; we outline existing amplify and forward (AF), decode and forward (DF), lattice based, and compress and forward (CF) relaying schemes and introduce the novel mixed forward scheme. The latter is a combination of CF in one direction and DF in the other. We derive achievable rate re-gions for the CF andMixed relaying schemes for the two and three phase protocols. We provide a comprehensive treatment of eight possible half-duplex bi-directional relaying protocols in Gaussian noise, obtaining their relative performance under different SNR and relay geometries. Index Terms—Achievable rate regions, bi-directional communi-cation, compress and forward, relaying. I.
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.
Analog network coding in the high-snr regime
- in Proc. IEEE Wireless Network Coding Workshop
"... Abstract—A node performing analog network coding simply forwards a signal it receives over a wireless channel. This allows for a (noisy) linear combination of signals simultaneously sent from multiple sources to be forwarded in the network. As such, analog network coding extends the idea of network ..."
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Cited by 20 (6 self)
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Abstract—A node performing analog network coding simply forwards a signal it receives over a wireless channel. This allows for a (noisy) linear combination of signals simultaneously sent from multiple sources to be forwarded in the network. As such, analog network coding extends the idea of network coding to wireless networks. However, the analog network coding performance is limited by propagated noise, and we expect this strategy to perform well only in high SNR. In this paper, we formalize this intuition and determine high-SNR conditions under which analog network coding approaches capacity in a layered relay network. By relating the received SNR at the nodes with the propagated noise, we determine the rate achievable with analog network coding. In particular, when all the received powers are lower bounded by 1/δ, the propagated noise power in a network with L layers is of the order Lδ. The result demonstrates that the analog network coding approaches the cut-set bound as the received powers at relays increase. As all powers in the network increase, the analog network coding rate is within a constant gap from the upper bound. The gap depends on number of nodes. We further demonstrate by an example that analog network coding can perform close to sum-capacity also in the multicast case. I.
Successive Compute-and-Forward
"... Abstract—In prior work, we proposed the compute-andforward framework for sending linear combinations of messages to relays. In this note, we extend the notion of successive interference cancellation to the compute-and-forward setting. We find that once a relay has decoded a linear combination, it ca ..."
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Cited by 19 (3 self)
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Abstract—In prior work, we proposed the compute-andforward framework for sending linear combinations of messages to relays. In this note, we extend the notion of successive interference cancellation to the compute-and-forward setting. We find that once a relay has decoded a linear combination, it can mix it with its channel output to create a new effective channel output. The resulting effective channel can be tuned so that it is more suitable for decoding a second linear combination than the original channel. I.
Interference Decoding for Deterministic Channels
, 2011
"... An inner bound to the capacity region of a class of deterministic interference channels with three user pairs is presented. The key idea is to simultaneously decode the combined interference signal and the intended message at each receiver. It is shown that this interference-decoding inner bound is ..."
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Cited by 15 (4 self)
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An inner bound to the capacity region of a class of deterministic interference channels with three user pairs is presented. The key idea is to simultaneously decode the combined interference signal and the intended message at each receiver. It is shown that this interference-decoding inner bound is tight under certain strong interference conditions. The inner bound is also shown to strictly contain the inner bound obtained by treating interference as noise, which includes interference alignment for deterministic channels. The gain comes from judicious analysis of the number of combined interference sequences in different regimes of input distributions and message rates. Finally, the inner bound is generalized to the case where each channel output is observed through a noisy channel.
