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56
An Algebraic Approach to PhysicalLayer Network Coding
 IEEE TRANS. INFORM. THEORY
, 2010
"... The problem of designing new physicallayer network coding (PNC) schemes via lattice partitions is considered. Building on recent work by Nazer and Gastpar, who demonstrated its asymptotic gain using informationtheoretic tools, we take an algebraic approach to show its potential in nonasymptotic ..."
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Cited by 41 (4 self)
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The problem of designing new physicallayer network coding (PNC) schemes via lattice partitions is considered. Building on recent work by Nazer and Gastpar, who demonstrated its asymptotic gain using informationtheoretic tools, we take an algebraic approach to show its potential in nonasymptotic settings. We first relate NazerGastpar’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.
Successive ComputeandForward
"... Abstract—In prior work, we proposed the computeandforward framework for sending linear combinations of messages to relays. In this note, we extend the notion of successive interference cancellation to the computeandforward 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 computeandforward framework for sending linear combinations of messages to relays. In this note, we extend the notion of successive interference cancellation to the computeandforward 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.
Computeandforward network coding design over multisource multirelay channels
 IEEE Trans. Wireless Communications
, 2012
"... Abstract—Network coding is a new and promising paradigm for modern communication networks by allowing intermediate nodes to mix messages received from multiple sources. Computeandforward strategy is one category of network coding in which a relay will decode and forward a linear combination of sou ..."
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Cited by 13 (4 self)
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Abstract—Network coding is a new and promising paradigm for modern communication networks by allowing intermediate nodes to mix messages received from multiple sources. Computeandforward strategy is one category of network coding in which a relay will decode and forward a linear combination of source messages according to the observed channel coefficients, based on the algebraic structure of lattice codes. The destination will recover all transmitted messages if enough linear equations are received. In this work, we design in a system level, the computeandforward network coding coefficients by FinckePohst based candidate set searching algorithm and network coding system matrix constructing algorithm, such that by those proposed algorithms, the transmission rate of the multisource multirelay system is maximized. Numerical results demonstrate the effectiveness of our proposed algorithms. Index Terms—Computeandforward, network coding, linear network coding, lattice codes, cooperative, relay channel.
Efficient computeandforward network codes search for twoway relay channel
 IEEE Commun. Letters
, 2012
"... Abstract—We consider the twoway relay channel (TWRC) with computeandforward network coding strategy. First a new lemma is proposed as network codes search criteria for TWRC. Then, instead of exhaustive search, we present an efficient network codes search algorithm based on modified FinckePohst m ..."
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Cited by 7 (4 self)
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Abstract—We consider the twoway relay channel (TWRC) with computeandforward network coding strategy. First a new lemma is proposed as network codes search criteria for TWRC. Then, instead of exhaustive search, we present an efficient network codes search algorithm based on modified FinckePohst method. Numerical results demonstrate the effectiveness and complexity reduction of our proposed lemma and algorithm. Index Terms—Computeandforward, twoway relay channel, lattice codes, network coding, cooperative.
Multistage computeandforward with multilevel lattice codes based on product constructions
 in Proc. IEEE ISIT
, 2014
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Realtime Implementation of Physicallayer Network Coding
"... This paper presents the first realtime physicallayer network coding (PNC) prototype for the twoway relay wireless channel (TWRC). Theoretically, PNC could boost the throughput of TWRC by a factor of 2 compared with traditional scheduling (TS) in the high signaltonoise (SNR) regime. Although ..."
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Cited by 5 (4 self)
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This paper presents the first realtime physicallayer network coding (PNC) prototype for the twoway relay wireless channel (TWRC). Theoretically, PNC could boost the throughput of TWRC by a factor of 2 compared with traditional scheduling (TS) in the high signaltonoise (SNR) regime. Although there have been many theoretical studies on PNC performance, there have been few experimental and implementation efforts. We built the first prototype of PNC about a year ago. It was, however, an offline system in which an offline PNC decoder was used at the relay. For a realtime PNC system, there are many additional challenges, including the needs for tighter coordination of the transmissions by the two end nodes, fast realtime PNC decoding at the relay, and a PNCcompatible retransmission scheme (i.e., an ARQ protocol) to ensure reliability of packet delivery. In this paper, we describe a realtime PNC prototype, referred to as RPNC, that provides practical solutions to these challenges. Indoor environment experimental results show that RPNC boosts the throughput of TWRC by a factor of 2 compared with TS, as predicted theoretically. RPNC prototype provides an interface to the application layer, with which we demonstrate the exchange of two image data files between the two end nodes.
Random Access with Physicallayer Network Coding
"... Abstract—Leveraging recent progress in computeandforward we propose an approach to random access that is based on physicallayer network coding: When packets collide, it is possible to recover a linear combination of the packets at the receiver. Over many rounds of transmission, the receiver can t ..."
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Cited by 4 (0 self)
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Abstract—Leveraging recent progress in computeandforward we propose an approach to random access that is based on physicallayer network coding: When packets collide, it is possible to recover a linear combination of the packets at the receiver. Over many rounds of transmission, the receiver can thus obtain many linear combinations and eventually recover all original packets. This is by contrast to slotted ALOHA where packet collisions lead to complete erasures. The throughput of the proposed strategy is derived for a system with two users and shown to be significantly superior to the best known strategies, including multipacket reception. I.
Simplified computeandforward and its performance analysis
 IET Commun
, 2013
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Relays that cooperate to compute
 in Proc. Int. Symp. Wireless Commun. Syst
, 2012
"... Abstract—This paper proposes a new coding scheme that combines the advantages of statistical cooperation and algebraic structure. Consider a multipleaccess relay channel where two transmitters attempt to send the modulosum of their finite field messages to the receiver with the help of the relay. ..."
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Cited by 3 (2 self)
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Abstract—This paper proposes a new coding scheme that combines the advantages of statistical cooperation and algebraic structure. Consider a multipleaccess relay channel where two transmitters attempt to send the modulosum of their finite field messages to the receiver with the help of the relay. The transmitters use nested lattice codes to ensure that sums of codewords are protected against noise and to preserve the modulo operation of the finite field. We develop a block Markov coding scheme where the relay recovers the real sum of the codewords and retransmits it coherently with the two transmitters. I.