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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.
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.
Compute-and-forward network coding design over multisource multi-relay 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. Compute-and-forward 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. Compute-and-forward 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 compute-and-forward network coding coefficients by Fincke-Pohst based candidate set searching algorithm and network coding system matrix constructing algorithm, such that by those proposed algorithms, the transmission rate of the multi-source multi-relay system is maximized. Numerical results demonstrate the effectiveness of our proposed algorithms. Index Terms—Compute-and-forward, network coding, linear network coding, lattice codes, cooperative, relay channel.
Efficient compute-and-forward network codes search for twoway relay channel
- IEEE Commun. Letters
, 2012
"... Abstract—We consider the two-way relay channel (TWRC) with compute-and-forward 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 Fincke-Pohst m ..."
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Cited by 7 (4 self)
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Abstract—We consider the two-way relay channel (TWRC) with compute-and-forward 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 Fincke-Pohst method. Numerical results demonstrate the effectiveness and complexity reduction of our proposed lemma and algorithm. Index Terms—Compute-and-forward, two-way relay channel, lattice codes, network coding, cooperative.
Multistage compute-and-forward with multilevel lattice codes based on product constructions
- in Proc. IEEE ISIT
, 2014
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Real-time Implementation of Physical-layer Network Coding
"... This paper presents the first real-time physical-layer net-work coding (PNC) prototype for the two-way relay wire-less channel (TWRC). Theoretically, PNC could boost the throughput of TWRC by a factor of 2 compared with tra-ditional scheduling (TS) in the high signal-to-noise (SNR) regime. Although ..."
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Cited by 5 (4 self)
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This paper presents the first real-time physical-layer net-work coding (PNC) prototype for the two-way relay wire-less channel (TWRC). Theoretically, PNC could boost the throughput of TWRC by a factor of 2 compared with tra-ditional scheduling (TS) in the high signal-to-noise (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 real-time PNC system, there are many additional challenges, includ-ing the needs for tighter coordination of the transmissions by the two end nodes, fast real-time PNC decoding at the relay, and a PNC-compatible retransmission scheme (i.e., an ARQ protocol) to ensure reliability of packet delivery. In this pa-per, we describe a real-time 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 pro-vides 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 Physical-layer Network Coding
"... Abstract—Leveraging recent progress in compute-and-forward we propose an approach to random access that is based on physical-layer 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 compute-and-forward we propose an approach to random access that is based on physical-layer 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 compute-and-forward 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 multiple-access relay channel where two transmitters attempt to send the modulo-sum 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 multiple-access relay channel where two transmitters attempt to send the modulo-sum 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.
