Practical code design for compute-and-forward

Ordentlich, Or; Zhan, Jiening; Erez, Uri; Gastpar, Michael; Nazer, Bobak

doi:10.1109/isit.2011.6033876

Cited by 33 publications

(33 citation statements)

References 4 publications

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“…A particular example along this direction is given in [46]. A third direction would be the construction of more powerful LNC schemes, which has been partially explored in several recent papers, e.g., [45,47,59,62]. We believe that the algebraic framework given in this chapter can serve as a good basis for these developments.…”

Section: Discussionmentioning

confidence: 93%

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An algebraic approach to physical-layer network coding

Feng

Silva

Kschischang

2010

2010 IEEE International Symposium on Information Theory

132

202

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This dissertation studies a family of the state-of-the-art PNC schemes called compute-and-forward (C&F). C&F was originally proposed and studied from an information-theoretic perspective. As such, it typically relies on several strong assumptions: very long block length, almost unbounded complexity, perfect channel state information, and no decoding errors at the relays; its benefit is often analyzed for simple network configurations. The aim of this dissertation is two-fold: first, to relax the above assumptions while preserving the performance of C&F, and second, to understand the benefit of C&F in more realistic network scenarios, such as random-access wireless networks.There are four main results in this dissertation. First, an algebraic framework is developed, which establishes a direct connection between C&F and module theory. This connection allows us to systematically design lattice codes for C&F with controlled block length and complexity. In particular, explicit design criteria are derived, concrete design examples are provided, and it is shown that nominal coding gains from 3 to 7.5 dB can be obtained with relatively short block length and reasonable decoding complexity. Second, a new C&F scheme is proposed, which, unlike conventional C&F schemes, does not require any channel state information (CSI). It is shown that this CSI-free scheme achieves, for a certain class of lattice codes, almost the same throughput as its CSI-enabled counterpart. Third, an end-to-end error control mechanism is designed, which effectively mitigates decoding errors introduced at wireless relays. In particular, the end-to-end error control problem is modeled as a finite-ring matrix channel problem, for which tight capacity bounds and capacity-approaching schemes are provided. The final part of this dissertation studies the benefit of C&F in random-access wireless networks. In particular, it is shown that C&F significantly improves the network throughput and delay performance of slotted-ALOHA-based random-access protocols.ii Acknowledgements This thesis is the result of the support, help, and advice that I have received from an amazing group of scholars and students at the University of Toronto. Without them this dissertation wouldn't have been possible. First, I feel very fortunate to have two great supervisors: Prof. Frank R. Kschischang and Prof.Baochun Li. As an advisor, Frank has consistently exceeded my expectation. He is not only a brilliant researcher and excellent teacher, but also truly a kind and caring person. He has given me a tremendous amount in the past six years, I can only thank him for a subset. In particular, I have benefited greatly from his focus on fundamental problems, his taste for beautiful mathematics, his emphasis on clarity and grace, and his dedication in developing his students to their full potential. I am very grateful to Frank for making my PhD journey so exciting and rewarding! Frank also has a great sense of humor.I will always remember how much fun we had together during our endless discus...

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Section: Discussionmentioning

confidence: 93%

“…There are some other practical code constructions for C&F in the literature (see, e.g., [43][44][45][46][47]). …”

Section: Introductionmentioning

confidence: 99%

An algebraic approach to physical-layer network coding

Feng

Silva

Kschischang

2010

2010 IEEE International Symposium on Information Theory

132

202

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“…See Figure 1 for an illustration. The achievable rates of this architecture can be written down in closed form and approached closely using either nested lattice codes incorporating shaping [46], [47] (suitable for low SNR) or linear codes with no shaping (sufficient for high SNR), such as a low-density parity-check (LDPC) code combined with quadrature amplitude modulation (QAM) [48]- [50]. More generally, any low-complexity coding framework for compute-and-forward [47], [49]- [56] can also be used to implement an integer-forcing linear receiver.…”

Section: Integer-forcing Linear Receiversmentioning

confidence: 99%

“…Furthermore, through the use of modern coding techniques (such as LDPC codes) and iterative decoding algorithms, these lattices can be efficiently encoded and decoded. Recent work has examined the performance of this approach for both compute-and-forward as well as integer-forcing [48]- [51], [53], [55], [70].…”

Section: G Implementation Issuesmentioning

confidence: 99%

Integer-Forcing Linear Receivers

Zhan

Nazer

Erez

et al. 2014

IEEE Trans. Inform. Theory

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171

269

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Abstract-Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multi-user uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard MIMO channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees-of-freedom.

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“…We can therefore first decode x 0 and then detect the uncoded bits using a slicer with double step size. For more details, see [27], [28].…”

Section: Lemmamentioning

confidence: 99%

Cyclic coded integer-forcing equalization

Ordentlich

Erez

2010

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Abstract-A discrete-time intersymbol interference channel with additive Gaussian noise is considered, where only the receiver has knowledge of the channel impulse response. An approach for combining decision-feedback equalization with channel coding is proposed, where decoding precedes the removal of intersymbol interference. This is accomplished by combining the recently proposed integer-forcing equalization approach with cyclic block codes. The channel impulse response is linearly equalized to an integer-valued response. This is then utilized by leveraging the property that a cyclic code is closed under (cyclic) integer-valued convolution. Explicit bounds on the performance of the proposed scheme are also derived.

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Practical code design for compute-and-forward

Cited by 33 publications

References 4 publications

An algebraic approach to physical-layer network coding

An algebraic approach to physical-layer network coding

Integer-Forcing Linear Receivers

Cyclic coded integer-forcing equalization

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