Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations

Nazer, Bobak; Cadambe, Viveck R.; Ntranos, Vasilis; Caire, Giuseppe

doi:10.1109/tit.2016.2593633

Cited by 51 publications

(78 citation statements)

References 98 publications

(280 reference statements)

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“…Corollary 2, stated in Section VI, shows that such an effective noise is semi normergodic regardless of the number of dithers contributing to it, as long as they are all independent and are induced by lattices that are good for MSE quantization. Consequently, nested lattice chains where all lattices are good for MSE quantization and coding, whose existence is guaranteed by Theorem 2, suffice to recover all results from [16]- [21] any many other achievable rate regions based on nested lattice coding schemes. Moreover, the analysis in the proof of Theorem 4 assumes that the additive noise is semi norm-ergodic, and not necessarily AWGN.…”

Section: Remarkmentioning

confidence: 90%

“…Moreover, the analysis in the proof of Theorem 4 assumes that the additive noise is semi norm-ergodic, and not necessarily AWGN. Consequently, using a similar analysis it is possible to extend all the results from [16]- [21] to networks with any semi norm-ergodic additive noise.…”

Section: Remarkmentioning

confidence: 95%

“…In the last decade lattice codes were found to play a new role in network information theory allowing to obtain new achievable rate regions, that are not achievable using the best known random coding schemes, for many problems [16]- [21]. See [22] for a comprehensive survey.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Simple Proof for the Existence of “Good” Pairs of Nested Lattices

Ordentlich

Erez

2016

IEEE Trans. Inform. Theory

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Abstract-This paper provides a simplified proof for the existence of nested lattice codebooks allowing to achieve the capacity of the additive white Gaussian noise channel, as well as the optimal rate-distortion trade-off for a Gaussian source. The proof is self-contained and relies only on basic probabilistic and geometrical arguments. An ensemble of nested lattices that is different, and more elementary, than the one used in previous proofs is introduced. This ensemble is based on lifting different subcodes of a linear code to the Euclidean space using Construction A. In addition to being simpler, our analysis is less sensitive to the assumption that the additive noise is Gaussian. In particular, for additive ergodic noise channels it is shown that the achievable rates of the nested lattice coding scheme depend on the noise distribution only via its power. Similarly, the nested lattice source coding scheme attains the same rate-distortion trade-off for all ergodic sources with the same second moment.

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Section: Remarkmentioning

confidence: 90%

Section: Remarkmentioning

confidence: 95%

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A Simple Proof for the Existence of “Good” Pairs of Nested Lattices

Ordentlich

Erez

2016

IEEE Trans. Inform. Theory

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“…We explain how C&F, SCF, and SIC can be used as MPR techniques. We give a brief summary of the C&F and SCF schemes proposed in [48], with a particular focus on the symmetric rates and complex-valued channel models. We refer our readers to [23,48] for more details on C&F.…”

Section: Symmetric Mpr Csma Vs Conventional Csmamentioning

confidence: 99%

Performance Analysis of Csma With Multi-Packet Reception: The Inhomogeneous Case

Ashrafi

Feng

Roy

2016

IEEE Trans. Commun.

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The problem of Carrier Sense Multiple Access (CSMA) with multi-packet reception (MPR) is studied. Most prior work has focused on the homogeneous case, where all the mobile users are assumed to have identical packet arrival rates and transmission probabilities. The inhomogeneous case remains largely open in the literature. In this work, we make a first step towards this open problem by deriving throughput and delay expressions for inhomogeneous CSMA, with a particular focus on a family of MPR models called the "all-or-nothing" symmetric MPR. This family of MPR models allows us to overcome several technical challenges associated with conventional analysis and to derive accurate throughput and delay expressions in the large-systems regime. Interestingly, this family of MPR models is still general enough to include a number of useful MPR techniques-such as successive interference cancellation (SIC), compute-and-forward (C&F), and successive computeand-forward (SCF)-as special cases. Based on these throughput and delay expressions, we provide theoretical guidelines for meeting quality-of-service requirements and for achieving global stability; we also evaluate the performances of various MPR techniques, highlighting the clear advantages offered by SCF.

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“…Our uplink (i.e., MIMO MAC) problem statement is taken from the expanded compute-and-forward framework [15]. See [15,Section II] for an in-depth discussion as well as intuition in terms of signal levels.…”

Section: A Uplink Channelmentioning

confidence: 99%

Dirty-paper integer-forcing

Nazer

Shamai

2015

2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton)

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Consider a Gaussian multiple-input multipleoutput (MIMO) multiple-access channel (MAC) with channel matrix H and a Gaussian MIMO broadcast channel (BC) with channel matrix H T . For the MIMO MAC, the integer-forcing architecture consists of first decoding integer-linear combinations of the transmitted codewords, which are then solved for the original messages. For the MIMO BC, the integer-forcing architecture consists of preinverting the integer-linear combinations at the transmitter so that each receiver can obtain its desired codeword by decoding an integer-linear combination. In both cases, integer-forcing offers higher achievable rates than zeroforcing. In recent work, we established an uplink-downlink duality relationship for integer-forcing, i.e., we showed that any rate tuple that is achievable via integer-forcing on the MIMO MAC can be achieved via integer-forcing on the MIMO BC with the same sum power and vice versa. It has also been shown that integer-forcing for the MIMO MAC can be enhanced via successive cancellation. Here, we introduce dirty-paper integer-forcing for the MIMO BC and establish uplink-downlink duality with successive integer-forcing for the MIMO MAC.

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Expanding the Compute-and-Forward Framework: Unequal Powers, Signal Levels, and Multiple Linear Combinations

Cited by 51 publications

References 98 publications

A Simple Proof for the Existence of “Good” Pairs of Nested Lattices

A Simple Proof for the Existence of “Good” Pairs of Nested Lattices

Performance Analysis of Csma With Multi-Packet Reception: The Inhomogeneous Case

Dirty-paper integer-forcing

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