Construction A of Lattices Over Number Fields and Block Fading (Wiretap) Coding

Kositwattanarerk, Wittawat; Ong, Soon Sheng; Oggier, Frédérique

doi:10.1109/tit.2015.2416340

Cited by 28 publications

(61 citation statements)

References 25 publications

(48 reference statements)

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“…We omit the details. Therefore, there exist a sequence of lattices in the ensemble (12) such that the decoding error probability vanishes as T → ∞ as long as the VNR…”

Section: Definition 10 (Semi Norm-ergodicity [24]) a Random Vectormentioning

confidence: 99%

“…Our model of block-fading channels is essentially that of parallel independent fading channels defined in [11,Section 5.4.4], which assumes channel state information (CSI) at the receiver only. While the block length (or coherence time) T in blockfading is dictated by properties of the physical world, and is a design parameter in parallel independent fading, the two models are equivalent if T is large enough (see also [12]- [14] for using term "block-fading"). The crux here is that multiple resources offer diversity, which a coding scheme may utilize to improve performance.…”

Section: Introductionmentioning

confidence: 99%

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Ring Compute-and-Forward Over Block-Fading Channels

Lyu

Campello

Ling

2019

IEEE Trans. Inform. Theory

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The Compute-and-Forward protocol in quasi-static channels normally employs lattice codes based on the rational integers Z, Gaussian integers Z [i] or Eisenstein integers Z [ω], while its extension to more general channels often assumes channel state information at transmitters (CSIT). In this paper, we propose a novel scheme for Compute-and-Forward in block-fading channels without CSIT, which is referred to as Ring Compute-and-Forward because the fading coefficients are quantized to the canonical embedding of a ring of algebraic integers. Thanks to the multiplicative closure of the algebraic lattices employed, a relay is able to decode an algebraic-integer linear combination of lattice codewords. We analyze its achievable computation rates and show it outperforms conventional Compute-and-Forward based on Zlattices. By investigating the effect of Diophantine approximation by algebraic conjugates, we prove that the degrees-of-freedom (DoF) of the optimized computation rate is n/L, where n is the number of blocks and L is the number of users.

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“…We omit the details. Therefore, there exist a sequence of lattices in the ensemble (12) such that the decoding error probability vanishes as T → ∞ as long as the VNR…”

Section: Definition 10 (Semi Norm-ergodicity [24]) a Random Vectormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Ring Compute-and-Forward Over Block-Fading Channels

Lyu

Campello

Ling

2019

IEEE Trans. Inform. Theory

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“…We follow closely the construction of [14]. For an introduction to the algebraic theory used in this section, the reader is referred to [2].…”

Section: Construction a From O K -Latticesmentioning

confidence: 99%

Algebraic lattice codes achieve the capacity of the compound block-fading channel

Campello

Ling

Belfiore

2016

2016 IEEE International Symposium on Information Theory (ISIT)

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Abstract-We propose a coding scheme that achieves the capacity of the compound block-fading channel with lattice decoding at the receiver. Our lattice construction exploits the multiplicative structure of number fields and their group of units to absorb ill-conditioned channel realizations. To shape the constellation, a discrete Gaussian distribution over the lattice points is applied. A by-product of our results is the proof that the lattice Gaussian distribution is capacity-achieving in the AWGN channel for any signal-to-noise ratio.

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“…A wide range of applicable lattices in digital communications have been treated including the well-known root lattices [ 21 ] , Construction A [22] and Construction Ac [23] . Unfortunately, the presence of random coding with Construction A is a main drawback making such a lattice ensemble too far from any practicality.…”

Section: Constructions Of Lattices and Practical Lattice Codesmentioning

confidence: 99%

Study Status and Prospect of Lattice Codes in Wireless Communication

Duan

Zhao

et al. 2015

2015 Fifth International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)

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Lattice codes can achieve the capacity of additive white Gaussian noise channel with and without power construction. It is well known that lattice codes can provide a classical information theoretic way to obtain achievable rate and performance gains for point-to-point Gaussian channels. The coding scheme based on lattice codes can be used as building blocks for practical applications, such as point-topoint communication systems, Gaussian networks and MIMO communication systems etc. More importantly, lattice codes can be used to investigate new link adaptive coding and modulation schemes and design sparse code multiple access codebooks. So, lattice codes could be a potential candidate for 5G communication. This paper provides a comprehensive review of the state-of-the-art of lattice codes. It first describes the theory of lattice codes. Then, a comprehensive survey to easily understand channel capacity, error exponents and practical lattice codes is outlined. The application of nested lattice codes is also presented for lossy source coding, dirty paper channel coding and relay communication. Finally, some unresolved issues and ongoing developments related to further improvements of lattice codes are highlighted.

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Construction A of Lattices Over Number Fields and Block Fading (Wiretap) Coding

Cited by 28 publications

References 25 publications

Ring Compute-and-Forward Over Block-Fading Channels

Ring Compute-and-Forward Over Block-Fading Channels

Algebraic lattice codes achieve the capacity of the compound block-fading channel

Study Status and Prospect of Lattice Codes in Wireless Communication

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