Construction of turbo lattices

Abstract-A key issue in compute-and-forward for physical layer network coding scheme is to determine a good function of the received messages to be reliably estimated at the relay nodes. We show that this optimization problem can be viewed as the problem of finding the closest point of Z [i] n to a line in the n-dimensional complex Euclidean space, within a bounded region around the origin. We then use the complex version of the LLL lattice basis reduction (CLLL) algorithm to provide a reduced complexity suboptimal solution as well as an upper bound to the minimum distance of the lattice point from the line. Using this bound we are able to find a lower bound to the ergodic rate and a union bound estimate on the error performance of a lattice constellation used for lattice network coding. We compare performance of the CLLL with a more complex iterative optimization method as well as with a simple quantized search. Simulations show how CLLL can trade some performance for a lower complexity.Index Terms-Ergodic rate, compute-and-forward, CLLL algorithm, quantized error, successive refinement.

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“…We will further study good lattice constellations derived from strong infinite lattices including the ones introduced in [13].…”

Section: Discussionmentioning

confidence: 99%

On the ergodic rate for compute-and-forward

Sakzad

Viterbo

Hong

et al. 2012

2012 International Symposium on Network Coding (NetCod)

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“…Construction D is exploited in [31][32], making possible a construction of lattices from turbo codes. The analysis of Construction D lattices is not very tractable where the LDPC or Turbo ensemble should be taken into account.…”

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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“…A multistage decoding algorithm was introduced in [10] and [5] which feeds soft values of the received vector s into the binary decoder on each level. The algorithm works on the real domain for multilevel codes, and in particular, for Construction D. Each level in Construction D may be viewed as Construction A.…”

Section: A a Multistage Soft Decoder For Construction Dmentioning

confidence: 99%

“…Lattice codes are an important class of bandwidth-efficient codes. There are a number of practical lattice codes introduced recently, for example, low-density parity-check (LDPC) lattices [3], low-density lattice codes (LDLC) [4] and turbo lattices [5]. LDPC codes and turbo codes are both capacityachieving codes.…”

Section: Introductionmentioning

confidence: 99%

A Construction of lattices from polar codes

Yan

Ling

2012

2012 IEEE Information Theory Workshop

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We employ polar codes as the building blocks of Construction D to construct lattices for the additive white Gaussian noise (AWGN) channel. The construction of these component polar codes is based on the idea of Pedarsani et al. for binary-input memoryless symmetric (BMS) channels. Our lattice construction takes the advantage of the performance gain of polar codes over Reed-Muller codes. Simulation results show the lattices constructed from polar codes outperform the benchmark Barnes-Wall lattices, which are constructed from Reed-Muller codes.

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Construction of turbo lattices

Cited by 32 publications

References 19 publications

On the ergodic rate for compute-and-forward

On the ergodic rate for compute-and-forward

Study Status and Prospect of Lattice Codes in Wireless Communication

A Construction of lattices from polar codes

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