72 research outputs found
Phase Precoded Compute-and-Forward with Partial Feedback
In this work, we propose phase precoding for the compute-and-forward (CoF)
protocol. We derive the phase precoded computation rate and show that it is
greater than the original computation rate of CoF protocol without precoder. To
maximize the phase precoded computation rate, we need to 'jointly' find the
optimum phase precoding matrix and the corresponding network equation
coefficients. This is a mixed integer programming problem where the optimum
precoders should be obtained at the transmitters and the network equation
coefficients have to be computed at the relays. To solve this problem, we
introduce phase precoded CoF with partial feedback. It is a quantized precoding
system where the relay jointly computes both a quasi-optimal precoder from a
finite codebook and the corresponding network equations. The index of the
obtained phase precoder within the codebook will then be fedback to the
transmitters. A "deep hole phase precoder" is presented as an example of such a
scheme. We further simulate our scheme with a lattice code carved out of the
Gosset lattice and show that significant coding gains can be obtained in terms
of equation error performance.Comment: 5 Pages, 4 figures, submitted to ISIT 201
Lattices from Codes for Harnessing Interference: An Overview and Generalizations
In this paper, using compute-and-forward as an example, we provide an
overview of constructions of lattices from codes that possess the right
algebraic structures for harnessing interference. This includes Construction A,
Construction D, and Construction (previously called product
construction) recently proposed by the authors. We then discuss two
generalizations where the first one is a general construction of lattices named
Construction subsuming the above three constructions as special cases
and the second one is to go beyond principal ideal domains and build lattices
over algebraic integers
Efficient Decoding Algorithms for the Compute-and-Forward Strategy
We address in this paper decoding aspects of the Compute-and-Forward (CF)
physical-layer network coding strategy. It is known that the original decoder
for the CF is asymptotically optimal. However, its performance gap to optimal
decoders in practical settings are still not known. In this work, we develop
and assess the performance of novel decoding algorithms for the CF operating in
the multiple access channel. For the fading channel, we analyze the ML decoder
and develop a novel diophantine approximation-based decoding algorithm showed
numerically to outperform the original CF decoder. For the Gaussian channel, we
investigate the maximum a posteriori (MAP) decoder. We derive a novel MAP
decoding metric and develop practical decoding algorithms proved numerically to
outperform the original one
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