9 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
Full Diversity Unitary Precoded Integer-Forcing
We consider a point-to-point flat-fading MIMO channel with channel state
information known both at transmitter and receiver. At the transmitter side, a
lattice coding scheme is employed at each antenna to map information symbols to
independent lattice codewords drawn from the same codebook. Each lattice
codeword is then multiplied by a unitary precoding matrix and sent
through the channel. At the receiver side, an integer-forcing (IF) linear
receiver is employed. We denote this scheme as unitary precoded integer-forcing
(UPIF). We show that UPIF can achieve full-diversity under a constraint based
on the shortest vector of a lattice generated by the precoding matrix . This constraint and a simpler version of that provide design criteria for
two types of full-diversity UPIF. Type I uses a unitary precoder that adapts at
each channel realization. Type II uses a unitary precoder, which remains fixed
for all channel realizations. We then verify our results by computer
simulations in , and MIMO using different QAM
constellations. We finally show that the proposed Type II UPIF outperform the
MIMO precoding X-codes at high data rates.Comment: 12 pages, 8 figures, to appear in IEEE-TW
Robust Successive Compute-and-Forward over Multi-User Multi-Relay Networks
This paper develops efficient Compute-and-forward (CMF) schemes in multi-user
multi-relay networks. To solve the rank failure problem in CMF setups and to
achieve full diversity of the network, we introduce two novel CMF methods,
namely, extended CMF and successive CMF. The former, having low complexity, is
based on recovering multiple equations at relays. The latter utilizes
successive interference cancellation (SIC) to enhance the system performance
compared to the state-of-the-art schemes. Both methods can be utilized in a
network with different number of users, relays, and relay antennas, with
negligible feedback channels or signaling overhead. We derive new concise
formulations and explicit framework for the successive CMF method as well as an
approach to reduce its computational complexity. Our theoretical analysis and
computer simulations demonstrate the superior performance of our proposed CMF
methods over the conventional schemes. Furthermore, based on our simulation
results, the successive CMF method yields additional signal-to-noise ratio
gains and shows considerable robustness against channel estimation error,
compared to the extended CMF method.Comment: 44 pages, 10 figures, 1 table, accepted to be published in IEEE
Trans. on Vehicular Tec