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Unitary Precoding for IntegerForcing MIMO Linear Receivers
 Proc. of IEEE Information Theory Workshop (ITW
, 2014
"... Abstract—A flat fading pointtopoint multipleantenna channel is considered where the channel state information is known at both transmitter and receiver. At the transmitter side, we use a lattice encoder to map information symbols to lattice codewords. The lattice coded layers are then precoded u ..."
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Abstract—A flat fading pointtopoint multipleantenna channel is considered where the channel state information is known at both transmitter and receiver. At the transmitter side, we use a lattice encoder to map information symbols to lattice codewords. The lattice coded layers are then precoded using unitary matrices satisfying nonvanishing minimum product distance. At the receiver side, an integerforcing linear receiver is employed. This scheme is called ‘unitary precoded integerforcing’. We show that by applying the proposed precoding technique fulldiversity can be achieved. We then verify this result by conducting computer simulations in a 2 × 2 and 4 × 4 multipleinput multipleoutput (MIMO) channel using fulldiversity algebraic rotation precoder matrices. Index Terms—IntegerForcing, unitary precoding, lattice codes, fulldiversity. I.
Asymmetric ComputeandForward: Going Beyond One Hop
"... Abstract — We consider a twohop relay model in which multiple sources communicate with a single destination via multiple distributed relays. We propose an asymmetric ComputeandForward (CoF) scheme that allows lattice coding with different coarse and fine lattices at the sources. The proposed sch ..."
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Abstract — We consider a twohop relay model in which multiple sources communicate with a single destination via multiple distributed relays. We propose an asymmetric ComputeandForward (CoF) scheme that allows lattice coding with different coarse and fine lattices at the sources. The proposed scheme is motivated by the observation that, in an asymmetric CoF system, a higher transmission power at a source does not necessarily translate to a higher achievable information rate. We show that significant performance enhancement can be achieved by optimizing the transmission powers of the sources below their respective budgets. Further, the asymmetric construction of lattice coding allows the relays to conduct different modulo operations to reduce their forwarding rates, thereby supporting higher rates at the sources. However, modulo operations in general incur information loss, and so need to be carefully designed to ensure that the destination can successfully recover the source messages. As such, we propose a novel successive recovering algorithm for decoding at the destination, and establish sufficient conditions to guarantee successful recovery. Numerical results are provided to verify the superiority of our proposed scheme over other schemes. I.
Full Diversity Unitary Precoded IntegerForcing
"... We consider a pointtopoint flatfading 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 lat ..."
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We consider a pointtopoint flatfading 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 P and sent through the channel. At the receiver side, an integerforcing (IF) linear receiver is employed. We denote this scheme as unitary precoded integerforcing (UPIF). We show that UPIF can achieve fulldiversity under a constraint based on the shortest vector of a lattice generated by the precoding matrix P. This constraint and a simpler version of that provide design criteria for two types of fulldiversity 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 2 × 2, and 4 × 4 MIMO using different QAM constellations. We finally show that the proposed Type II UPIF outperform the MIMO precoding Xcodes at high data rates.