Jiening Zhan

Integer-Forcing Linear Receivers

Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code, which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multiuser uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean-squared error receiver. In the high signal-to-noise ratio regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard multiple-input multiple-output (MIMO) channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees of freedom.

Integer-forcing linear receivers

Linear receivers are often used to reduce the implementation complexity of multiple-antenna systems. In a traditional linear receiver architecture, the receive antennas are used to separate out the codewords sent by each transmit antenna, which can then be decoded individually. Although easy to implement, this approach can be highly suboptimal when the channel matrix is near singular. This paper develops a new linear receiver architecture that uses the receive antennas to create an effective channel matrix with integer-valued entries. Rather than attempting to recover transmitted codewords directly, the decoder recovers integer combinations of the codewords according to the entries of the effective channel matrix. The codewords are all generated using the same linear code, which guarantees that these integer combinations are themselves codewords. Provided that the effective channel is full rank, these integer combinations can then be digitally solved for the original codewords. This paper focuses on the special case where there is no coding across transmit antennas and no channel state information at the transmitter(s), which corresponds either to a multiuser uplink scenario or to single-user V-BLAST encoding. In this setting, the proposed integer-forcing linear receiver significantly outperforms conventional linear architectures such as the zero forcing and linear minimum mean-squared error receiver. In the high signal-to-noise ratio regime, the proposed receiver attains the optimal diversity-multiplexing tradeoff for the standard multiple-input multiple-output (MIMO) channel with no coding across transmit antennas. It is further shown that in an extended MIMO model with interference, the integer-forcing linear receiver achieves the optimal generalized degrees of freedom.

MIMO compute-and-forward

In many network communication scenarios, a relay in the network may only need to recover and retransmit an equation of the transmitted messages. In previous work, it has been shown that if each transmitter employs the same lattice code, the interference structure of the channel can be exploited to recover an equation much more efficiently than possible with standard multiple-access strategies. Here, we generalize this compute-and-forward framework to the multiple antenna setting. Our results show that it is often beneficial to use extra antennas at the receiver to rotate the channel coefficients towards the nearest integer vector instead of separating out the transmitted signals. We also demonstrate that in contrast to classical strategies, the multiplexing gain of compute-and-forward increases if the transmitters have channel state information. Finally, we apply our scheme to the two way relay network and observe performance gains over traditional strategies.

Practical code design for compute-and-forward

The Compute-and-Forward approach has been proven to be very beneficial for communication over Gaussian networks. While the theoretical results are promising, it is still not completely understood how to best apply this scheme in practice. The objective of this work is to provide a low complexity scheme suitable for Compute-and-Forward. The scheme is based on utilizing linear codes over ℤq where q is not restricted to be prime and allows to achieve high transmission rates following Ungerboecks set partitioning principle.

Integer-Forcing Linear Receivers: A New Low-Complexity MIMO Architecture

We propose a new framework for MIMO decoding based on a recently developed technique for reliably conveying linear equations over wireless channels. Each transmit antenna sends an independent data stream using the same linear code. As a result, any integer combination of the codewords is itself a codeword. Each receive antenna observes a random complex-valued combination of the codewords according to the fading coefficients. We use a linear pre-processing step at the receiver to transform the effective channel into a (full-rank) integer matrix. A single stream decoder is then used to recover integer combinations of the codewords. These equations of codewords are then translated into equations of the transmitted data streams over a finite field which can be easily solved for the original data. We examine the performance of our scheme in terms of the probability of outage and show that significant gains are possible over standard linear architectures for both i.i.d. and correlated Rayleigh fading.

Integer-Forcing architectures for MIMO: Distributed implementation and SIC

Linear receivers are often used in multiple-antenna systems due to ease of implementation. However, traditional linear receivers such as the Decorrelator and the linear minimum-mean squared error (MMSE) receiver often have a significant performance loss compared to the optimal joint maximum likelihood (ML) receiver. In previous work, we proposed the Integer-Forcing linear receiver, which bridges the rate gap between traditional linear receivers and the joint ML receiver at the cost of some additional signal processing. In this paper, we examine a distributed implementation of the Integer-Forcing architecture where the front-end linear receiver is eliminated. This reduces the signal processing complexity at the receiver side and allows for distribution in the MIMO system. Our results show that although this distributedness does come at a price in performance, the Integer-Forcing architecture still achieves both rate and diversity gains over traditional linear architectures. We also propose the use of Successive Interference Cancellation (SIC) in the Integer-Forcing Linear Receiver.

Linear Function Computation in Networks: Duality and Constant Gap Results

In linear function computation, multiple source nodes communicate across a relay network to a single destination whose goal is to recover linear functions of the original source data. When the relay network is a linear deterministic network, a duality relation is established between function computation and broadcast with common messages. Using this relation, a compact sufficient condition is found describing those cases where the cut-set bound is tight. These insights are used to develop results for the case where the relay network contains Gaussian multiple-access channels. The proposed scheme decouples the physical and network layers. Using lattice codes for both source quantization and computation in the physical layer, the original Gaussian sources are converted into discrete sources and the Gaussian network into a linear deterministic network. Network codes for computing functions of discrete sources across the deterministic network are then found by applying the duality relation. The distortion for computing the sum of an arbitrary number of independent Gaussian sources over the Gaussian network is proven to be within a constant factor of the optimal performance. Furthermore, the constant factor results are extended to include asymmetric functions for the case of two sources.

Function computation in networks: Duality and constant gap results

In the linear function computation problem, multiple source nodes communicate across a relay network to a single destination whose goal is to recover a linear function of the original source data. For the case when the relay network is a deterministic network, a duality relation is established between the linear function computation problem and the standard, well-known multicast problem. Using this relation, a compact sufficient condition is found describing those cases where the cut-set bound is tight. Then, these insight are used to develop results for the case where the relay network contains Gaussian superposition channels. Assuming the original source sequences are independent Gaussians, the resulting distortion for the recovery of their sum is found to within a constant gap.

Mitigating interference with integer-forcing architectures

We show that the recently proposed integer-forcing linear receiver provides an attractive approach to the problem of mitigating external interference in MIMO channels. The integer-forcing receiver proceeds by first decoding a set of full rank integer linear combinations of the data streams. The resulting full rank equations are then inverted to find the original data. By selecting equation coefficients in a direction that depends on both the interference space and the channel matrix, the impact of external interference can be effectively reduced. We show that this technique attains a non-trivial gain over traditional linear receivers. Furthermore, the integer-forcing linear receiver achieves the same generalized degrees of freedom for the M×M MIMO channel with K dimensional external interference as the joint decoder.

Functional Forwarding of Channel State Information

Based on the recent compute-and-forward technique , a novel communication strategy is proposed under which functions of the channel state information are forwarded along the network. Those functions are chosen such that on the one hand, they can be efficiently forwarded, and on the other hand, they are maximally useful to the final decoder of the message. It is illustrated that there is generally a tension between these two requirements. The strategy is shown to perform well for certain classes of multilayer networks where channel state information is acquired locally at each receiver. For example, for a two-stage Gaussian relay network with local channel state information, it is shown that the proposed strategy performs optimally in a scaling-law sense, as the number of relays increases.