In recent years increasingly complex architectures for deep convolution networks (DCNs) have been proposed to boost the performance on image recognition tasks. However, the gains in performance have come at a cost of substantial increase in computation and model storage resources. Fixed point implementation of DCNs has the potential to alleviate some of these complexities and facilitate potential deployment on embedded hardware. In this paper, we propose a quantizer design for fixed point implementation of DCNs. We formulate and solve an optimization problem to identify optimal fixed point bit-width allocation across DCN layers. Our experiments show that in comparison to equal bit-width settings, the fixed point DCNs with optimized bit width allocation offer >20% reduction in the model size without any loss in accuracy on CIFAR-10 benchmark. We also demonstrate that fine-tuning can further enhance the accuracy of fixed point DCNs beyond that of the original floating point model. In doing so, we report a new state-of-the-art fixed point performance of 6.78% error-rate on CIFAR-10 benchmark.

Coordinated multipoint (CoMP) transmission is an infrastructural enhancement under consideration for next generation wireless networks. In this paper, the capacity gain achieved through CoMP transmission is studied in various models of wireless networks that have practical significance. The capacity gain is analyzed through the degrees of freedom (DoF) criterion. The DoF available for communication provides an analytically tractable way to characterize the capacity of interference channels. The considered channel model has K transmitter/receiver pairs, and each receiver is interested in one unique message from a set of K independent messages. Each message can be available at more than one transmitter. The maximum number of transmitters at which each message can be available, is defined as the cooperation order M. For fully connected interference channels, it is shown that the asymptotic per user DoF, as K goes to infinity, remains at 1/2 as M is increased from 1 to 2. Furthermore, the same negative result is shown to hold for all M ≥ 2 for any message assignment that satisfies a local cooperation constraint. On the other hand, when the assumption of full connectivity is relaxed to local connectivity, and each transmitter is connected only to its own receiver as well as L neighboring receivers, it is shown that local cooperation is optimal. The asymptotic per user DoF is shown to be at least max {1/2, 2M/(2M + L)} for locally connected channels, and is shown to be 2M/(2M + 1) for the special case of Wyner's asymmetric model where L = 1. An interesting feature of the proposed achievability scheme is that it relies on simple zero-forcing transmit beams and does not require symbol extensions. Also, to achieve the optimal per user DoF for Wyner's model, messages are assigned to transmitters in an asymmetric fashion unlike traditional assignments where message i has to be available at transmitter i. It is also worth noting that some receivers have to be inactive, and fractional reuse is needed to achieve equal DoF for all users.

The degrees of freedom (DoF) available for communication provides an analytically tractable way to characterize the information-theoretic capacity of interference channels. In this paper, the DoF of a K-user interference channel is studied under the assumption that the transmitters can cooperate via coordinated multi-point (CoMP) transmission. In [1], the authors considered the linear asymmetric model of Wyner, where each transmitter is connected to its own receiver and its successor, and is aware of its own message as well as M − 1 preceding messages. The per user DoF was shown to go to M/M+1 as the number of users increases to infinity. In this work, the same model of channel connectivity is considered, with a relaxed cooperation constraint that bounds the maximum number of transmitters at which each message can be available, by a cooperation order M. We show that the relaxation of the cooperation constraint, while maintaining the same load imposed on a backhaul link needed to distribute the messages, results in a gain in the DoF. In particular, the asymptotic limit of the per user DoF under the cooperation order constraint is 2M/2M+1. Moreover, the optimal transmit set selection satisfies a local cooperation constraint. i.e., each message needs only to be available at neighboring transmitters.

We consider locally connected K-user MISO interference channels where each transmitter has N antennas and is connected to the receiver with the same index as well as [L/2] successively preceding receivers and [L/2] following receivers. We assume that each receiver is interested in one message, which can be available at a maximum of M transmitters. Under these assumptions, we study the available degrees of freedom as well as the optimal way to assign messages to transmitters. For the case where each message is assigned to the transmitter with the same index, we know from [1] that [KN/N+1] DoF is achievable for the considered locally connected channel using interference alignment as the number of symbol extensions goes to infinity. In this work, we show that a simple linear strategy employing zero forcing transmit beams achieves min {2MN/M(N+1)+L, 1} per user degrees of freedom. In particular, the N/N+1 per user DoF is achievable by coding over only one channel realization, for any value of M ≥ L/N+1. Moreover, we show that the proposed scheme is optimal among a class of linear strategies where each receiver is either inactive or enjoys interference-free communication. Finally, we generalize the upper bound proved for Wyner's asymmetric channel model (L = 1) in [2], and show that message assignments satisfying a local cooperation constraint are optimal for a general setting of the parameters.

We study the degrees of freedom (DoF) of the$K$-user interference channel with coordinated multipoint (CoMP) transmission and reception. Each message is jointly transmitted by$M_{t}$successive transmitters, and is jointly received by$M_{r}$successive receivers. We refer to this channel as the CoMP channel with a transmit cooperation order of$M_{t}$and receive cooperation order of$M_{r}$. Since the channel has a total of$K$transmit antennas and$K$receive antennas, the maximum possible DoF is equal to$K$. We show that the CoMP channel has$K$DoF if and only if$M_{t} + M_{r} \geq K+1$. The key idea is that the zero forcing of the interference corresponding to the$i{{\rm th}}$message at the decoder of the$j{{\rm th}}$message, where$j \ne i$, can be viewed as a shared responsibility between the$M_{t}$transmitters carrying the$i{{\rm th}}$message, and the$M_{r}$receivers decoding the$j{{\rm th}}$message. For the general case, we derive an outer bound that states that the DoF is bounded above by$\left \lceil (K+M_{t}+M_{r}-2)/2\right \rceil$. For the special case with only CoMP transmission, i.e,$M_{r} = 1$, we propose a scheme that can achieve$(K+M_{t}-1)/2$DoF for all$K < 10$, and conjecture that the result holds true for all$K$. In the proposed coding scheme, the$M_{t}$transmitters carrying each message are used to cancel the interference introduced by this message at the first$M_{t}-1$receivers, thereby allowing each of these receivers to enjoy 1 DoF, and asymptotic interference alignment is used to align the interfering signals at each other receiver to occupy half the signal space. The achievability proofs are based on the notion of algebraic independence from algebraic geometry.

We study the degrees of freedom (DoF) of a Gaussian interference network with K transmitters and K receivers, where the transmitters are allowed to cooperate (partially) to transmit information to the receivers.

Using Gaussian inputs and treating interference as noise at the receivers has recently been shown to be sum capacity achieving for the two-user single-input single-output (SISO) Gaussian interference channel in a low interference regime, where the interference levels are below certain thresholds. In this paper, such a low interference regime is characterized for multiple-input multiple-output (MIMO) Gaussian interference channels. Conditions are provided on the direct and cross channel gain matrices under which using Gaussian inputs and treating interference as noise at the receivers is sum capacity achieving. For the special cases of the symmetric multiple-input single-output (MISO) and single-input multiple-output (SIMO) Gaussian interference channels, more explicit expressions for the low interference regime are derived. In particular, the threshold on the interference levels that characterize low interference regime is related to the input SNR and the angle between the direct and cross channel gain vectors. It is shown that the low interference regime can be quite significant for MIMO interference channels, with the low interference threshold being at least as large as the sine of the angle between the direct and cross channel gain vectors for the MISO and SIMO cases.

We consider the K-user Gaussian interference channel in the context of the downlink of a cellular system where the base stations can exchange messages through a backhaul network, and the interfering users can be jointly served by multiple base stations. To limit the load on the backhaul network, the number of (base station) transmitters sharing a given message is bounded by a number M, which we call the cooperation order. We provide outer bounds on the sum degrees of freedom of this system, which are shown to be tight in special cases.

We investigate the effect of feedback delay on the outage probability of multiple-input single-output (MISO) fading channels. Channel state information at the transmitter (CSIT) is a delayed version of the channel state information available at the receiver (CSIR). We consider two cases of CSIR: (a) perfect CSIR and (b) CSI estimated at the receiver using training symbols. With perfect CSIR, under a short-term power constraint, we determine: (a) the outage probability for beamforming with imperfect CSIT (BF-IC) analytically, and (b) the optimal spatial power allocation (OSPA) scheme that minimizes outage numerically. Results show that, for delayed CSIT, BF-IC is close to optimal for low SNR and uniform spatial power allocation (USPA) is close to optimal at high SNR. Similarly, under a longterm power constraint, we show that BF-IC is better for low SNR and USPA is better at high SNR. With imperfect CSIR, we obtain an upper bound on the outage probability with USPA and BF-IC. Results show that the loss in performance due to imperfection in CSIR is not significant, if the training power is chosen appropriately.

Establishing the capacity region of a Gaussian interference network is an open problem in information theory. Recent progress on this problem has led to the characterization of the capacity region of a general two-user Gaussian interference channel within one bit. In this paper, we develop new, improved outer bounds on the capacity region. Using these bounds, we show thattreatinginterferenceasnoiseachieves thesumcapacityof the two-user Gaussian interference channel in alow-interferenceregime, where the interference parameters are below certain thresholds. We then generalize our techniques and results to Gaussian interference networks with more than two users. In particular, we demonstrate that the total interference threshold, below which treating interference as noise achieves the sum capacity, increases with the number of users.

Genie based arguments are used to derive new outer bounds on the sum capacity of the two user, symmetric three user, one-to-many and many-to-one Gaussian interference channels. Using these bounds, it is shown that treating interference as noise achieves the sum capacity in a low interference regime, where the interference parameters are below certain thresholds.