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.

We propose a unified framework for deriving and studying soft-in soft-out (SISO) detection in multiple-access channels using the concept of variational inference. The proposed framework may be used in multiple-access interference (MAI), intersymbol interference (ISI), and multiple-input multiple-output (MIMO) channels. Without loss of generality, we will focus our attention on turbo multiuser detection, to facilitate a more concrete discussion. It is shown that, with some loss of optimality, variational inference avoids the exponential complexity ofaposterioriprobability (APP) detection by optimizing a closely related, but much more manageable, objective function calledvariationalfreeenergy. In addition to its systematic appeal, there are several other advantages to this viewpoint. First of all, it provides unified and rigorous justifications for numerous detectors that were proposed on radically different grounds, and facilitates convenient joint detection and decoding (utilizing the turbo principle) when error-control codes are incorporated. Second, efficient joint parameter estimation and data detection is possible via the variational expectation maximization (EM) algorithm, such that the detrimental effect of inaccurate channel knowledge at the receiver may be dealt with systematically. We are also able to extend BPSK-based SISO detection schemes to arbitrary square QAM constellations in a rigorous manner using a variational argument.

This correspondence investigates iterative soft-in-soft-out (SISO) detection in coded multiple access channels, with Gray-codedM-ary quadrature amplitude modulation (QAM) for the channel symbols. The proposed solution may be summarized as a generic iterative detection scheme called bit-level equalization and soft detection (BLESD), which is an extension of a unified variational inference framework for binary SISO detection proposed in our prior work. This new strategy fundamentally differs from the conventional symbol detector, in that data symbols are transparent to the new detector. Rather, soft estimates of the bits that make up the symbols are directly and naturally obtained by the detector in terms of posterior probabilities given the channel observation, facilitating efficient message-passing in joint detection and decoding. Case studies that illustrate the applications of the proposed scheme are presented for turbo multiuser detection (MUD) for multiple-access interference (MAI) channels and turbo equalization for inter-symbol interference (ISI) channels.

This paper investigates the soft-in soft-out (SISO) equalization of multilevel QAM symbols in coded inter-symbol interference (ISI) channels. Unlike the conventional approach of performing equalization at the symbol level, the proposed scheme targets the channel bits directly. This solution can be seen to belong to a family of SISO detection schemes which we call Bit-Level Equalization and Soft Detection (BLESD), stemming from the minimization of variational free energy given different postulates about the prior and posterior distributions of the channel bits. Simulation results demonstrate that the bit-level approach outperforms the symbol-level alternative in terms of error rate in the Porat-Friedlander channel.

We propose an efficient training-based OFDM channel impulse response (CIR) and carrier frequency offset (CFO) estimation algorithm that addresses the problem of phase noise (PHN), assuming that the PHN has a known prior distribution. The optimal joint estimation of CIR, PHN and CFO was described in an earlier work of ours. In this paper, we focus on the case where a training symbol consists of two identical halves in the time domain, and propose a variant to Moose's CFO estimation algorithm that accounts for PHN in CFO estimation. This is followed by an optimal joint CIR and PHN estimation scheme tailored for this "repeating training symbol" setup. It is assumed that the PHN process is Gaussian with known mean and covariance matrix. This encompasses both Wiener PHN and Gaussian PHN. It is shown through simulations that the proposed algorithm performs almost as well as the optimal JCPCE algorithm at much lower complexity. To further reduce the complexity of the proposed scheme, the conjugate gradient (CG) method is used and we show that it can be realized using the Fast Fourier Transform (FFT).

Building upon a unified framework for CDMA multiuser detection proposed in our prior work, we investigate the detection of M-QAM symbols in a multiuser CDMA channel. The solution proposed may be summarized as a generic iterative detection scheme for coded interference channels called bit-level equalization and soft detection (BLESD). It is shown that this novel approach avoids the exponential complexity of a posteriori probability (APP) detection by optimizing a closely-related, but much more manageable, objective function called variational free energy. It also fundamentally differs from the conventional symbol detector, in that data symbols are transparent to the new detector. Instead, soft estimates of the bits that make up the symbols are directly and naturally obtained at the detector output, in terms of posterior probabilities given the channel observation, facilitating efficient message-passing in joint detection and decoding

We propose an optimal training-based OFDM channel impulse response (CIR) estimation algorithm that addresses the phase noise (PHN) and carrier frequency offset (CFO) problem. If left unattended, these combined problems severely degrade the accuracy of the channel estimate and ultimately the quality of the wireless link. The solution involves the joint optimization of a complete log-likelihood function over the unknown CIR, PHN and CFO. To reduce the complexity of the proposed algorithm, a simplification based on the conjugate gradient method is introduced, yielding an efficient realization using the fast Fourier transform (FFT) with only minor performance degradation

We propose a unified approach for deriving and studying multiuser detection algorithms using the concept of variational free energy minimization. Under this generalized framework, we readily arrive at many popular multiuser detection schemes. In addition to its systematic appeal, there are several other advantages of this viewpoint. First of all, by condensing the design of multiuser detectors into the selection of a few key probability distributions, namely p(b), p(r|b) and Q(b), we provide rigorous justifications for numerous detectors that were proposed on heuristic grounds and recommend new and improved designs. Furthermore, the free energy formulation facilitates convenient joint detection and decoding (utilizing the turbo principle) when error-control codes are incorporated, as well as efficient parameter estimation via the variational expectation maximization (EM) algorithm.

We propose a systematic probabilistic framework to address the phase noise (PHN) problem in OFDM. In addition to deriving the optimal data detection scheme in the presence of PHN, we introduce a series of suboptimal approaches to blindly cancel the effect of PHN without the aid of pilot symbols. Not only do these algorithms provide the means to efficiently eliminate the effect of PHN in OFDM, they also open the door to much wider applications of advanced probabilistic inference algorithms in solving communications problems.

We propose a novel spreading code scheme, transmitter-receiver-based code, for wireless ad hoc networks. The design facilitates collision resolution using multiuser detection at each node, and is more bandwidth efficient than creating orthogonal channels in time or frequency. A subspace-based receiver structure is introduced, which identifies users of interest, or "active" users, with minimal prior information on the spreading code ensemble. A subspace-based blind multiuser detector can then be implemented to suppress multiaccess interference. The performance of the proposed active user identifier is studied by investigating its false alarm rate P/sub f/ and miss rate P/sub m/. Tradeoffs between P/sub f/ and P/sub m/ are discussed, and a graphical method to determine the threshold value d/sub th/ of the decision statistic used in discriminating between active and inactive channels is introduced.