Morteza Varasteh

Joint source-channel coding with one-bit ADC front end

This paper considers the zero-delay transmission of a Gaussian source over an additive white Gaussian noise (AWGN) channel with a one-bit analog-to-digital converter (ADC) front end. The optimization of the encoder and decoder is tackled under both the mean squared error (MSE) distortion and the outage distortion criteria with an average power constraint. For MSE distortion, the optimal transceiver is identified over the space of symmetric encoders. This result demonstrates that the linear encoder, which is optimal with a full-precision front end, approaches optimality only in the low signal-to-noise ratio (SNR) regime; while, digital transmission is optimal in the high SNR regime. For the outage distortion criterion, the structure of the optimal encoder and decoder are obtained. In particular, it is shown that the encoder mapping is piecewise constant and can take only two opposite values when it is non-zero.

Zero-delay joint source-channel coding

In zero-delay joint source-channel coding each source sample is mapped to a channel input, and the samples are directly estimated at the receiver based on the corresponding channel output. Despite its simplicity, uncoded transmission achieves the optimal end-to-end distortion performance in some communication scenarios, significantly simplifying the encoding and decoding operations, and reducing the coding delay. Three different communication scenarios are considered here, for which uncoded transmission is shown to achieve either optimal or near-optimal performance. First, the problem of transmitting a Gaussian source over a block-fading channel with block-fading side information is considered. In this problem, uncoded linear transmission is shown to achieve the optimal performance for certain side information distributions, while separate source and channel coding fails to achieve the optimal performance. Then, uncoded transmission is shown to be optimal for transmitting correlated multivariate Gaussian sources over a multiple-input multiple-output (MIMO) channel in the low signal to noise ratio (SNR) regime. Finally, motivated by practical systems a peak-power constraint (PPC) is imposed on the transmitters channel input. Since linear transmission is not possible in this case, nonlinear transmission schemes are proposed and shown to perform very close to the lower bound.

Gaussian Multiple Access Channels with One-Bit Quantizer at the Receiver

The capacity region of a two-transmitter Gaussian multiple access channel (MAC) under average input power constraints is studied, when the receiver employs a zero-threshold one-bit analogue-to-digital converter (ADC). It is proven that the input distributions of the two transmitters that achieve the boundary points of the capacity region are discrete. Based on the position of a boundary point, upper bounds on the number of the mass points of the corresponding distributions are derived. Furthermore, a lower bound on the sum capacity is proposed that can be achieved by time division with power control. Finally, inspired by the numerical results, the proposed lower bound is conjectured to be tight.

Zero-delay joint source-channel coding in the presence of interference known at the encoder

Zero-delay transmission of a Gaussian source over an additive white Gaussian noise (AWGN) channel is considered in the presence of an independent additive Gaussian interference signal. The mean squared error (MSE) distortion is minimized under an average power constraint assuming that the interference signal is known at the transmitter. Optimality of simple linear transmission does not hold in this setting due to the presence of the known interference signal. While the optimal encoder-decoder pair remains an open problem, various non-linear transmission schemes are proposed in this paper. In particular, interference concentration (ICO) and one-dimensional lattice (1DL) strategies, using both uniform and non-uniform quantization of the interference signal, are studied. It is shown that, in contrast to typical scalar quantization of Gaussian sources, a non-uniform quantizer, whose quantization intervals become smaller as we go further from zero, improves the performance. Given that the optimal decoder is the minimum MSE (MMSE) estimator, a necessary condition for the optimality of the encoder is derived, and the numerically optimized encoder (NOE) satisfying this condition is obtained. Based on the numerical results, it is shown that 1DL with non-uniform quantization performs closer (compared with the other schemes) to the NOE while requiring significantly lower complexity.

Zero-Delay Source-Channel Coding With a Low-Resolution ADC Front End

Motivated by the practical constraints arising in emerging sensor network and Internet-of-Things (IoT) applications, the zero-delay transmission of a Gaussian measurement over a real single-input multiple-output (SIMO) additive white Gaussian noise (AWGN) channel is studied with a low-resolution analog-to-digital converter (ADC) front end. Joint optimization of the encoder and the decoder mapping is tackled under both the mean squared error (MSE) distortion and the distortion outage probability (DOP) criteria, with an average power constraint on the channel input. Optimal encoder and decoder mappings are identified for a one-bit ADC front end under both criteria. For the MSE distortion, the optimal encoder mapping is shown to be non-linear in general, while it tends to a linear encoder in the low signal-to-noise ratio (SNR) regime, and to an antipodal digital encoder in the high SNR regime. This is in contrast to the optimality of linear encoding at all SNR values in the presence of a full-precision front end. For the DOP criterion, it is shown that the optimal encoder mapping is piecewise constant and can take only two opposite values when it is non-zero. For both the MSE distortion and the DOP criteria, necessary optimality conditions are then derived for

Capacity region of a one-bit quantized Gaussian multiple access channel

K

Zero-Delay Source-Channel Coding With a 1-Bit ADC Front End and Correlated Receiver Side Information

-level ADC front ends as well as front ends with multiple one-bit ADCs. These conditions are used to obtain numerically optimized solutions. Extensive numerical results are also provided in order to gain insights into the structure of the optimal encoding and decoding mappings.

Delay limited transmission of a uniform source over an AWGN channel

The capacity region of a two-transmitter Gaussian multiple access channel (MAC) under average input power constraints is studied, when the receiver employs a zero-threshold one-bit analog-to-digital converter (ADC). It is proved that the input distributions that achieve the boundary points of the capacity region are discrete. Based on the position of a boundary point, upper bounds on the number of the mass points of the corresponding distributions are derived. Finally, a conjecture on the sufficiency of K mass points in a point-to-point real AWGN with a K-bin ADC front end (symmetric or asymmetric) is settled.1

Wireless information and power transfer over an AWGN channel: Nonlinearity and asymmetric Gaussian signaling

Zero-delay transmission of a Gaussian source over an additive white Gaussian noise (AWGN) channel is considered with a 1-bit analog-to-digital converter (ADC) front end and correlated side information at the receiver. The design of the optimal encoder and decoder is studied for two different performance criteria, namely the mean squared error (MSE) distortion and the distortion outage probability (DOP), under an average power constraint on the channel input. For both criteria, necessary optimality conditions for the encoder and the decoder are derived, which are then used to numerically obtain encoder and decoder mappings that satisfy these conditions. Using these conditions, it is observed that the numerically optimized encoder (NOE) under the MSE distortion criterion is periodic, and its period increases with the correlation between the source and the receiver side information. For the DOP, it is instead seen that the NOE mappings periodically acquire positive and negative values, which decay to zero with increasing source magnitude, and the interval over which the mapping takes non-zero values becomes wider with the correlation between the source and the side information. Finally, inspired by the mentioned properties of the NOE mappings, parameterized encoder mappings with a small number of degrees of freedom are proposed for both distortion criteria, and their performance is compared with that of the NOE mappings.

On Capacity-Achieving Distributions Over Complex AWGN Channels Under Nonlinear Power Constraints and their Applications to SWIPT.

Delay limited transmission of a uniform source over an additive white Gaussian noise (AWGN) channel under an average power constraint is considered. Assuming that the channel can be used only once, mean squared error (MSE) distortion is studied for both the bandwidth matched, and the 2:1 bandwidth compression cases. In the bandwidth matched scenario, simply scaling the source sample, i.e., analog transmission, performs better than transmitting the scalar quantized source samples. For the bandwidth compression scenario, a hybrid digital analog transmission scheme that quantizes the first source sample and superimposes the quantized sample with the scaled version of the second sample is studied. It is shown that, in this scheme, as opposed to the bandwidth matched case, a finite number of quantization indices minimizes the achievable distortion. The performance of this hybrid scheme is then compared with a numerically optimized encoder using the steepest decent algorithm iteratively. It is observed that the performance of the hybrid scheme is reasonably close to the numerically optimized scheme, while having a significantly lower computational complexity. The theoretical Ziv-Zakai (ZZ) bound on the average distortion is also considered to better understand the gap between the optimal performance and the proposed scheme.