Integer-Forcing Source Coding

Integer-Forcing (IF) is a new framework, based on compute-and-forward, for decoding multiple integer linear combinations from the output of a Gaussian multiple-input multiple-output channel. This work applies the IF approach to arrive at a new low-complexity scheme, IF source coding, for distributed lossy compression of correlated Gaussian sources under a minimum mean squared error distortion measure. All encoders use the same nested lattice codebook. Each encoder quantizes its observation using the fine lattice as a quantizer and reduces the result modulo the coarse lattice, which plays the role of binning. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. In general, the linear combinations have smaller average powers than the original signals. This allows to increase the density of the coarse lattice, which in turn translates to smaller compression rates. We also propose and analyze a one-shot version of IF source coding, that is simple enough to potentially lead to a new design principle for analog-to-digital converters that can exploit spatial correlations between the sampled signals.Comment: Submitted to IEEE Transactions on Information Theor

Capacity Bounds for Communication Systems with Quantization and Spectral Constraints

Low-resolution digital-to-analog and analog-to-digital converters (DACs and ADCs) have attracted considerable attention in efforts to reduce power consumption in millimeter wave (mmWave) and massive MIMO systems. This paper presents an information-theoretic analysis with capacity bounds for classes of linear transceivers with quantization. The transmitter modulates symbols via a unitary transform followed by a DAC and the receiver employs an ADC followed by the inverse unitary transform. If the unitary transform is set to an FFT matrix, the model naturally captures filtering and spectral constraints which are essential to model in any practical transceiver. In particular, this model allows studying the impact of quantization on out-of-band emission constraints. In the limit of a large random unitary transform, it is shown that the effect of quantization can be precisely described via an additive Gaussian noise model. This model in turn leads to simple and intuitive expressions for the power spectrum of the transmitted signal and a lower bound to the capacity with quantization. Comparison with non-quantized capacity and a capacity upper bound that does not make linearity assumptions suggests that while low resolution quantization has minimal impact on the achievable rate at typical parameters in 5G systems today, satisfying out-of-band emissions are potentially much more of a challenge.Comment: Appears in the Proceedings of IEEE International Symposium on Information Theory (ISIT) 202

A Modulo-Based Architecture for Analog-to-Digital Conversion

Systems that capture and process analog signals must first acquire them through an analog-to-digital converter. While subsequent digital processing can remove statistical correlations present in the acquired data, the dynamic range of the converter is typically scaled to match that of the input analog signal. The present paper develops an approach for analog-to-digital conversion that aims at minimizing the number of bits per sample at the output of the converter. This is attained by reducing the dynamic range of the analog signal by performing a modulo operation on its amplitude, and then quantizing the result. While the converter itself is universal and agnostic of the statistics of the signal, the decoder operation on the output of the quantizer can exploit the statistical structure in order to unwrap the modulo folding. The performance of this method is shown to approach information theoretical limits, as captured by the rate-distortion function, in various settings. An architecture for modulo analog-to-digital conversion via ring oscillators is suggested, and its merits are numerically demonstrated