Dithered GMD Transform Coding

The geometric mean decomposition (GMD) transform coder (TC) was recently introduced and was shown to achieve the optimal coding gain without bit loading under the high bit rate assumption. However, the performance of the GMD transform coder is degraded in the low rate case. There are mainly two reasons for this degradation. First, the high bit rate quantizer model becomes invalid. Second, the quantization error is no longer negligible in the prediction process when the bit rate is low. In this letter, we introduce dithered quantization to tackle the first difficulty, and then redesign the precoders and predictors in the GMD transform coders to tackle the second. We propose two dithered GMD transform coders: the GMD subtractive dithered transform coder (GMD-SD) where the decoder has access to the dither information and the GMD nonsubtractive dithered transform coder (GMD-NSD) where the decoder has no knowledge about the dither. Under the uniform bit loading scheme in scalar quantizers, it is shown that the proposed dithered GMD transform coders perform significantly better than the original GMD coder in the low rate case

Multiple-Description Coding by Dithered Delta-Sigma Quantization

We address the connection between the multiple-description (MD) problem and Delta-Sigma quantization. The inherent redundancy due to oversampling in Delta-Sigma quantization, and the simple linear-additive noise model resulting from dithered lattice quantization, allow us to construct a symmetric and time-invariant MD coding scheme. We show that the use of a noise shaping filter makes it possible to trade off central distortion for side distortion. Asymptotically as the dimension of the lattice vector quantizer and order of the noise shaping filter approach infinity, the entropy rate of the dithered Delta-Sigma quantization scheme approaches the symmetric two-channel MD rate-distortion function for a memoryless Gaussian source and MSE fidelity criterion, at any side-to-central distortion ratio and any resolution. In the optimal scheme, the infinite-order noise shaping filter must be minimum phase and have a piece-wise flat power spectrum with a single jump discontinuity. An important advantage of the proposed design is that it is symmetric in rate and distortion by construction, so the coding rates of the descriptions are identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has been fixed. Accepted for publication in the IEEE Transactions on Information Theor

Asymptotic Task-Based Quantization with Application to Massive MIMO

Quantizers take part in nearly every digital signal processing system which operates on physical signals. They are commonly designed to accurately represent the underlying signal, regardless of the specific task to be performed on the quantized data. In systems working with high-dimensional signals, such as massive multiple-input multiple-output (MIMO) systems, it is beneficial to utilize low-resolution quantizers, due to cost, power, and memory constraints. In this work we study quantization of high-dimensional inputs, aiming at improving performance under resolution constraints by accounting for the system task in the quantizers design. We focus on the task of recovering a desired signal statistically related to the high-dimensional input, and analyze two quantization approaches: We first consider vector quantization, which is typically computationally infeasible, and characterize the optimal performance achievable with this approach. Next, we focus on practical systems which utilize hardware-limited scalar uniform analog-to-digital converters (ADCs), and design a task-based quantizer under this model. The resulting system accounts for the task by linearly combining the observed signal into a lower dimension prior to quantization. We then apply our proposed technique to channel estimation in massive MIMO networks. Our results demonstrate that a system utilizing low-resolution scalar ADCs can approach the optimal channel estimation performance by properly accounting for the task in the system design

Data compression with low distortion and finite blocklength

This paper considers lossy source coding of n-dimensional continuous memoryless sources with low mean-square error distortion and shows a simple, explicit approximation to the minimum source coding rate. More precisely, a nonasymptotic version of Shannon's lower bound is presented. Lattice quantizers are shown to approach that lower bound, provided that the source density is smooth enough and the distortion is low, which implies that fine multidimensional lattice coverings are nearly optimal in the rate-distortion sense even at finite n. The achievability proof technique avoids both the usual random coding argument and the simplifying assumption of the presence of a dither signal