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

Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms

It is well known that Shannon's rate-distortion function (RDF) in the colored quadratic Gaussian (QG) case can be parametrized via a single Lagrangian variable (the "water level" in the reverse water filling solution). In this work, we show that the symmetric colored QG multiple-description (MD) RDF in the case of two descriptions can be parametrized in the spectral domain via two Lagrangian variables, which control the trade-off between the side distortion, the central distortion, and the coding rate. This spectral-domain analysis is complemented by a time-domain scheme-design approach: we show that the symmetric colored QG MD RDF can be achieved by combining ideas of delta-sigma modulation and differential pulse-code modulation. Specifically, two source prediction loops, one for each description, are embedded within a common noise shaping loop, whose parameters are explicitly found from the spectral-domain characterization.Comment: Accepted for publications in the IEEE Transactions on Information Theory. Title have been shortened, abstract clarified, and paper significantly restructure

Multi Terminal Probabilistic Compressed Sensing

In this paper, the `Approximate Message Passing' (AMP) algorithm, initially developed for compressed sensing of signals under i.i.d. Gaussian measurement matrices, has been extended to a multi-terminal setting (MAMP algorithm). It has been shown that similar to its single terminal counterpart, the behavior of MAMP algorithm is fully characterized by a `State Evolution' (SE) equation for large block-lengths. This equation has been used to obtain the rate-distortion curve of a multi-terminal memoryless source. It is observed that by spatially coupling the measurement matrices, the rate-distortion curve of MAMP algorithm undergoes a phase transition, where the measurement rate region corresponding to a low distortion (approximately zero distortion) regime is fully characterized by the joint and conditional Renyi information dimension (RID) of the multi-terminal source. This measurement rate region is very similar to the rate region of the Slepian-Wolf distributed source coding problem where the RID plays a role similar to the discrete entropy. Simulations have been done to investigate the empirical behavior of MAMP algorithm. It is observed that simulation results match very well with predictions of SE equation for reasonably large block-lengths.Comment: 11 pages, 13 figures. arXiv admin note: text overlap with arXiv:1112.0708 by other author

An evaluation of intrusive instrumental intelligibility metrics

Instrumental intelligibility metrics are commonly used as an alternative to listening tests. This paper evaluates 12 monaural intrusive intelligibility metrics: SII, HEGP, CSII, HASPI, NCM, QSTI, STOI, ESTOI, MIKNN, SIMI, SIIB, and $\text{sEPSM}^\text{corr}$. In addition, this paper investigates the ability of intelligibility metrics to generalize to new types of distortions and analyzes why the top performing metrics have high performance. The intelligibility data were obtained from 11 listening tests described in the literature. The stimuli included Dutch, Danish, and English speech that was distorted by additive noise, reverberation, competing talkers, pre-processing enhancement, and post-processing enhancement. SIIB and HASPI had the highest performance achieving a correlation with listening test scores on average of $\rho=0.92$ and $\rho=0.89$, respectively. The high performance of SIIB may, in part, be the result of SIIBs developers having access to all the intelligibility data considered in the evaluation. The results show that intelligibility metrics tend to perform poorly on data sets that were not used during their development. By modifying the original implementations of SIIB and STOI, the advantage of reducing statistical dependencies between input features is demonstrated. Additionally, the paper presents a new version of SIIB called $\text{SIIB}^\text{Gauss}$, which has similar performance to SIIB and HASPI, but takes less time to compute by two orders of magnitude.Comment: Published in IEEE/ACM Transactions on Audio, Speech, and Language Processing, 201