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

The Arbitrarily Varying Channel with Colored Gaussian Noise

We address the arbitrarily varying channel (AVC) with colored Gaussian noise. The work consists of three parts. First, we study the general discrete AVC with fixed parameters, where the channel depends on two state sequences, one arbitrary and the other fixed and known. This model can be viewed as a combination of the AVC and the time-varying channel. We determine both the deterministic code capacity and the random code capacity. Super-additivity is demonstrated, showing that the deterministic code capacity can be strictly larger than the weighted sum of the parametric capacities. In the secon…

有色高斯信道的识别

Identification for Colored Gaussian Channels

研究受相关噪声和符号间干扰影响的高斯信道的识别容量，证明在次线性记忆长度下码本大小仍呈超指数增长，并给出识别容量界。

Error Exponents of Typical Random Codes for the Colored Gaussian Channel

The error exponent of the typical random code is defined as the asymptotic normalized expectation of the logarithm of the probability of error, as opposed to the traditional definition of the random coding exponent as the normalized logarithm of the expectation of the probability of error with respect to a given ensemble of codes. For a certain ensemble of independent codewords, with a given power spectrum, and a generalized stochastic mismatched decoder, we characterize the error exponent the typical random codes (TRC) for the colored Gaussian channel, with emphasis on the range of low rates,…

有色噪声高斯信道容量计算的复杂度刻画

Characterization of the Complexity of Computing the Capacity of Colored Noise Gaussian Channels

本文研究带限加性有色高斯噪声信道容量及可达功率谱密度的计算复杂度，证明该问题为#P₁完全，且在FP₁≠#P₁假设下存在无法多项式时间求解的情形。

有色噪声谱图的零点

Zeros of the Spectrogram of Colored Noise

本文研究了有色噪声下STFT谱图零点的期望数量，给出精确公式与渐近行为，并提出从零点分布恢复功率谱密度的算法，验证了基于零点的检测算法在中等有色噪声下的有效性。

Approximate Message Passing with a Colored Aliasing Model for Variable Density Fourier Sampled Images

The Approximate Message Passing (AMP) algorithm efficiently reconstructs signals which have been sampled with large i.i.d. sub-Gaussian sensing matrices. Central to AMP is its "state evolution", which guarantees that the difference between the current estimate and ground truth (the "aliasing") at every iteration obeys a Gaussian distribution that can be fully characterized by a scalar. However, when Fourier coefficients of a signal with non-uniform spectral density are sampled, such as in Magnetic Resonance Imaging (MRI), the aliasing is intrinsically colored, AMP's scalar state evolution is n…

Vector Gaussian Multiple Description with Individual and Central Receivers

L multiple descriptions of a vector Gaussian source for individual and central receivers are investigated. The sum rate of the descriptions with covariance distortion measure constraints, in a positive semidefinite ordering, is exactly characterized. For two descriptions, the entire rate region is characterized. Jointly Gaussian descriptions are optimal in achieving the limiting rates. The key component of the solution is a novel information-theoretic inequality that is used to lower bound the achievable multiple description rates.

The Sum Rate of Vector Gaussian Multiple Description Coding with Tree-Structured Covariance Distortion Constraints

A single-letter lower bound on the sum rate of multiple description coding with tree-structured distortion constraints is established by generalizing Ozarow's celebrated converse argument through the introduction of auxiliary random variables that form a Markov tree. For the quadratic vector Gaussian case, this lower bound is shown to be achievable by an extended version of the El Gamal-Cover scheme, yielding a complete sum-rate characterization.

Fundamental Limits of Obfuscation for Linear Gaussian Dynamical Systems: An Information-Theoretic Approach

In this paper, we study the fundamental limits of obfuscation in terms of privacy-distortion tradeoffs for linear Gaussian dynamical systems via an information-theoretic approach. Particularly, we obtain analytical formulas that capture the fundamental privacy-distortion tradeoffs when privacy masks are to be added to the outputs of the dynamical systems, while indicating explicitly how to design the privacy masks in an optimal way: The privacy masks should be colored Gaussian with power spectra shaped specifically based upon the system and noise properties.