On the Second-Order Achievabilities of Indirect Quadratic Lossy Source Coding
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| Format: | Preprint |
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2024
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| _version_ | 1866916436684832768 |
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| author | Yang, Huiyuan Yuan, Xiaojun |
| author_facet | Yang, Huiyuan Yuan, Xiaojun |
| contents | This paper studies the second-order achievabilities of indirect quadratic lossy source coding for a specific class of source models, where the term "quadratic" denotes that the reconstruction fidelity of the hidden source is quantified by a squared error distortion measure. Specifically, it is assumed that the hidden source $S$ can be expressed as $S = φ(X) + W$, where $X$ is the observable source with alphabet $\mathcal{X}$, $φ(\cdot)$ is a deterministic function, and $W$ is a random variable independent of $X$, satisfying $\mathbb{E}[W] = 0$, $\mathbb{E}[W^2] > 0$, $\mathbb{E}[W^3] = 0$, and $\mathbb{E}[W^6] < \infty$. Additionally, both the set $\{φ(x):\ x \in \mathcal{X} \}$ and the reconstruction alphabet for $S$ are assumed to be bounded. Under the above settings, a second-order achievability bound is established using techniques based on distortion-tilted information. This result is then generalized to the case of indirect quadratic lossy source coding with observed source reconstruction, where reconstruction is required for both the hidden source $S$ and the observable source $X$, and the distortion measure for $X$ is not necessarily quadratic. These obtained bounds are consistent in form with their finite-alphabet counterparts, which have been proven to be second-order tight. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_08110 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Second-Order Achievabilities of Indirect Quadratic Lossy Source Coding Yang, Huiyuan Yuan, Xiaojun Information Theory This paper studies the second-order achievabilities of indirect quadratic lossy source coding for a specific class of source models, where the term "quadratic" denotes that the reconstruction fidelity of the hidden source is quantified by a squared error distortion measure. Specifically, it is assumed that the hidden source $S$ can be expressed as $S = φ(X) + W$, where $X$ is the observable source with alphabet $\mathcal{X}$, $φ(\cdot)$ is a deterministic function, and $W$ is a random variable independent of $X$, satisfying $\mathbb{E}[W] = 0$, $\mathbb{E}[W^2] > 0$, $\mathbb{E}[W^3] = 0$, and $\mathbb{E}[W^6] < \infty$. Additionally, both the set $\{φ(x):\ x \in \mathcal{X} \}$ and the reconstruction alphabet for $S$ are assumed to be bounded. Under the above settings, a second-order achievability bound is established using techniques based on distortion-tilted information. This result is then generalized to the case of indirect quadratic lossy source coding with observed source reconstruction, where reconstruction is required for both the hidden source $S$ and the observable source $X$, and the distortion measure for $X$ is not necessarily quadratic. These obtained bounds are consistent in form with their finite-alphabet counterparts, which have been proven to be second-order tight. |
| title | On the Second-Order Achievabilities of Indirect Quadratic Lossy Source Coding |
| topic | Information Theory |
| url | https://arxiv.org/abs/2410.08110 |