[논문 리뷰] Subjective Distortion: Achievability and Outer Bounds for Distortion Functions with Memory

Hamidreza Abin, Amin Gohari외 1명|arXiv (Cornell University)|2026. 01. 29.

Wireless Communication Security Techniques인용 수 0

한 줄 요약

논문은 기억을 가진 주관적 왜곡을 비율-왜곡 문제에 정의하고, 달성 가능한(내부) 경계와 외부 경계, 볼록화 및 예시 응용을 제공한다.

ABSTRACT

In some rate-distortion-type problems, the required fidelity of information is affected by past actions. As a result, the distortion function depends not only on the instantaneous distortion between a source symbol and its representation symbol, but also on past representations. In this paper, we give a formal definition of this problem and introduce both inner (achievable) and outer bounds on the rate-distortion tradeoff. We also discuss convexification of the problem, which makes it easier to find bounds. Problems of this type arise in biological information processing, as well as in recommendation engines; we provide an example applied to a simplified biological information processing problem.

연구 동기 및 목표

• Generalize rate-distortion theory to distortions that depend on past reconstructed symbols.
• Derive achievable (inner) bounds using Markov kernels and memory models.
• Derive outer bounds and discuss convexification to enable computable bounds.

제안 방법

• Define the distortion with memory as d(x_i,y_i,y_{i-1}) and frame the problem under an information-rate constraint I(M; X^n) ≤ nR.
• Provide an achievable rate expression via a Markov kernel W_{Y|X, Ŷ} and stationary distribution analysis.
• Introduce memoryless kernel specialization to obtain a computable single-letter bound R_{I2}(D).
• Discuss convexity of the solution space through the function Λ and conditions for convexity of the bounds.
• Define D_min and D_max to delineate feasibility and zero-rate regimes, and present Gaussian and binary examples.
• Offer outer bounds through relaxation and convex envelope arguments to bound the true rate-distortion function.

실험 결과

연구 질문

• RQ1 What are the fundamental rate-distortion limits when distortion depends on the current and previous decoder outputs?
• RQ2 How can we compute usable (single-letter) bounds for the subjective distortion problem?
• RQ3 When does the memory-dependent problem reduce to classical rate-distortion bounds?
• RQ4 How can convexification help in bounding R(D) for subjective distortion?
• RQ5 What are illustrative examples (binary and Gaussian) that demonstrate achievable and outer bounds?

주요 결과

• An inner bound (achievability) is obtained via a Markov kernel that generates a stationary X,Y pair under a certain distortion constraint.
• A memoryless specialization yields a computable single-letter bound R_{I2}(D) with explicit conditions for feasibility (D_min) and zero-rate regime (D_max).
• Convexity results show R(D) is non-increasing and convex in D, and under certain conditions the convex envelope matches the bound.
• Outer bounds are derived using convex envelope arguments and relaxation techniques that relax memory, providing infeasible-rate certificates when appropriate.
• The paper provides illustrative examples for binary and Gaussian sources to demonstrate the behavior of inner and outer bounds and the impact of memory in distortion.
• A practical interpretation connects subjective distortion to biological information processing and semantic/task-oriented communication contexts.