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The achievability part of the rate-distortion theorem is proved by showing existence of good codes. For i.i.d. sources, two methods showing existence are known; random coding and non-random coding. For general sources, however, no proof in which good codes are constructed with non-random coding is found. In this paper, with a non-random method of code construction, we prove the achievability part of the rate-distortion theorem for general sources. Moreover, we also prove a stochastic variation of the rate-distortion theorem with the same method.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E107-A No.3 pp.404-408

- Publication Date
- 2024/03/01

- Publicized
- 2023/10/10

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2023TAP0009

- Type of Manuscript
- Special Section PAPER (Special Section on Information Theory and Its Applications)

- Category
- Source Coding and Data Compression

Mikihiko NISHIARA

Shinshu University

Yuki ITO

Shinshu University

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Mikihiko NISHIARA, Yuki ITO, "Proof of Achievability Part of Rate-Distortion Theorem without Random Coding" in IEICE TRANSACTIONS on Fundamentals,
vol. E107-A, no. 3, pp. 404-408, March 2024, doi: 10.1587/transfun.2023TAP0009.

Abstract: The achievability part of the rate-distortion theorem is proved by showing existence of good codes. For i.i.d. sources, two methods showing existence are known; random coding and non-random coding. For general sources, however, no proof in which good codes are constructed with non-random coding is found. In this paper, with a non-random method of code construction, we prove the achievability part of the rate-distortion theorem for general sources. Moreover, we also prove a stochastic variation of the rate-distortion theorem with the same method.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2023TAP0009/_p

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@ARTICLE{e107-a_3_404,

author={Mikihiko NISHIARA, Yuki ITO, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Proof of Achievability Part of Rate-Distortion Theorem without Random Coding},

year={2024},

volume={E107-A},

number={3},

pages={404-408},

abstract={The achievability part of the rate-distortion theorem is proved by showing existence of good codes. For i.i.d. sources, two methods showing existence are known; random coding and non-random coding. For general sources, however, no proof in which good codes are constructed with non-random coding is found. In this paper, with a non-random method of code construction, we prove the achievability part of the rate-distortion theorem for general sources. Moreover, we also prove a stochastic variation of the rate-distortion theorem with the same method.},

keywords={},

doi={10.1587/transfun.2023TAP0009},

ISSN={1745-1337},

month={March},}

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TY - JOUR

TI - Proof of Achievability Part of Rate-Distortion Theorem without Random Coding

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 404

EP - 408

AU - Mikihiko NISHIARA

AU - Yuki ITO

PY - 2024

DO - 10.1587/transfun.2023TAP0009

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E107-A

IS - 3

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - March 2024

AB - The achievability part of the rate-distortion theorem is proved by showing existence of good codes. For i.i.d. sources, two methods showing existence are known; random coding and non-random coding. For general sources, however, no proof in which good codes are constructed with non-random coding is found. In this paper, with a non-random method of code construction, we prove the achievability part of the rate-distortion theorem for general sources. Moreover, we also prove a stochastic variation of the rate-distortion theorem with the same method.

ER -