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This paper presents extended-domain Golomb (XDG) code, an extension of Golomb code for sparse geometric sources as well as a generalization of extended-domain Golomb-Rice (XDGR) code, based on the idea of almost instantaneous fixed-to-variable length (AIFV) codes. Showing that the XDGR encoding can be interpreted as extended usage of the code proposed in the previous works, this paper discusses the following two facts: The proposed XDG code can be constructed as an AIFV code relating to Golomb code as XDGR code does to Rice code; XDG and Golomb codes are symmetric in the sense of relative redundancy. The proposed XDG code can be efficiently used for losslessly compressing geometric sources too sparse for the conventional Golomb and Rice codes. According to the symmetry, its relative redundancy is guaranteed to be as low as Golomb code compressing non-sparse geometric sources. Awing to this fact, the parameter of the proposed XDG code, which is more finely tunable than the conventional XDGR code, can be optimized for given inputs using the conventional techniques. Therefore, it is expected to be more useful for many coding applications that deal with geometric sources at low bit rates.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.8 pp.1033-1042

- Publication Date
- 2021/08/01

- Publicized
- 2021/02/08

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2020EAP1099

- Type of Manuscript
- PAPER

- Category
- Coding Theory

Ryosuke SUGIURA

Nippon Telegraph and Telephone Corporation

Yutaka KAMAMOTO

Nippon Telegraph and Telephone Corporation

Takehiro MORIYA

Nippon Telegraph and Telephone Corporation

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Ryosuke SUGIURA, Yutaka KAMAMOTO, Takehiro MORIYA, "Extended-Domain Golomb Code and Symmetry of Relative Redundancy" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 8, pp. 1033-1042, August 2021, doi: 10.1587/transfun.2020EAP1099.

Abstract: This paper presents extended-domain Golomb (XDG) code, an extension of Golomb code for sparse geometric sources as well as a generalization of extended-domain Golomb-Rice (XDGR) code, based on the idea of almost instantaneous fixed-to-variable length (AIFV) codes. Showing that the XDGR encoding can be interpreted as extended usage of the code proposed in the previous works, this paper discusses the following two facts: The proposed XDG code can be constructed as an AIFV code relating to Golomb code as XDGR code does to Rice code; XDG and Golomb codes are symmetric in the sense of relative redundancy. The proposed XDG code can be efficiently used for losslessly compressing geometric sources too sparse for the conventional Golomb and Rice codes. According to the symmetry, its relative redundancy is guaranteed to be as low as Golomb code compressing non-sparse geometric sources. Awing to this fact, the parameter of the proposed XDG code, which is more finely tunable than the conventional XDGR code, can be optimized for given inputs using the conventional techniques. Therefore, it is expected to be more useful for many coding applications that deal with geometric sources at low bit rates.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020EAP1099/_p

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@ARTICLE{e104-a_8_1033,

author={Ryosuke SUGIURA, Yutaka KAMAMOTO, Takehiro MORIYA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Extended-Domain Golomb Code and Symmetry of Relative Redundancy},

year={2021},

volume={E104-A},

number={8},

pages={1033-1042},

abstract={This paper presents extended-domain Golomb (XDG) code, an extension of Golomb code for sparse geometric sources as well as a generalization of extended-domain Golomb-Rice (XDGR) code, based on the idea of almost instantaneous fixed-to-variable length (AIFV) codes. Showing that the XDGR encoding can be interpreted as extended usage of the code proposed in the previous works, this paper discusses the following two facts: The proposed XDG code can be constructed as an AIFV code relating to Golomb code as XDGR code does to Rice code; XDG and Golomb codes are symmetric in the sense of relative redundancy. The proposed XDG code can be efficiently used for losslessly compressing geometric sources too sparse for the conventional Golomb and Rice codes. According to the symmetry, its relative redundancy is guaranteed to be as low as Golomb code compressing non-sparse geometric sources. Awing to this fact, the parameter of the proposed XDG code, which is more finely tunable than the conventional XDGR code, can be optimized for given inputs using the conventional techniques. Therefore, it is expected to be more useful for many coding applications that deal with geometric sources at low bit rates.},

keywords={},

doi={10.1587/transfun.2020EAP1099},

ISSN={1745-1337},

month={August},}

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TY - JOUR

TI - Extended-Domain Golomb Code and Symmetry of Relative Redundancy

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 1033

EP - 1042

AU - Ryosuke SUGIURA

AU - Yutaka KAMAMOTO

AU - Takehiro MORIYA

PY - 2021

DO - 10.1587/transfun.2020EAP1099

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E104-A

IS - 8

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - August 2021

AB - This paper presents extended-domain Golomb (XDG) code, an extension of Golomb code for sparse geometric sources as well as a generalization of extended-domain Golomb-Rice (XDGR) code, based on the idea of almost instantaneous fixed-to-variable length (AIFV) codes. Showing that the XDGR encoding can be interpreted as extended usage of the code proposed in the previous works, this paper discusses the following two facts: The proposed XDG code can be constructed as an AIFV code relating to Golomb code as XDGR code does to Rice code; XDG and Golomb codes are symmetric in the sense of relative redundancy. The proposed XDG code can be efficiently used for losslessly compressing geometric sources too sparse for the conventional Golomb and Rice codes. According to the symmetry, its relative redundancy is guaranteed to be as low as Golomb code compressing non-sparse geometric sources. Awing to this fact, the parameter of the proposed XDG code, which is more finely tunable than the conventional XDGR code, can be optimized for given inputs using the conventional techniques. Therefore, it is expected to be more useful for many coding applications that deal with geometric sources at low bit rates.

ER -