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In the source coding problem with cost constraint, a cost function is defined over the code alphabet. This can be regarded as a noiseless channel coding problem with cost constraint. In this case, we will not distinguish between the input alphabet and the output alphabet of the channel. However, we must distinguish them for a noisy channel. In the channel coding problem with cost constraint so far, the cost function is defined over the input alphabet of the noisy channel. In this paper, we define the cost function over the output alphabet of the channel. And, the cost is paid only after the received word is observed. Note that the cost is a random variable even if the codeword is fixed. We show the channel capacity with cost constraint defined over the output alphabet. Moreover, we generalize it to tolerate some decoding error and some cost overrun. Finally, we show that the cost constraint can be described on a subset of arbitrary set which may have no structure.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E105-A No.3 pp.345-352

- Publication Date
- 2022/03/01

- Publicized
- 2021/07/27

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2021TAP0002

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

- Category
- Information Theory

Mikihiko NISHIARA

Shinshu University

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Mikihiko NISHIARA, "Channel Coding with Cost Paid on Delivery" in IEICE TRANSACTIONS on Fundamentals,
vol. E105-A, no. 3, pp. 345-352, March 2022, doi: 10.1587/transfun.2021TAP0002.

Abstract: In the source coding problem with cost constraint, a cost function is defined over the code alphabet. This can be regarded as a noiseless channel coding problem with cost constraint. In this case, we will not distinguish between the input alphabet and the output alphabet of the channel. However, we must distinguish them for a noisy channel. In the channel coding problem with cost constraint so far, the cost function is defined over the input alphabet of the noisy channel. In this paper, we define the cost function over the output alphabet of the channel. And, the cost is paid only after the received word is observed. Note that the cost is a random variable even if the codeword is fixed. We show the channel capacity with cost constraint defined over the output alphabet. Moreover, we generalize it to tolerate some decoding error and some cost overrun. Finally, we show that the cost constraint can be described on a subset of arbitrary set which may have no structure.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021TAP0002/_p

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@ARTICLE{e105-a_3_345,

author={Mikihiko NISHIARA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Channel Coding with Cost Paid on Delivery},

year={2022},

volume={E105-A},

number={3},

pages={345-352},

abstract={In the source coding problem with cost constraint, a cost function is defined over the code alphabet. This can be regarded as a noiseless channel coding problem with cost constraint. In this case, we will not distinguish between the input alphabet and the output alphabet of the channel. However, we must distinguish them for a noisy channel. In the channel coding problem with cost constraint so far, the cost function is defined over the input alphabet of the noisy channel. In this paper, we define the cost function over the output alphabet of the channel. And, the cost is paid only after the received word is observed. Note that the cost is a random variable even if the codeword is fixed. We show the channel capacity with cost constraint defined over the output alphabet. Moreover, we generalize it to tolerate some decoding error and some cost overrun. Finally, we show that the cost constraint can be described on a subset of arbitrary set which may have no structure.},

keywords={},

doi={10.1587/transfun.2021TAP0002},

ISSN={1745-1337},

month={March},}

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TY - JOUR

TI - Channel Coding with Cost Paid on Delivery

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 345

EP - 352

AU - Mikihiko NISHIARA

PY - 2022

DO - 10.1587/transfun.2021TAP0002

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E105-A

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JA - IEICE TRANSACTIONS on Fundamentals

Y1 - March 2022

AB - In the source coding problem with cost constraint, a cost function is defined over the code alphabet. This can be regarded as a noiseless channel coding problem with cost constraint. In this case, we will not distinguish between the input alphabet and the output alphabet of the channel. However, we must distinguish them for a noisy channel. In the channel coding problem with cost constraint so far, the cost function is defined over the input alphabet of the noisy channel. In this paper, we define the cost function over the output alphabet of the channel. And, the cost is paid only after the received word is observed. Note that the cost is a random variable even if the codeword is fixed. We show the channel capacity with cost constraint defined over the output alphabet. Moreover, we generalize it to tolerate some decoding error and some cost overrun. Finally, we show that the cost constraint can be described on a subset of arbitrary set which may have no structure.

ER -