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A Numeral System Based Framework for Improved One-Lambda Crosstalk Avoidance Code Using Recursive Symmetry Formula

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Abstract

Crosstalk fault on the chip wires seriously jeopardizes data reliability. One of the most effective methods to reduce crosstalk fault is crosstalk fault avoidance coding (CAC) based on numeral systems. CAC methods reduce crosstalk fault by preventing certain transitions from occurring. Improved One-Lambda Coding (IOLC) demonstrates the best performance among all types of CAC methods since it shows the least delay and area occupancy overhead. However, designers of larger-width buses need a systematic framework for generating cost-effective Improved One-Lambda Codes (IOLC). Such a framework should have two distinctive features: Firstly, it should specify the number of code words in each particular width, which is referred to as cardinality. Secondly, it should provide an algorithm for producing complete and unambiguous numeral systems. In this paper, the following items have been provided to achieve these two features. 1) A recursive formula called recursive symmetry has been proposed to determine the extent of cardinality for Improved One-Lambda Coding. 2) Using the recursive symmetry formula, an algorithm has been developed to generate different numeral systems for Improved One-Lambda Coding. The evaluation results showed that sending code words through the Improved One-Lambda Coding method using our proposed algorithm improves the status of delay in the worst cases

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Abbreviations

CAC:

Crosstalk Avoidance Code

FTC:

Forbidden Transition Code

FOC:

Forbidden Overlap Code

FPC:

Forbidden Pattern Code

OLC:

One-Lambda Code

IOLC:

Improved One-Lambda Code

SOTA:

Same and Opposite Transition Avoidance

ITRS:

International Technology Roadmap for Semiconductors

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Acknowledgments

The authors would like to thank any comment and suggestion of reviewers on this article. The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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Authors and Affiliations

  1. Computer Engineering Faculty, Shahid Rajaee Teacher Training University, Tehran, Iran

    M. Taali & Z. Shirmohammadi

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  1. M. Taali
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  2. Z. Shirmohammadi
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Contributions

Z. Shirmohammadi and M. Taali collected the data and designed the experiments. Z. Shirmohammadi carried out the data analysis. Z. Shirmohammadi and M. Taali interpreted the results and wrote the manuscript.

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Correspondence to Z. Shirmohammadi.

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The author declares that there is no conflict of interests regarding the publication of this manuscript. In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancy have been completely observed by the authors.

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Taali, M., Shirmohammadi, Z. A Numeral System Based Framework for Improved One-Lambda Crosstalk Avoidance Code Using Recursive Symmetry Formula. J Electron Test 37, 395–408 (2021). https://doi.org/10.1007/s10836-021-05950-4

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