Two-dimensional RC/SW constrained codes: bounded weight and almost balanced weight
In this work, we study two types of constraints on two-dimensional binary arrays. Given p\in [0,1],\in [0,1/2] , we study 1) the p -bounded constraint: a binary vector of size n is said to be p -bounded if its weight is at most pn , and 2) the -balanced constraint: a binary vector of size n is said...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2023
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| Online Access: | https://hdl.handle.net/10356/170742 |
| _version_ | 1811688153092718592 |
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| author | Nguyen, Tuan Thanh Cai, Kui Kiah, Han Mao Immink, Kees A. Schouhamer Chee, Yeow Meng |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Nguyen, Tuan Thanh Cai, Kui Kiah, Han Mao Immink, Kees A. Schouhamer Chee, Yeow Meng |
| author_sort | Nguyen, Tuan Thanh |
| collection | NTU |
| description | In this work, we study two types of constraints on two-dimensional binary arrays. Given p\in [0,1],\in [0,1/2] , we study 1) the p -bounded constraint: a binary vector of size n is said to be p -bounded if its weight is at most pn , and 2) the -balanced constraint: a binary vector of size n is said to be -balanced if its weight is within big [(1/2-)n, (1/2+)n\big]. Such constraints are crucial in several data storage systems, those regard the information data as two-dimensional (2D) instead of one-dimensional (1D), such as the crossbar resistive memory arrays and the holographic data storage. In this work, efficient encoding/decoding algorithms are presented for binary arrays so that the weight constraint (either p -bounded constraint or -balanced constraint) is enforced over every row and every column, regarded as 2D row-column (RC) constrained codes; or over every window (where each window refers to as a subarray consisting of consecutive rows and consecutive columns), regarded as 2D sliding-window (SW) constrained codes. While low-complexity designs have been proposed in the literature, mostly focusing on 2D RC constrained codes where p=1/2 and =0 , this work provides efficient coding methods that work for both 2D RC constrained codes and 2D SW constrained codes, and more importantly, the methods are applicable for arbitrary values of p and. Furthermore, for certain values of p and we show that, for sufficiently large array size, there exists linear-time encoding/decoding algorithm that incurs at most one redundant bit. |
| first_indexed | 2024-10-01T05:27:40Z |
| format | Journal Article |
| id | ntu-10356/170742 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:27:40Z |
| publishDate | 2023 |
| record_format | dspace |
| spelling | ntu-10356/1707422023-10-02T01:38:03Z Two-dimensional RC/SW constrained codes: bounded weight and almost balanced weight Nguyen, Tuan Thanh Cai, Kui Kiah, Han Mao Immink, Kees A. Schouhamer Chee, Yeow Meng School of Physical and Mathematical Sciences Science::Mathematics Two-Dimensional Constrained Codes Sliding-Window Constrained Codes In this work, we study two types of constraints on two-dimensional binary arrays. Given p\in [0,1],\in [0,1/2] , we study 1) the p -bounded constraint: a binary vector of size n is said to be p -bounded if its weight is at most pn , and 2) the -balanced constraint: a binary vector of size n is said to be -balanced if its weight is within big [(1/2-)n, (1/2+)n\big]. Such constraints are crucial in several data storage systems, those regard the information data as two-dimensional (2D) instead of one-dimensional (1D), such as the crossbar resistive memory arrays and the holographic data storage. In this work, efficient encoding/decoding algorithms are presented for binary arrays so that the weight constraint (either p -bounded constraint or -balanced constraint) is enforced over every row and every column, regarded as 2D row-column (RC) constrained codes; or over every window (where each window refers to as a subarray consisting of consecutive rows and consecutive columns), regarded as 2D sliding-window (SW) constrained codes. While low-complexity designs have been proposed in the literature, mostly focusing on 2D RC constrained codes where p=1/2 and =0 , this work provides efficient coding methods that work for both 2D RC constrained codes and 2D SW constrained codes, and more importantly, the methods are applicable for arbitrary values of p and. Furthermore, for certain values of p and we show that, for sufficiently large array size, there exists linear-time encoding/decoding algorithm that incurs at most one redundant bit. Ministry of Education (MOE) The work of Tuan Thanh Nguyen and Kui Cai was supported by the Singapore Ministry of Education Academic Research Funds Tier 2 under Grant MOE2019-T2-2-123 and Grant T2EP50221-0036. The work of Han Mao Kiah was supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 Award under Grant MOE-T2EP20121-0007. 2023-10-02T01:38:03Z 2023-10-02T01:38:03Z 2023 Journal Article Nguyen, T. T., Cai, K., Kiah, H. M., Immink, K. A. S. & Chee, Y. M. (2023). Two-dimensional RC/SW constrained codes: bounded weight and almost balanced weight. IEEE Transactions On Information Theory, 69(8), 4961-4976. https://dx.doi.org/10.1109/TIT.2023.3244979 0018-9448 https://hdl.handle.net/10356/170742 10.1109/TIT.2023.3244979 2-s2.0-85149397420 8 69 4961 4976 en MOE-T2EP20121-0007 IEEE Transactions on Information Theory © 2023 IEEE. All rights reserved. |
| spellingShingle | Science::Mathematics Two-Dimensional Constrained Codes Sliding-Window Constrained Codes Nguyen, Tuan Thanh Cai, Kui Kiah, Han Mao Immink, Kees A. Schouhamer Chee, Yeow Meng Two-dimensional RC/SW constrained codes: bounded weight and almost balanced weight |
| title | Two-dimensional RC/SW constrained codes: bounded weight and almost balanced weight |
| title_full | Two-dimensional RC/SW constrained codes: bounded weight and almost balanced weight |
| title_fullStr | Two-dimensional RC/SW constrained codes: bounded weight and almost balanced weight |
| title_full_unstemmed | Two-dimensional RC/SW constrained codes: bounded weight and almost balanced weight |
| title_short | Two-dimensional RC/SW constrained codes: bounded weight and almost balanced weight |
| title_sort | two dimensional rc sw constrained codes bounded weight and almost balanced weight |
| topic | Science::Mathematics Two-Dimensional Constrained Codes Sliding-Window Constrained Codes |
| url | https://hdl.handle.net/10356/170742 |
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