Rameshwar, VA and Kashyap, N (2022) Linear Runlength-Limited Subcodes of Reed-Muller Codes and Coding Schemes for Input-Constrained BMS Channels. In: 2022 IEEE Information Theory Workshop, ITW 2022, 1 - 9 November 2022, Mumbai, pp. 624-629.
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Abstract
In this work, we address the question of the largest rate of linear subcodes of Reed-Muller (RM) codes, all of whose codewords respect a runlength-limited (RLL) constraint. Our interest is in the 3. 1-RLL constraint, which mandates that every pair of successive 1s be separated by at least 3 0s. Consider any sequence fC g 1 of RM codes with increasing blocklength, whose rates approach ', in the limit as the blocklength goes to infinity. We show that for any linear 3. 1-RLL subcode, C, of the code C, it holds that the rate of C is at most ' 3 1 , in the limit as the blocklength goes to infinity. We also consider scenarios where the coordinates of the RM codes are not ordered according to the standard lexicographic ordering, and derive rate upper bounds for linear 3. 1-RLL subcodes, in those cases as well. Next, for the setting of a 3. 1-RLL input-constrained binary memoryless symmetric (BMS) channel, we devise a new coding scheme, based on cosets of RM codes. Again, in the limit of blocklength going to infinity, this code outperforms any linear subcode of an RM code, in terms of rate, for low noise regimes of the channel. © 2022 IEEE.
| Item Type: | Conference Paper |
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| Publication: | 2022 IEEE Information Theory Workshop, ITW 2022 |
| Publisher: | Institute of Electrical and Electronics Engineers Inc. |
| Additional Information: | The copyright for this article belongs to the Authors. |
| Keywords: | Block codes; Channel coding; Forward error correction, Code scheme; Code-words; Coding scheme; Memoryless; Reed Muller coding; Reed-Muller codes; Run length limiteds; Run-length limited constraints; Subcodes; Symmetric channels, C (programming language) |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 31 Jan 2023 06:31 |
| Last Modified: | 31 Jan 2023 06:31 |
| URI: | https://eprints.iisc.ac.in/id/eprint/79592 |
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