On the Performance of Reed-Muller Codes Over (d, ∞)-RLL Input-Constrained BMS Channels

Arvind Rameshwar, V and Kashyap, N (2022) On the Performance of Reed-Muller Codes Over (d, ∞)-RLL Input-Constrained BMS Channels. In: 2022 IEEE International Symposium on Information Theory, ISIT 2022, 26 June - 1 July 2022, Espoo, pp. 1755-1760.

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Abstract

This paper considers the input-constrained binary memoryless symmetric (BMS) channel, without feedback. The channel input sequence respects the (d, ∞)-runlength limited (RLL) constraint, which mandates that any pair of successive 1s be separated by at least d 0s. We consider the problem of designing explicit codes for such channels. In particular, we work with the Reed-Muller (RM) family of codes, which were shown by Reeves and Pfister (2021) to achieve the capacity of any unconstrained BMS channel, under bit-MAP decoding. We show that it is possible to pick (d, ∞)-RLL subcodes of a capacity-achieving (over the unconstrained BMS channel) sequence of RM codes such that the subcodes achieve, under bit-MAP decoding, rates of C · 2 - ⌈ log 2(d + 1) ⌉, where C is the capacity of the BMS channel. Finally, we also introduce techniques for upper bounding the rate of any (1, ∞)-RLL subcode of a specific capacity-achieving sequence of RM codes.

Item Type:	Conference Paper
Publication:	IEEE International Symposium on Information Theory - Proceedings
Publisher:	Institute of Electrical and Electronics Engineers Inc.
Additional Information:	The copyright for this article belongs to Institute of Electrical and Electronics Engineers Inc.
Keywords:	Block codes; C (programming language); Forward error correction, Channel inputs; Input sequence; MAP decoding; Memoryless; Performance; Reed-Muller codes; Run length limiteds; Run-length limited constraints; Subcodes; Symmetric channels, Decoding
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	15 Sep 2022 10:05
Last Modified:	15 Sep 2022 10:05
URI:	https://eprints.iisc.ac.in/id/eprint/76478

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