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- W4308829306 abstract "The paper considers coding schemes derived from Reed-Muller (RM) codes, for transmission over input-constrained memoryless channels. Our focus is on the $(d,infty)$-runlength limited (RLL) constraint, which mandates that any pair of successive $1$s be separated by at least $d$ $0$s. In our study, we first consider $(d,infty)$-RLL subcodes of RM codes, taking the coordinates of the RM codes to be in the standard lexicographic ordering. We show, via a simple construction, that RM codes of rate $R$ have linear $(d,infty)$-RLL subcodes of rate $Rcdot{2^{-left lceil log_2(d+1)right rceil}}$. We then show that our construction is essentially rate-optimal, by deriving an upper bound on the rates of linear $(d,infty)$-RLL subcodes of RM codes of rate $R$. Next, for the special case when $d=1$, we prove the existence of potentially non-linear $(1,infty)$-RLL subcodes that achieve a rate of $maxleft(0,R-frac38right)$. This, for $R > 3/4$, beats the $R/2$ rate obtainable from linear subcodes. We further derive upper bounds on the rates of $(1,infty)$-RLL subcodes, not necessarily linear, of a certain canonical sequence of RM codes of rate $R$. We then shift our attention to settings where the coordinates of the RM code are not ordered according to the lexicographic ordering, and derive rate upper bounds for linear $(d,infty)$-RLL subcodes in these cases as well. Finally, we present a new two-stage constrained coding scheme, again using RM codes of rate $R$, which outperforms any linear coding scheme using $(d,infty)$-RLL subcodes, for values of $R$ close to $1$." @default.
- W4308829306 created "2022-11-16" @default.
- W4308829306 creator A5059452861 @default.
- W4308829306 creator A5087839421 @default.
- W4308829306 date "2022-11-10" @default.
- W4308829306 modified "2023-10-17" @default.
- W4308829306 title "Coding Schemes Based on Reed-Muller Codes for $(d,infty)$-RLL Input-Constrained Channels" @default.
- W4308829306 doi "https://doi.org/10.48550/arxiv.2211.05513" @default.
- W4308829306 hasPublicationYear "2022" @default.
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