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Abstract

Coding techniques are used in communication systems to increase the efficiency of the channel. Not only is coding equipment being used in point-to-point communication channels, but coding methods are also used in digital recording devices such as sophisticated computer disk files and numerous domestic electronics such as stationary- and rotary-head digital audio tape recorders, the Compact Disc, and floppy disk drives. Since the early 1970s, coding methods based on runlength-limited sequences have played a key role for increasing the storage capacity of magnetic and optical disks or tapes. A detailed description is furnished of the limiting properties of runlength-limited sequences, and a comprehensive review is given of the practical aspects involved in the translation of arbitrary data into runlength-limited sequences.
... Below we discuss properties of Construction I-based codes for special cases of and t. 1) Case t = − 1: The ( , t = − 1) constraint is in the data storage world [16] also known as a minimum runlength constraint, or d-constraint, where d = t denotes the minimum zero runlength. Freiman and Wyner [7] presented maximal block codes whose codewords start with at least t one's; only n − t bits of the codeword require (de)coding. ...
... 2) Case t = 1: Codes with a maximum runlength of 0's, or k-constraint, where k denotes the maximum zero runlength, have found widespread application in data storage devices [16]. Note that an ( = k + 1, t = 1)-constrained sequence can be obtained by inverting the binary symbols of a k-constrained sequence. ...
... For the case = 4 and t = 2, using (3), (16), and (17), we find A 4,2 ≈ 0.6636 and λ ≈ 1.7143, see Section II, so that η ≈ 1 − 0.76/n. ...
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Energy-harvesting sliding-window constrained block codes guarantee that within any prescribed window of ℓ consecutive bits the constrained sequence has at least t, t≥1, 1’s. Prior art code design methods build upon the finite-state machine description of the (ℓ,t) constraint, but as the number of states equals ℓ choose t, a code design becomes prohibitively complex for mounting ℓ and t. We present a new block code construction that circumvents the enumeration of codewords using a finite-state description of the (ℓ,t)-constraint. The codewords of the block code are encoded and decoded using a single look-up table. For (ℓ=4,t=2), the new block codes are maximal, that is, they have the largest possible number of codewords for its parameters.
... Figure 2 shows a state transition graph that represents the constraint. This constraint is a special case of the ( , )-RLL constraint, which admits only binary sequences with at least and at most 0s between successive 1s (see [3] for examples of ( , )-RLL codes used in practice). input sequences that respect the ( , ∞)-RLL constraint, passed through the classical BMS channel, which is a special case of the discrete memoryless channel (DMC), introduced by Shannon in [4]. ...
... This constraint is a special case of the ( , )-RLL constraint, which admits only binary sequences with at least and at most 0s between successive 1s. Reference [3] includes examples of ( , )-RLL codes used in practice in magnetic storage and recording. The system model under investigation in this paper considers input sequences that respect the ( , ∞)-RLL constraint, passed through the classical BMS channel, which is a special case of the discrete memoryless channel (DMC), introduced by Shannon in [4]. ...
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This paper considers the input-constrained binary memoryless symmetric (BMS) channel, without feedback. The channel input sequence respects the $(d,\infty)$-runlength limited (RLL) constraint, which mandates that any pair of successive $1$s be separated by at least $d$ $0$s. 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 $(d,\infty)$-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 $C\cdot{2^{-\left \lceil \log_2(d+1)\right \rceil}}$, where $C$ is the capacity of the BMS channel. Finally, we also introduce techniques for upper bounding the rate of any $(1,\infty)$-RLL subcode of a specific capacity-achieving sequence of RM codes.
... One-dimensional (1D) run-length limited (RLL) code was previously proposed for magnetic and optical recording systems [4][5][6] to specify the minimum and maximum run-length of bit 1's that may occur in a recorded data sequence. In practice, the RLL code is normally defined by two parameters that are d and k, where the parameter d is used for controlling the highest transition frequency that means it can avoid the ISI effect, while the parameter k is used to ensure that the transition of the 978-1-7281-6486-1/20/$31.00 ©2020 IEEE recorded bit data has properly appeared, which can help the synchronization process to precisely recover the sampled data sequence [7]. ...
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