Maximum Run-length Constraints Research Articles

Weakly mutually uncorrelated codes with maximum run length constraint for DNA storage

DNA storage systems have begun to attract considerable attention as next-generation storage technologies due to their high densities and longevity. However, efficient primer design for random-access in synthesized DNA strands is still an issue that needs to be solved. Although previous studies have explored various constraints for primer design in DNA storage systems, there is no attention paid to the combination of weakly mutually uncorrelated codes with the maximum run length constraint. In this paper, we first propose a code design by combining weakly mutually uncorrelated codes with the maximum run length constraint. Moreover, we also explore the weakly mutually uncorrelated codes to satisfy combinations of maximum run length constraint with more constraints such as being almost-balanced and having large Hamming distance, which are also efficient constraints for random-access in DNA storage systems. To guarantee that the proposed codes can be adapted to primer design with variable length, we present modified code construction methods to achieve different lengths of the code. Then, we provide an analysis of the size of the proposed codes, which indicates the capacity to support primer design. Finally, we compare the codes with those of previous works to show that the proposed codes can always guarantee the maximum run length constraint, which is helpful for random-access for DNA storage.

Design of Nonbinary Error Correction Codes With a Maximum Run-Length Constraint to Correct a Single Insertion or Deletion Error for DNA Storage

Due to the advantages of high information densities and longevity, DNA storage systems have begun to attract a lot of attention. However, common obstacles to DNA storage are caused by insertion, deletion, and substitution errors occurring in DNA synthesis and sequencing. In this paper, we first explain a method to convert binary data into general maximum run-length $r$ sequences with specific length construction, which can be used as the message sequence of our proposed code. Then, we propose a new single insertion/deletion nonbinary systematic error correction code and its corresponding encoding algorithm. For the proposed code, we design the fixed maximum run-length $r$ in the parity sequence of the proposed code to be three. Additionally, the last parity symbol and the first message symbol are always different. Hence, the overall maximum run-length $r$ of the output codeword is guaranteed to be three when the maximum run-length of the message sequence is three. Finally, we determine the feasibility of the proposed encoding algorithm, verify successful decoding when a single insertion/deletion error occurs in the codeword, and present the comparison results with relevant works.

Highly efficient run-length-limited (3, 7) code

A highly efficient run-length-limited code for high density storage systems is presented. The minimum and maximum run-length constraints are d = 3 and k = 7, respectively. The code rate is 2/5, and the efficiency of the code is 98.6%.

Run-length limited (3, 11) code for high density optical storage systems

A run-length limited (RLL) code for high density optical storage systems is proposed. The minimum and maximum run-length constraints are d = 3 and k = 11, respectively. The code rate is 2/5, and the resulting density ratio is 1.6, which is larger than that of eight-to-fourteen (EFM) and EFMPlus codes.

4-ary (1,2) run-length limited code for optical storage channels

A 4-ary run-length limited (RLL) code with minimum run-length constraint d = 1 and maximum run-length constraint k = 2 is presented. The proposed code can be represented by a finite state diagram with two states. This is the lowest number of states necessary for representing the code yet presented. A simple docoding rule for the code is also introduced and a scheme for reducing the DC content of the coded sequence in the sense of multilevel running digital sum (RDS) is discussed.

Combined source/channel coding and a new coding scheme for data storage systems

Research has tended to concentrate on the separate areas of source coding (for data compression) and channel coding (for data storage), this paper proposes data compression codes that combine source and channel codings under minimum and maximum run-length constraints for storage channels. The encoding methods, decoding procedure, and average codeword lengths of the proposed codes are presented. Also, a new encoding scheme for data storage systems, one which employs the error control coding and modulation coding to make full use of the combined source/channel codes, is suggested. The suggested encoding scheme, together with the combined source/channel codes, enables the storing of more data within a given size storage system.

Antiwhistle codes

Besides timing recovery and automatic gain control, data receivers often perform adaptive slope or bandwidth control. This note presents a set of maximum run-length constraints that facilitates the joint accomplishment of these three tasks. Simple polarity-bit codes that introduce these constraints are described. The study is of particular interest in digital magnetic recording.

Combined modulation and error correction codes for storage channels

Multitrack codes that have recently been proposed for the magnetic storage channel promise larger capacities than conventional run-length limited (RLL) single-track codes. This paper proposes an approach that combines modulation and error-correcting capabilities with resilience to intertrack interference (ITI) in the magnetic storage channel with constraints on the minimum run-length for each track, in conjunction with the minimum run-length constraint between tracks and the maximum run-length constraint satisfied by at least one track. Comparison is made with previously proposed approaches.

Multilevel run-length-limited modulation codes for optical disk recording system

A generalization of the run-length-limited (RLL) code has been studied for multilevel recording systems where more than one kind of mark is used to record information. The run-length constraints have been generalized to include the spacing in addition to the minimum and maximum run-length constraints. The ratic of the minimum run length to the detection window has become arbitrarily adjustable. This provides the flexibility to design the modulation codes which match with the resolution and jitter characteristics of the recording system. The method of the calculus of variations has been applied to the asymptotic behavior of the amount of information stored in a sufficiently long code sequence. The formulation has been obtained for the code characteristics, which include the maximum density ratio, the maximum amount of information contained in the detection window, the average rate of appearance for individual run lengths, etc. The effect of the multilevel recording scheme depends on the number of the levels, the minimum and maximum run length, and the spacing. The optimum selection of these parameters can realize a large recording capacity close to the intrinsic potential of the multilevel recording system.

Soft decision decoding techniques for a class of runlength-limited error control codes

Two soft decision decoding algorithms for a new class of runlength-limited error control codes with maximum runlength constraints 2, 6 and 14 are presented. Software simulation results for illustrative codes of block length 16 and 64 provide a comparison with the general soft decision decoders proposed by Chase (1972).

Maximum likelihood decoding of RLL-FEC array codes on partial response channels

A technique for performing maximum likelihood decoding (MLD) of RLL-FEC array codes on partial response channels is introduced. Attention is focused on the (1-D) channel and a (16, 9, 4) code having a maximum runlength constraint of 6, however, the idea is applicable to all partial response channels and RLL-FEC array codes.

Optimization of low-frequency properties of eight-to-fourteen modulation

A description is given of the eight to fourteen modulation system (EFM) designed for the Compact Disc Digital Audio System with optical read-out. EFM combines high information density and immunity to tolerances in the light path with low power at the low-frequency end of the modulation bit stream spectrum. In this modulation scheme, blocks of eight data input bits are transformed into fourteen channel bits, which follow certain minimum and maximum run-length constraints by using a code book. To prevent violation of the minimum and maximum run-length constraints a certain number of merging bits are needed to concatenate the blocks. There are cases where the merging bits are not uniquely determined by the concatenation rules. This freedom of choice thus created is used for minimizing the power of the modulated bit sequence at low frequencies. The paper presents the results of algorithms that were used to minimize this low frequency content.