タイトル：Asymptotic Behavior and Typicality Properties of Runlength-Limited Sequences
著者名 : Mladen Kovačević; Dejan Vukobratovi
ジャーナルIEEE Transactions on Information Theory
DOI : https://doi.org/10.1109/TIT.2021.3134871
Abstract : This paper studies properties of binary runlength-limited sequences with additional constraints on their Hamming weight and/or their number of runs of identical symbols. An algebraic and a probabilistic (entropic) characterization of the exponential growth rate of the number of such sequences, i.e., their information capacity, are obtained by using the methods of multivariate analytic combinatorics, and properties of the capacity as a function of its parameters are stated. The second-order term in the asymptotic expansion of the rate of these sequences is also given, and the typical values of the relevant quantities are derived. Several applications of the results are illustrated, including bounds on codes for weight-preserving and run-preserving channels (e.g., the run-preserving insertion-deletion channel), a sphere-packing bound for channels with sparse error patterns, and the asymptotics of constant-weight sub-block constrained sequences. In addition, the asymptotics of a closely related notion—q-ary sequences with fixed Manhattan weight—is briefly discussed, and an application in coding for molecular timing channels is illustrated.
タイトル：A Quaternary Code Correcting a Burst of at Most Two Deletion or Insertion Errors in DNA Storage
著者名 : Thi-Huong Khuat; Sunghwan Kim
号数 : Volume 23 Issue 12
DOI : https://doi.org/10.3390/e23121592
Abstract : Due to the properties of DNA data storage, the errors that occur in DNA strands make error correction an important and challenging task. In this paper, a new code design of quaternary code suitable for DNA storage is proposed to correct at most two consecutive deletion or insertion errors. The decoding algorithms of the proposed codes are also presented when one and two deletion or insertion errors occur, and it is proved that the proposed code can correct at most two consecutive errors. Moreover, the lower and upper bounds on the cardinality of the proposed quaternary codes are also evaluated, then the redundancy of the proposed code is provided as roughly 2log48n.