Zero-Error Capacity of Duplication Channels

• Published in: IEEE transactions on communications Vol. 67; no. 10; pp. 6735 - 6742
• Main Author: Kovacevic, Mladen
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Channel capacity; Channel models; Data storage; Data storage systems; DNA storage; duplication error; error-free communication; Errors; Monte Carlo methods; Mutation; Random numbers; Random variables; Receivers; repetition error; Reproduction (copying); sticky insertion; Storage systems; Synchronization; Synchronization error; tandem duplication; zero-error code
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2019.2931342

This paper is concerned with the problem of error-free communication over the i.i.d. duplication channel which acts on a transmitted sequence x 1 · · · x n by inserting a random number of copies of each symbol x next to the original symbol. The random variables representing the numbers of inserted copies at each position i are independent and take values in {0, 1, . . . , r}, where r is a fixed parameter. A more general model in which blocks of ℓ consecutive symbols are being duplicated, and which is inspired by DNA-based data storage systems wherein the stored molecules are subject to tandem-duplication mutations, is also analyzed. A construction of optimal codes correcting all patterns of errors of this type is described, and the zero-error capacity of the duplication channel-the largest rate at which information can be transmitted through it in an error-free manner-is determined for each ℓ and r.