Innovation in Constrained Codes

Constrained coding is a somewhat nebulous term which we may define by either inclusion or exclusion. A constrained system is defined by a constrained set of “good” or “allowable” sequences to be recorded or transmitted. Constrained coding focuses on the analysis of constrained systems and the design of efficient encoders and decoders that transform arbitrary user sequences into constrained sequences. Constrained coding has extensively been used since the advent in the 1950s of digital storage and communication devices. They have found application in all hard disk, non-volatile memories, and optical discs, such as CD, DVD, and Blu-Ray Disc, and they are now projected for usage in DNA-based storage. We survey theory and practice of constrained coding, tracing the evolution of the subject from its origins in Shannon's classic 1948 paper to present-day applications in DNA-based data storage systems.