On Bi-Modal Constrained Coding

• Published in: IEEE transactions on information theory Vol. 67; no. 3; pp. 1609 - 1621
• Main Authors: Roth, Ron M., Siegel, Paul H.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-03-2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Approximate eigenvectors; bi-modal encoders; Coders; Coding; constrained codes; Constraints; Decoding; Delays; Encoding; Labeling; multi-modal encoders; Optical disks; parity-preserving encoders; Tagging; Windows
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2020.3042958

Bi-modal (respectively, multi-modal) constrained coding refers to an encoding model whereby a user input block can be mapped to two (respectively, multiple) codewords. In current storage applications, such as optical disks, multi-modal coding allows to achieve DC control, in addition to satisfying the runlength limited (RLL) constraint specified by the recording channel. In this work, a study is initiated on bi-modal fixed-length constrained encoders. Necessary and sufficient conditions are presented for the existence of such encoders for a given constraint. It is also shown that under somewhat stronger conditions, one can guarantee a bi-modal encoder with finite decoding delay.