In data storage and data transmission, certain patterns are more likely to be
subject to error when written (transmitted) onto the media. In magnetic
recording systems with binary data and bipolar non-return-to-zero signaling,
patterns that have insufficient separation between consecutive transitions
exacerbate inter-symbol interference. Constrained codes are used to eliminate
such error-prone patterns. A recent example is a new family of
capacity-achieving constrained codes, named lexicographically-ordered
constrained codes (LOCO codes). LOCO codes are symmetric, that is, the set of
forbidden patterns is closed under taking pattern complements. LOCO codes are
suboptimal in terms of rate when used in Flash devices where block erasure is
employed since the complement of an error-prone pattern is not detrimental in
these devices. This paper introduces asymmetric LOCO codes (A-LOCO codes),
which are lexicographically-ordered constrained codes that forbid only those
patterns that are detrimental for Flash performance. A-LOCO codes are also
capacity-achieving, and at finite-lengths, they offer higher rates than the
available state-of-the-art constrained codes designed for the same goal. The
mapping-demapping between the index and the codeword in A-LOCO codes allows
low-complexity encoding and decoding algorithms that are simpler than their
LOCO counterparts.Comment: 9 pages (double column), 0 figures, accepted at the Annual Allerton
Conference on Communication, Control, and Computin