Asymmetric LOCO Codes: Constrained Codes for Flash Memories

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.