|| Minimizing the alphabet size in codes with restricted error sets
||Mira Gonen, Ariel University, Israel; Michael Langberg, State University of New-York at Buffalo, United States; Alex Sprintson, Texas A\&M University, United States|
||D2-S7-T2: Combinatorial Coding Theory
||Wednesday, 14 July, 00:00 - 00:20
||Wednesday, 14 July, 00:20 - 00:40
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In many such settings, a smaller field size is achievable than that offered by MDS and other standard codes. We establish a connection between the minimum alphabet size for this generalized setting and the combinatorial properties of a hypergraph that represents the prespecified collection of error patterns. We also show a connection between error and erasure correcting codes in this specialized setting. This allows us to establish bounds on the minimum alphabet size and show an advantage of non-linear codes over linear codes in a generalized setting. We also consider a variation of the problem which allows a small probability of decoding error and relate it to an approximate version of hypergraph coloring.