A constructive lower bound for cardinality of codebooks capable of correcting multiple deletion and insertions

Error Correcting Codes;Deletion and Insertion Correcting Codes;Coding theory;"Concatenation of Codes, Levenshteins bound"]

Khajouei, Farzaneh ; Kiyavash ; Negar

关键词: Error Correcting Codes;    Deletion and Insertion Correcting Codes;    Coding theory;    "Concatenation of Codes, Levenshteins bound"];   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/31180/Khajouei_Farzaneh.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

The construction of the largest codebook capable of correcting multiple number of deletions and insertions is an open problem in coding theory.The efforts in the design of these codes mostly concentrate on finding the largest codebook size for a fixed number of deletions and a codeword length.In fact, most of these codebooks are designed for a specific number of deletions as few as one or two.We are interested in finding the largest codebook that can correct multiple deletion and insertion errors. Previous research focused on block codes in dealing with deletion and insertion errors.The problem of constructing the largest codebook can be converted into an independent set problem in some specific graphs.The exact solution for the maximal independent set in these graphs is equivalent to finding the largest possible codebooks capable of correcting specific number of deletions and insertions.We propose a greedy algorithm which can find a maximal solution in polynomial time in the number of vertices of the graph. Results are presented for block codes of length n and the lower bounds are proved from analyzing the greedy algorithm on these graphs.A general construction for binary block codes, capable of correcting up to s number of deletion and insertion errors, is proposed. The construction is based on the concatenation of codes with shorter blocks. The algorithm will construct an s deletion and insertion correcting code based on a given s/2-deletion insertion correcting code.The size of the codebook grows exponentially and is comparable to asymptotic lower bound of Levenshtein.The greedy algorithm combined with the concatenation method can give codebooks of larger sizes.