Duplication-correcting codes

Abstract

In this work, we propose constructions that correct duplications of multiple consecutive symbols. These errors are known as tandem duplications, where a sequence of symbols is repeated; respectively as palindromic duplications, where a sequence is repeated in reversed order. We compare the redundancies of these constructions with code size upper bounds that are obtained from sphere packing arguments. Proving that an upper bound on the code cardinality for tandem deletions is also an upper bound for inserting tandem duplications, we derive the bounds based on this special tandem deletion error as this results in tighter bounds. Our upper bounds on the cardinality directly imply lower bounds on the redundancy which we compare with the redundancy of the best known construction correcting arbitrary burst insertions.Our results indicate that the correction of palindromic duplications requires more redundancy than the correction of tandem duplications and both significantly less than arbitrary burst insertions.

Asymptotically Optimal Codes Correcting Fixed-Length Duplication Errors in DNA Storage Systems

“…However, constructions of optimal codes in the ℓ 1 metric for general parameters are not known at this point, and hence no estimate of the cardinality of the resulting duplication-correcting codes was given in [5]. An explicit construction of codes for the special case t = 1 was recently given in [10].…”

Construction of Duplication Correcting Codes

“…The construction given in Theorem 3 can be modified to obtain codes of lengths n and 2n that satisfy the TABLE 3. Comparison of the proposed constructions with the construction in [30].…”

“…In [29], codes for correcting TD errors of length at most k, 4 k 9, were presented. Lenz et al [30] provided a construction for codes that can correct one PD error. In [31], codes were given which can correct a combination of TD errors of fixed length k and at most one substitution error.…”

“…compares some 4-ary codes constructed using Theorems 2 and 4 with codes constructed using[30, Construction 3]. Our code construction can correct any number of PD errors of length 2 or 3 and the codes from[30, Construction 3] can correct only one PD error of length l where l n and n is the length of code. Note that the rate of a q-ary code C of length n is R =log q |C| n .…”

Construction of tandem duplication correcting codes

“…Insertion, deletion, substitution and tandem or palindromic duplication errors can occur in DNA data stored in a living organism. Codes to correct insertion, deletion, and substitution errors have been developed [12][13][14][15], but little has been done to construct codes for correcting tandem duplication (TD) errors [16][17][18].…”