Zero Deletion/Insertion Codes and Zero Error Capacity

Tallini, Luca G.; Alqwaifly, Nawaf; Bose, B.

doi:10.1109/isit50566.2022.9834523

Cited by 3 publications

(2 citation statements)

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“…In [46], some theory and design of (t d , t i )-A0EC codes capable of correcting all zero deletion errors up to t d and all zero insertion errors up to t i in each 0-run is proposed for any given t d , t i ∈ N. It is shown that this problem is equivalent to the design problem of All Error Correcting Codes in limited magnitude error channels [7] where the the following max L 1 distance, D…”

Section: A Limited Magnitude Based Codes For Small T/kmentioning

confidence: 99%

“…In fact, a theorem analogous to Theorem 2 holds for the A0EC code design problem in [46], and a code is (t d , t i )-A0EC if, and only if, its minimum max L 1 distance is greater than D − 1 def = t d + t i (see Theorem 1 in [46]). In particular, efficient (t d , t i )-A0EC binary codes, C, of length n ∈ N containing (see (9) in [46])…”

Section: A Limited Magnitude Based Codes For Small T/kmentioning

confidence: 99%

See 1 more Smart Citation

Efficient Systematic Deletions/Insertions of 0’s Error Control Codes

Tallini

Alqwaifly

Bose

2022

2022 IEEE Information Theory Workshop (ITW)

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This paper gives some theory and efficient design of binary block systematic codes capable of controlling the deletions of the symbol "0" (referred to as 0-deletions) and/or the insertions of the symbol "0" (referred to as 0-insertions). The problem of controlling 0-deletions and/or 0-insertions (referred to as 0-errors) is known to be equivalent to the efficient design of L 1 metric asymmetric error control codes over the natural alphabet, N. So, t 0-insertion correcting codes can actually correct t 0-errors, detect (t + 1) 0-errors and, simultaneously, detect all occurrences of only 0-deletions or only 0-insertions in every received word (briefly, they are t-Symmetric 0-Error Correcting/(t + 1)-Symmetric 0-Error Detecting/All Unidirectional 0-Error Detecting (t-Sy0EC/(t + 1)-Sy0ED/AU0ED) codes). From the relations with the L 1 distance, optimal systematic code designs are given. In general, for all t, k ∈ N, a recursive method is presented to encode k information bits into efficient systematic t-Sy0EC/(t + 1)-Sy0ED/AU0ED codes of lengthas n ∈ N increases. Decoding can be efficiently performed by algebraic means using the Extended Euclidean Algorithm (EEA).

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Section: A Limited Magnitude Based Codes For Small T/kmentioning

confidence: 99%