On multiple insertion/deletion correcting codes

Helberg, A.S.J.; Ferreira, H.C.

doi:10.1109/18.971760

Cited by 144 publications

(69 citation statements)

References 6 publications

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“…At receiver, we can recover f (x 7 ) as g(x 7 ) ∈ C 2 (6). Furthermore, we know that the symbols 2 and 1 were deleted due to the constraints in (5). However, we do not know which symbol came first in the original codeword x 7 .…”

Section: Ieee Information Theory Workhopmentioning

confidence: 93%

“…Our construction is based on any [2] Tenengol'ts [4] Multiple Ins./Del. Correction Helberg [5] Proposed Construction Method (This Paper) binary multiple insertion/deletion correcting code, such as the Helberg code. Table I places our construction in context in comparison to other insertion/deletion correcting codes.…”

Section: Introductionmentioning

confidence: 99%

“…An important generalisation of the Levenshtein code is the Helberg code [5] 1 . However, the Helberg code suffers from a low cardinality.…”

Section: Introductionmentioning

confidence: 99%

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A note on non-binary multiple insertion/deletion correcting codes

Palunčić

Swart

Weber

et al. 2011

2011 IEEE Information Theory Workshop

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We propose the construction of a non-binary multiple insertion/deletion correcting code based on a binary multiple insertion/deletion correcting code. In essence, it is a generalisation of Tenengol'ts' non-binary single insertion/deletion correcting code. We evaluate the cardinality of the proposed construction based on the asymptotic upper bound on the cardinality of a maximal binary multiple insertion/deletion correcting code derived by Levenshtein.

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Section: Ieee Information Theory Workhopmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

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A note on non-binary multiple insertion/deletion correcting codes

Palunčić

Swart

Weber

et al. 2011

2011 IEEE Information Theory Workshop

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“…However, this code is inefficient because it requires δn redundant bits, i.e., a redundancy that is linear in n. Helberg codes [12] are a generalization of VT codes for multiple deletions. These codes can correct mutiple deletions but their redundancy is at least linear in n even for two deletions.…”

Section: Introductionmentioning

confidence: 99%

“…Contributions: While the work on codes that correct multiple deletions in [12]- [15] focuses on zero-error codes, in our approach we relax this requirement and allow an asymptotically vanishing probability of decoding failure 1 . Our contributions are the following: (i) we propose new explicit codes, which we call Guess & Check (GC) codes, that can correct, with high probability, and in polynomial time, a constant number of deletions 2 δ occurring at uniformly random positions within an arbitrary binary string.…”

Section: Introductionmentioning

confidence: 99%

Guess & check codes for deletions and synchronization

Hanna

Rouayheb

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Abstract-We consider the problem of constructing codes that can correct δ deletions occurring in an arbitrary binary string of length n bits. Varshamov-Tenengolts (VT) codes can correct all possible single deletions (δ = 1) with an asymptotically optimal redundancy. Finding similar codes for δ ≥ 2 deletions is an open problem. We propose a new family of codes, that we call Guess & Check (GC) codes, that can correct, with high probability, a constant number of deletions δ occurring at uniformly random positions within an arbitrary string. The GC codes are based on MDS codes and have an asymptotically optimal redundancy that is Θ(δ log n). We provide deterministic polynomial time encoding and decoding schemes for these codes. We also describe the applications of GC codes to file synchronization.

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Aniline and Its Derivatives

Amini

Lowenkron

2003

Kirk-Othmer Encyclopedia of Chemical Technology

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Aniline (benzenamine) is the simplest of the primary aromatic amines. Aromatic amines can be produced by reduction of the corresponding nitro compound, the ammonolysis of an aromatic halide or phenol, and by direct amination of the aromatic ring. At present, the catalytic reduction of nitrobenzene is the predominant process for manufacture of aniline. Pure, freshly distilled aniline is a colorless, oily liquid that darkens on exposure to light and air. It has a characteristic sweet, amine‐like aromatic odor. Aromatic amines are usually weaker bases than aliphatic amines. Aromatic amines form addition compounds and complexes with many inorganic substances, such as zinc chloride, copper chloride, uranium tetrachloride, or boron trifluoride. Various metals react with the amino group to form metal anilides; and hydrochloric, sulfuric, or phosphoric acid salts of aniline are important intermediates in the dye industry. Important reactions include n ‐alkylation, ring alkylation, acylation, condensation, cyclization, reaction with nitrous acid, oxidation, halogenation, sulfonation, nitration, and reduction. The predominant process for manufacture of aniline is the catalytic reduction of nitrobenzene with hydrogen. The flash point of aniline (70°C) is well above its normal storage temperature, but aniline should be stored and used in areas with minimum fire hazard. Aniline is slightly corrosive to some metals. It attacks copper, brass, and other copper alloys, and use of these metals should be avoided in equipment that is used to handle aniline. Aniline is shipped in tank truck and tank car quantities and is classified by the U.S. Department of Transportation (DOT) as a Class B poison (UN 1547), and must carry a poison label. Wastes contaminated with aniline may be listed as RCRA Hazardous Waste. Aniline is highly toxic and may be fatal if swallowed, inhaled, or absorbed through the skin. Aniline vapor is mildly irritating to the eye, and in liquid form it can be a severe eye irritant and cause corneal damage. Based on tests with laboratory animals, aniline may cause cancer. Aniline should be handled in areas with adequate ventilation and skin exposure should be avoided by the wearing of proper safety equipment. The major uses of aniline are in the manufacture of polymers, rubber, agricultural chemicals, dyes and pigments, pharmaceuticals, and photographic chemicals. Most derivatives of aniline are prepared by hydrogenation of their nitroaromatic precursors. An important derivative of aniline is 4,4′‐methylenedianiline (4,4′‐MDA). Manufacture is carried out by the acid‐catalyzed reaction of formaldehyde with aniline. All processes produce polymeric MDA (PMDA), which consists of mixtures of isomers and oligomers of MDA. More than 99% of the manufactured PMDA products are used in reactions with phosgene to produce the corresponding isocyanates for use in polyurethanes. The resultant polymeric isocyanates (PMDI) are either sold commercially or are purified to isolate 4‐4′‐methylenediphyenyldiisocyanate (MDI). MDI is an important intermediate in the manufacture of spandex fibers, thermoplastic resins, and coatings, and it is used in reaction injection molding (RIM) for automotive applications. The primary use of PMDI products is in rigid foam insulation, but they are also used in semiflexible foams, foundry core binders, and particle board manufacture.

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On multiple insertion/deletion correcting codes

Cited by 144 publications

References 6 publications

A note on non-binary multiple insertion/deletion correcting codes

A note on non-binary multiple insertion/deletion correcting codes

Guess & check codes for deletions and synchronization

Aniline and Its Derivatives

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