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| Content Provider | IEEE Xplore Digital Library |
|---|---|
| Author | Tallini, L.G. Bose, B. |
| Copyright Year | 2013 |
| Description | Author affiliation: Sch. of EECS, Oregon State Univ., Corvallis, OR, USA (Bose, B.) || Dip. di Sci. della Comun., Univ. degli Studi di Teramo, Teramo, Italy (Tallini, L.G.) |
| Abstract | The general theory on partially asymmetric (t, $t_{+})-EC/(d_{-},$ $d_{+})-ED$ m-ary codes for the $L_{1}$ distance is developed. In this metric, such codes are capable of correcting $t_{-}$ or less negative errors, detecting d or less negative errors, correcting $t_{+}$ or less positive errors, and simultaneously detecting $d_{+}$ or less positive errors. Based on the elementary symmetric function, a wide class of these codes with efficient decoding algorithms are given. Let S(m, n, w, D) be the set of all the m-ary words of length n with real sum of their components being equal to w mod D. Any subset of S(m, n, w, D) is called m-ary constrained weight (CW) code of length n and is known to be a (D - 1)-UED code. Given a field, K, of prime characteristic p, some m-ary CW codes of length n ≤ |K| - 1 are defined. Such codes are $(t_{-},$ $t_{+})-EC/(d_{-},$ $d_{+})-ED$ and have a redundancy of ρ(c) = n - $log_{m}$ |C| ≤ ρ {S(m, n, w, d + 1)) + t $log_{m}$ |K|, with t = min{t_ + $d_{+},$ d_ + $t_{+}\},$ d = max{t_ + $d_{+},$ d_ + $t_{+}\}$ and w ∈ IN. In particular, for t ≤ p-1, a class of essentially linear and systematic (hence, easy to encode) m-ary (t_, $t_{+})-EC/(d_,$ $d_{+})-ED$ CW σ-codes with length n <; |K| + ⌈d/(m - 1)] - 1, k ≤ |K| - |K| - 1 information digits and n - k = $tlog_{m}$ |K| + ⌈d/(m-1)⌉ check digits are given. Also, some new hybrid partially asymmetric/unidirectional/symmetric error control codes are given and shown to be equivalent to the partially asymmetric (t_, $t_{+})-EC/(d_,$ $d_{+})-ED$ m-ary codes. |
| Starting Page | 694 |
| Ending Page | 698 |
| File Size | 168097 |
| Page Count | 5 |
| File Format | |
| ISBN | 9781479904464 |
| ISSN | 21578117 |
| DOI | 10.1109/ISIT.2013.6620315 |
| Language | English |
| Publisher | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher Date | 2013-07-07 |
| Publisher Place | Turkey |
| Access Restriction | Subscribed |
| Rights Holder | Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subject Keyword | Error correction Decoding Measurement Algorithm design and analysis Indexes Ash L1 distance m-ary alphabet error control codes symmetric errors unidirectional errors asymmetric errors flash memories insertion and deletion errors repetition errors |
| Content Type | Text |
| Resource Type | Article |
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