5,994 research outputs found
New Constructions of Codes for Asymmetric Channels via Concatenation
We present new constructions of codes for asymmetric channels for both binary and nonbinary alphabets, based on methods of generalized code concatenation. For the binary asymmetric channel, our methods construct nonlinear single-error-correcting codes from ternary outer codes. We show that some of the Varshamov-Tenengol'ts-Constantin-Rao codes, a class of binary nonlinear codes for this channel, have a nice structure when viewed as ternary codes. In many cases, our ternary construction yields even better codes. For the nonbinary asymmetric channel, our methods construct linear codes for many lengths and distances which are superior to the linear codes of the same length capable of correcting the same number of symmetric errors
Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories
Several physical effects that limit the reliability and performance of multilevel flash memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by â. The constructions utilize known codes for symmetric errors, over small alphabets, to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown to exceed the sizes of known codes (for related error models), and asymptotic rate-optimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation
On q-ary codes correcting all unidirectional errors of a limited magnitude
We consider codes over the alphabet Q={0,1,..,q-1}intended for the control of
unidirectional errors of level l. That is, the transmission channel is such
that the received word cannot contain both a component larger than the
transmitted one and a component smaller than the transmitted one. Moreover, the
absolute value of the difference between a transmitted component and its
received version is at most l.
We introduce and study q-ary codes capable of correcting all unidirectional
errors of level l. Lower and upper bounds for the maximal size of those codes
are presented.
We also study codes for this aim that are defined by a single equation on the
codeword coordinates(similar to the Varshamov-Tenengolts codes for correcting
binary asymmetric errors). We finally consider the problem of detecting all
unidirectional errors of level l.Comment: 22 pages,no figures. Accepted for publication of Journal of Armenian
Academy of Sciences, special issue dedicated to Rom Varshamo
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