711 research outputs found
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
Two-batch liar games on a general bounded channel
We consider an extension of the 2-person R\'enyi-Ulam liar game in which lies
are governed by a channel , a set of allowable lie strings of maximum length
. Carole selects , and Paul makes -ary queries to uniquely
determine . In each of rounds, Paul weakly partitions and asks for such that . Carole responds with some
, and if , then accumulates a lie . Carole's string of
lies for must be in the channel . Paul wins if he determines within
rounds. We further restrict Paul to ask his questions in two off-line
batches. We show that for a range of sizes of the second batch, the maximum
size of the search space for which Paul can guarantee finding the
distinguished element is as ,
where is the number of lie strings in of maximum length . This
generalizes previous work of Dumitriu and Spencer, and of Ahlswede, Cicalese,
and Deppe. We extend Paul's strategy to solve also the pathological liar
variant, in a unified manner which gives the existence of asymptotically
perfect two-batch adaptive codes for the channel .Comment: 26 page
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