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The Capacity of Online (Causal) $q$ -Ary Error-Erasure Channels.
- Source :
-
IEEE Transactions on Information Theory . Jun2019, Vol. 65 Issue 6, p3384-3411. 28p. - Publication Year :
- 2019
-
Abstract
- In the $q$ -ary online (or “causal”) channel coding model, a sender wishes to communicate a message to a receiver by transmitting a codeword $\mathbf {x} =(x_{1},\ldots,x_{n}) \in \{0,1,\ldots,q-1\}^{n}$ symbol-by-symbol via a channel limited to at most $pn$ errors and $p^{*} n$ erasures. The channel is “online” in the sense that at the $i$ th step of communication the channel decides whether to corrupt the $i$ th symbol or not based on its view so far, i.e., its decision depends only on the transmitted symbols $(x_{1},\ldots,x_{i})$. This is in contrast to the classical adversarial channel in which the corruption is chosen by a channel that has full knowledge of the sent codeword $\mathbf {x}$. In this paper, we study the capacity of $q$ -ary online channels for a combined corruption model, in which the channel may impose at most $pn$ errors and at most $p^{*} n$ erasures on the transmitted codeword. The online channel (in both the error and erasure case) has seen a number of recent studies, which present both upper and lower bounds on its capacity. In this paper, we give a full characterization of the capacity as a function of $q,p$ , and $p^{*}$. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00189448
- Volume :
- 65
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- IEEE Transactions on Information Theory
- Publication Type :
- Academic Journal
- Accession number :
- 136543527
- Full Text :
- https://doi.org/10.1109/TIT.2019.2898863