An upperbound on the zero-error list-coding capacity

Cataloged from PDF version of article.We present an upper bound on the zero-error list-coding capacity of discrete memoryless channels. Using this bound, we show that the list3 capacity of the 4/3 channel is at most 03512 b, improving the best previous bound. The relatien of the bound to earlier similar bouads, in particular, to Korner's graph+ntropy bound, is discussed

The Capacity of Online (Causal) qq-ary Error-Erasure Channels

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/or $p^{*} n$ 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 a full knowledge on the sent codeword $\mathbf{x}$. In this work we study the capacity of $q$-ary online channels for a combined corruption model, in which the channel may impose at most $pn$ {\em errors} and at most $p^{*} n$ {\em 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 work, we give a full characterization of the capacity as a function of $q,p$, and $p^{*}$.Comment: This is a new version of the binary case, which can be found at arXiv:1412.637

Negligible Cooperation: Contrasting the Maximal- and Average-Error Cases

In communication networks, cooperative strategies are coding schemes where network nodes work together to improve network performance metrics such as the total rate delivered across the network. This work studies encoder cooperation in the setting of a discrete multiple access channel (MAC) with two encoders and a single decoder. A network node, here called the cooperation facilitator (CF), that is connected to both encoders via rate-limited links, enables the cooperation strategy. Previous work by the authors presents two classes of MACs: (i) one class where the average-error sum-capacity has an infinite derivative in the limit where CF output link capacities approach zero, and (ii) a second class of MACs where the maximal-error sum-capacity is not continuous at the point where the output link capacities of the CF equal zero. This work contrasts the power of the CF in the maximal- and average-error cases, showing that a constant number of bits communicated over the CF output link can yield a positive gain in the maximal-error sum-capacity, while a far greater number of bits, even numbers that grow sublinearly in the blocklength, can never yield a non-negligible gain in the average-error sum-capacity