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Capacity regions of discrete asynchronous multiple access channels

Motivated by the importance of asynchronous multiple access channels we give an exact formalization. This formalization admits different distributions on delays. The two classical settings when the delay is uniformly distributed and when it is bounded are discussed as special cases of this model. Our method also allows for the analysis of a so far unexplored class of models, where the known distribution of the delay has a special form, leading to new interesting capacity regions.

Random access and source-channel coding error exponents for Multiple Access Channels

A new universal coding/decoding scheme for random access with collision detection is given in case of two senders. The result is used to give achievable joint source-channel coding error exponents for multiple access channel and independent sources. In a modified model admitting zero rate communication between the senders, an improved exponent is derived, of form similar to Csiszárs joint source-channel exponent for the one-sender case.

Testability of minimum balanced multiway cut densities

Testability of certain balanced minimum multiway cut densities is investigated for vertex- and edge-weighted graphs with no dominant vertex-weights. We apply the results for fuzzy clustering and noisy graph sequences.

Universal error exponent for discrete asynchronous multiple access channels

Exponential error bounds achievable via universal decoder are derived for frame-asynchronous discrete memoryless multiple access channels with two senders. The exponent is strictly positive inside the capacity region. The method of types and a modified maximal mutual information decoder are used.

Controlled asynchronism improves error exponent

Improved exponential error bounds are derived for frame-asynchronous discrete memoryless multiple access channels with two senders. By numerical evaluation for a particular case, it follows that the best error exponent known for synchronous transmission may be beaten if the senders are allowed to transmit with a chosen delay.

Random Access and Source-Channel Coding Error Exponents for Multiple Access Channels

A new universal coding/decoding scheme for random access with collision detection is given in case of two senders. The result is used to give achievable joint source-channel coding error exponents for multiple access channel and independent sources. In a modified model admitting zero rate communication between the senders, an improved exponent is derived, of form similar to Csiszar’s joint source-channel exponent for the one-sender case.

Error exponents for sparse communication

Communication over a discrete memoryless channel is addressed when codewords are transmitted in certain time intervals of arbitrary locations, at other times the channel outputs pure noise. The receiver has to locate and decode the codewords. Exponential error bounds are derived, jointly achievable via a semi-universal or universal decoder. Implications are discussed for the familiar model of communication under strong asynchronism when in exponentially long time only one codeword is transmitted.

On capacity regions of discrete asynchronous multiple access channels

Motivated by the importance of asynchronous multiple access channels we give an exact formalization. This formalization admits different distributions on delays. The two classical settings when the delay is uniformly distributed and when it is bounded are discussed as special cases of this model. Our method also allows for the analysis of a so far unexplored class of models, where the known distribution of the delay has a special form, leading to new interesting capacity regions.

Capacity regions of partly asynchronous multiple access channels

Frame asynchronous discrete memoryless multiple access channels are analyzed, where some groups of senders are synchronized but the groups are not synchronized with each other. A single-letter characterization of the capacity region is obtained.

Universal Random Access Error Exponents for Codebooks of Different Blocklengths

Csiszár’s channel coding theorem for multiple codebooks is generalized allowing the code word lengths differ across codebooks. Also in this case, for each codebook an error exponent can be achieved that equals the random coding exponent for this codebook alone. In addition, when the rate and code word-type of the employed codebook do not admit reliable transmission over the given channel, overload is detected with probability approaching 1. This is proved even for a sender and receiver not knowing the channel beyond the alphabets. A substantial improvement is obtained when the sender knows the channel while the receiver still does not.