Upper bounds on the capacity of deletion channels using channel fragmentation
Duman, T. M.
IEEE Transactions on Information Theory
Institute of Electrical and Electronics Engineers Inc.
146 - 156
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We study memoryless channels with synchronization errors as defined by a stochastic channel matrix allowing for symbol drop-outs or symbol insertions with particular emphasis on the binary and non-binary deletion channels. We offer a different look at these channels by considering equivalent models by fragmenting the input sequence where different subsequences travel through different channels. The resulting output symbols are combined appropriately to come up with an equivalent input-output representation of the original channel which allows for derivation of new upper bounds on the channel capacity. We consider both random and deterministic types of fragmentation processes applied to binary and nonbinary deletion channels. With two specific applications of this idea, a random fragmentation applied to a binary deletion channel and a deterministic fragmentation process applied to a nonbinary deletion channel, we prove certain inequality relations among the capacities of the original channels and those of the introduced subchannels. The resulting inequalities prove useful in deriving tighter capacity upper bounds for: 1) independent identically distributed (i.i.d.) deletion channels when the deletion probability exceeds 0.65 and 2) nonbinary deletion channels. Some extensions of these results, for instance, to the case of deletion/substitution channels are also explored. © 1963-2012 IEEE.
KeywordsBinary deletion channel
Capacity upper bounds
non-binary deletion channel
Published Version (Please cite this version)http://dx.doi.org/10.1109/TIT.2014.2368553
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Rahmati, M.; Duman, T. M. (IEEE, 2013)We develop several analytical lower bounds on the capacity of binary insertion and deletion channels by considering independent uniformly distributed (i.u.d.) inputs and computing lower bounds on the mutual information ...
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