26,941 research outputs found
Upper Bounds on the Capacities of Noncontrollable Finite-State Channels with/without Feedback
Noncontrollable finite-state channels (FSCs) are FSCs in which the channel
inputs have no influence on the channel states, i.e., the channel states evolve
freely. Since single-letter formulae for the channel capacities are rarely
available for general noncontrollable FSCs, computable bounds are usually
utilized to numerically bound the capacities. In this paper, we take the
delayed channel state as part of the channel input and then define the {\em
directed information rate} from the new channel input (including the source and
the delayed channel state) sequence to the channel output sequence. With this
technique, we derive a series of upper bounds on the capacities of
noncontrollable FSCs with/without feedback. These upper bounds can be achieved
by conditional Markov sources and computed by solving an average reward per
stage stochastic control problem (ARSCP) with a compact state space and a
compact action space. By showing that the ARSCP has a uniformly continuous
reward function, we transform the original ARSCP into a finite-state and
finite-action ARSCP that can be solved by a value iteration method. Under a
mild assumption, the value iteration algorithm is convergent and delivers a
near-optimal stationary policy and a numerical upper bound.Comment: 15 pages, Two columns, 6 figures; appears in IEEE Transaction on
Information Theor
Identification via Quantum Channels in the Presence of Prior Correlation and Feedback
Continuing our earlier work (quant-ph/0401060), we give two alternative
proofs of the result that a noiseless qubit channel has identification capacity
2: the first is direct by a "maximal code with random extension" argument, the
second is by showing that 1 bit of entanglement (which can be generated by
transmitting 1 qubit) and negligible (quantum) communication has identification
capacity 2.
This generalises a random hashing construction of Ahlswede and Dueck: that 1
shared random bit together with negligible communication has identification
capacity 1.
We then apply these results to prove capacity formulas for various quantum
feedback channels: passive classical feedback for quantum-classical channels, a
feedback model for classical-quantum channels, and "coherent feedback" for
general channels.Comment: 19 pages. Requires Rinton-P9x6.cls. v2 has some minor errors/typoes
corrected and the claims of remark 22 toned down (proofs are not so easy
after all). v3 has references to simultaneous ID coding removed: there were
necessary changes in quant-ph/0401060. v4 (final form) has minor correction
The Capacity of Channels with Feedback
We introduce a general framework for treating channels with memory and
feedback. First, we generalize Massey's concept of directed information and use
it to characterize the feedback capacity of general channels. Second, we
present coding results for Markov channels. This requires determining
appropriate sufficient statistics at the encoder and decoder. Third, a dynamic
programming framework for computing the capacity of Markov channels is
presented. Fourth, it is shown that the average cost optimality equation (ACOE)
can be viewed as an implicit single-letter characterization of the capacity.
Fifth, scenarios with simple sufficient statistics are described
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