125 research outputs found
Channel Detection in Coded Communication
We consider the problem of block-coded communication, where in each block,
the channel law belongs to one of two disjoint sets. The decoder is aimed to
decode only messages that have undergone a channel from one of the sets, and
thus has to detect the set which contains the prevailing channel. We begin with
the simplified case where each of the sets is a singleton. For any given code,
we derive the optimum detection/decoding rule in the sense of the best
trade-off among the probabilities of decoding error, false alarm, and
misdetection, and also introduce sub-optimal detection/decoding rules which are
simpler to implement. Then, various achievable bounds on the error exponents
are derived, including the exact single-letter characterization of the random
coding exponents for the optimal detector/decoder. We then extend the random
coding analysis to general sets of channels, and show that there exists a
universal detector/decoder which performs asymptotically as well as the optimal
detector/decoder, when tuned to detect a channel from a specific pair of
channels. The case of a pair of binary symmetric channels is discussed in
detail.Comment: Submitted to IEEE Transactions on Information Theor
Coding Theorems for Quantum Channels
The more than thirty years old issue of the (classical) information capacity
of quantum communication channels was dramatically clarified during the last
years, when a number of direct quantum coding theorems was discovered. The
present paper gives a self contained treatment of the subject, following as
much in parallel as possible with classical information theory and, on the
other side, stressing profound differences of the quantum case. An emphasis is
made on recent results, such as general quantum coding theorems including cases
of infinite (possibly continuous) alphabets and constrained inputs, reliability
function for pure state channels and quantum Gaussian channel. Several still
unsolved problems are briefly outlined.Comment: 41 pages, Latex, eps figure. Extended version of report appeared in
"Tamagawa University Research Review", no. 4, 199
Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels
Tradeoffs between the information rate and fidelity of quantum
error-correcting codes are discussed. Quantum channels to be considered are
those subject to independent errors and modeled as tensor products of copies of
a general completely positive linear map, where the dimension of the underlying
Hilbert space is a prime number. On such a quantum channel, the highest
fidelity of a quantum error-correcting code of length and rate R is proven
to be lower bounded by 1 - \exp [-n E(R) + o(n)] for some function E(R). The
E(R) is positive below some threshold R', which implies R' is a lower bound on
the quantum capacity. The result of this work applies to general discrete
memoryless channels, including channel models derived from a physical law of
time evolution, or from master equations.Comment: 19 pages, 2 figures. Ver.2: Comparisons with the previously known
bounds and examples were added. Except for very noisy channels, this work's
bound is, in general, better than those previously known. Ver.3: Introduction
shortened. Minor change
Lower bounds on the Probability of Error for Classical and Classical-Quantum Channels
In this paper, lower bounds on error probability in coding for discrete
classical and classical-quantum channels are studied. The contribution of the
paper goes in two main directions: i) extending classical bounds of Shannon,
Gallager and Berlekamp to classical-quantum channels, and ii) proposing a new
framework for lower bounding the probability of error of channels with a
zero-error capacity in the low rate region. The relation between these two
problems is revealed by showing that Lov\'asz' bound on zero-error capacity
emerges as a natural consequence of the sphere packing bound once we move to
the more general context of classical-quantum channels. A variation of
Lov\'asz' bound is then derived to lower bound the probability of error in the
low rate region by means of auxiliary channels. As a result of this study,
connections between the Lov\'asz theta function, the expurgated bound of
Gallager, the cutoff rate of a classical channel and the sphere packing bound
for classical-quantum channels are established.Comment: Updated to published version + bug fixed in Figure
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