46,256 research outputs found
A Minimax Converse for Quantum Channel Coding
We prove a one-shot "minimax" converse bound for quantum channel coding
assisted by positive partial transpose channels between sender and receiver.
The bound is similar in spirit to the converse by Polyanskiy, Poor, and Verdu
[IEEE Trans. Info. Theory 56, 2307-2359 (2010)] for classical channel coding,
and also enjoys the saddle point property enabling the order of optimizations
to be interchanged. Equivalently, the bound can be formulated as a semidefinite
program satisfying strong duality. The convex nature of the bound implies
channel symmetries can substantially simplify the optimization, enabling us to
explicitly compute the finite blocklength behavior for several simple qubit
channels. In particular, we find that finite blocklength converse statements
for the classical erasure channel apply to the assisted quantum erasure
channel, while bounds for the classical binary symmetric channel apply to both
the assisted dephasing and depolarizing channels. This implies that these qubit
channels inherit statements regarding the asymptotic limit of large
blocklength, such as the strong converse or second-order converse rates, from
their classical counterparts. Moreover, for the dephasing channel, the finite
blocklength bounds are as tight as those for the classical binary symmetric
channel, since coding for classical phase errors yields equivalently-performing
unassisted quantum codes.Comment: merged with arXiv:1504.04617 version 1 ; see version
Zero-error communication over adder MAC
Adder MAC is a simple noiseless multiple-access channel (MAC), where if users
send messages , then the receiver receives with addition over . Communication over the
noiseless adder MAC has been studied for more than fifty years. There are two
models of particular interest: uniquely decodable code tuples, and -codes.
In spite of the similarities between these two models, lower bounds and upper
bounds of the optimal sum rate of uniquely decodable code tuple asymptotically
match as number of users goes to infinity, while there is a gap of factor two
between lower bounds and upper bounds of the optimal rate of -codes.
The best currently known -codes for are constructed using
random coding. In this work, we study variants of the random coding method and
related problems, in hope of achieving -codes with better rate. Our
contribution include the following. (1) We prove that changing the underlying
distribution used in random coding cannot improve the rate. (2) We determine
the rate of a list-decoding version of -codes achieved by the random
coding method. (3) We study several related problems about R\'{e}nyi entropy.Comment: An updated version of author's master thesi
Precoding for Outage Probability Minimization on Block Fading Channels
The outage probability limit is a fundamental and achievable lower bound on
the word error rate of coded communication systems affected by fading. This
limit is mainly determined by two parameters: the diversity order and the
coding gain. With linear precoding, full diversity on a block fading channel
can be achieved without error-correcting code. However, the effect of precoding
on the coding gain is not well known, mainly due to the complicated expression
of the outage probability. Using a geometric approach, this paper establishes
simple upper bounds on the outage probability, the minimization of which yields
to precoding matrices that achieve very good performance. For discrete
alphabets, it is shown that the combination of constellation expansion and
precoding is sufficient to closely approach the minimum possible outage
achieved by an i.i.d. Gaussian input distribution, thus essentially maximizing
the coding gain.Comment: Submitted to Transactions on Information Theory on March 23, 201
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