6,966 research outputs found
Communication over Finite-Chain-Ring Matrix Channels
Though network coding is traditionally performed over finite fields, recent
work on nested-lattice-based network coding suggests that, by allowing network
coding over certain finite rings, more efficient physical-layer network coding
schemes can be constructed. This paper considers the problem of communication
over a finite-ring matrix channel , where is the channel
input, is the channel output, is random error, and and are
random transfer matrices. Tight capacity results are obtained and simple
polynomial-complexity capacity-achieving coding schemes are provided under the
assumption that is uniform over all full-rank matrices and is uniform
over all rank- matrices, extending the work of Silva, Kschischang and
K\"{o}tter (2010), who handled the case of finite fields. This extension is
based on several new results, which may be of independent interest, that
generalize concepts and methods from matrices over finite fields to matrices
over finite chain rings.Comment: Submitted to IEEE Transactions on Information Theory, April 2013.
Revised version submitted in Feb. 2014. Final version submitted in June 201
Multiplicatively Repeated Non-Binary LDPC Codes
We propose non-binary LDPC codes concatenated with multiplicative repetition
codes. By multiplicatively repeating the (2,3)-regular non-binary LDPC mother
code of rate 1/3, we construct rate-compatible codes of lower rates 1/6, 1/9,
1/12,... Surprisingly, such simple low-rate non-binary LDPC codes outperform
the best low-rate binary LDPC codes so far. Moreover, we propose the decoding
algorithm for the proposed codes, which can be decoded with almost the same
computational complexity as that of the mother code.Comment: To appear in IEEE Transactions on Information Theor
Additivity and multiplicativity properties of some Gaussian channels for Gaussian inputs
We prove multiplicativity of maximal output norm of classical noise
channels and thermal noise channels of arbitrary modes for all under the
assumption that the input signal states are Gaussian states. As a direct
consequence, we also show the additivity of the minimal output entropy and that
of the energy-constrained Holevo capacity for those Gaussian channels under
Gaussian inputs. To the best of our knowledge, newly discovered majorization
relation on symplectic eigenvalues, which is also of independent interest,
plays a central role in the proof.Comment: 9 pages, no figures. Published Versio
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