19,840 research outputs found
Achievable Rates for K-user Gaussian Interference Channels
The aim of this paper is to study the achievable rates for a user
Gaussian interference channels for any SNR using a combination of lattice and
algebraic codes. Lattice codes are first used to transform the Gaussian
interference channel (G-IFC) into a discrete input-output noiseless channel,
and subsequently algebraic codes are developed to achieve good rates over this
new alphabet. In this context, a quantity called efficiency is introduced which
reflects the effectiveness of the algebraic coding strategy. The paper first
addresses the problem of finding high efficiency algebraic codes. A combination
of these codes with Construction-A lattices is then used to achieve non trivial
rates for the original Gaussian interference channel.Comment: IEEE Transactions on Information Theory, 201
Nonuniform Fuchsian codes for noisy channels
We develop a new transmission scheme for additive white Gaussian noisy (AWGN)
channels based on Fuchsian groups from rational quaternion algebras. The
structure of the proposed Fuchsian codes is nonlinear and nonuniform, hence
conventional decoding methods based on linearity and symmetry do not apply.
Previously, only brute force decoding methods with complexity that is linear in
the code size exist for general nonuniform codes. However, the properly
discontinuous character of the action of the Fuchsian groups on the complex
upper half-plane translates into decoding complexity that is logarithmic in the
code size via a recently introduced point reduction algorithm
Golden codes: quantum LDPC codes built from regular tessellations of hyperbolic 4-manifolds
We adapt a construction of Guth and Lubotzky [arXiv:1310.5555] to obtain a
family of quantum LDPC codes with non-vanishing rate and minimum distance
scaling like where is the number of physical qubits. Similarly as
in [arXiv:1310.5555], our homological code family stems from hyperbolic
4-manifolds equipped with tessellations. The main novelty of this work is that
we consider a regular tessellation consisting of hypercubes. We exploit this
strong local structure to design and analyze an efficient decoding algorithm.Comment: 30 pages, 4 figure
Low Complexity Encoding for Network Codes
In this paper we consider the per-node run-time complexity of network multicast codes. We show that the randomized algebraic network code design algorithms described extensively in the literature result in codes that on average require a number of operations that scales quadratically with the blocklength m of the codes. We then propose an alternative type of linear network code whose complexity scales linearly in m and still enjoys the attractive properties of random algebraic network codes. We also show that these codes are optimal in the sense that any rate-optimal linear network code must have at least a linear scaling in run-time complexity
- …