3,593 research outputs found
Spectral Shape of Doubly-Generalized LDPC Codes: Efficient and Exact Evaluation
This paper analyzes the asymptotic exponent of the weight spectrum for
irregular doubly-generalized LDPC (D-GLDPC) codes. In the process, an efficient
numerical technique for its evaluation is presented, involving the solution of
a 4 x 4 system of polynomial equations. The expression is consistent with
previous results, including the case where the normalized weight or stopping
set size tends to zero. The spectral shape is shown to admit a particularly
simple form in the special case where all variable nodes are repetition codes
of the same degree, a case which includes Tanner codes; for this case it is
also shown how certain symmetry properties of the local weight distribution at
the CNs induce a symmetry in the overall weight spectral shape function.
Finally, using these new results, weight and stopping set size spectral shapes
are evaluated for some example generalized and doubly-generalized LDPC code
ensembles.Comment: 17 pages, 6 figures. To appear in IEEE Transactions on Information
Theor
Cyclic labellings with constraints at two distances
Motivated by problems in radio channel assignment, we consider the vertex-labelling of graphs with non-negative integers. The objective is to minimise the span of the labelling, subject to constraints imposed at graph distances one and two. We show that the minimum span is (up to rounding) a piecewise linear function of the constraints, and give a complete specification, together with associated optimal assignments, for trees and cycles
On classical and quantum liftings
We analyze the procedure of lifting in classical stochastic and quantum
systems. It enables one to `lift' a state of a system into a state of
`system+reservoir'. This procedure is important both in quantum information
theory and the theory of open systems. We illustrate the general theory of
liftings by a particular class related to so called circulant states.Comment: 25 page
Interference Localization for Uplink OFDMA Systems in Presence of CFOs
Multiple carrier frequency offsets (CFOs) present in the uplink of orthogonal
frequency division multiple access (OFDMA) systems adversely affect subcarrier
orthogonality and impose a serious performance loss. In this paper, we propose
the application of time domain receiver windowing to concentrate the leakage
caused by CFOs to a few adjacent subcarriers with almost no additional
computational complexity. This allows us to approximate the interference matrix
with a quasi-banded matrix by neglecting small elements outside a certain band
which enables robust and computationally efficient signal detection. The
proposed CFO compensation technique is applicable to all types of subcarrier
assignment techniques. Simulation results show that the quasi-banded
approximation of the interference matrix is accurate enough to provide almost
the same bit error rate performance as that of the optimal solution. The
excellent performance of our proposed method is also proven through running an
experiment using our FPGA-based system setup.Comment: Accepted in IEEE WCNC 201
Representation theory for high-rate multiple-antenna code design
Multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment, but the practical success of using multiple antennas depends crucially on our ability to design high-rate space-time constellations with low encoding and decoding complexity. It has been shown that full transmitter diversity, where the constellation is a set of unitary matrices whose differences have nonzero determinant, is a desirable property for good performance. We use the powerful theory of fixed-point-free groups and their representations to design high-rate constellations with full diversity. Furthermore, we thereby classify all full-diversity constellations that form a group, for all rates and numbers of transmitter antennas. The group structure makes the constellations especially suitable for differential modulation and low-complexity decoding algorithms. The classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd. We, therefore, also consider extensions of the constellation designs to nongroups. We conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels
- …