38 research outputs found
Optimum Asymptotic Multiuser Efficiency of Pseudo-Orthogonal Randomly Spread CDMA
A -user pseudo-orthogonal (PO) randomly spread CDMA system, equivalent to
transmission over a subset of single-user Gaussian channels, is
introduced. The high signal-to-noise ratio performance of the PO-CDMA is
analyzed by rigorously deriving its asymptotic multiuser efficiency (AME) in
the large system limit. Interestingly, the -optimized PO-CDMA transceiver
scheme yields an AME which is practically equal to 1 for system loads smaller
than 0.1 and lower bounded by 1/4 for increasing loads. As opposed to the
vanishing efficiency of linear multiuser detectors, the derived efficiency is
comparable to the ultimate CDMA efficiency achieved for the intractable optimal
multiuser detector.Comment: WIC 27th Symposium on Information Theory in the Benelux, 200
Low-Density Code-Domain NOMA: Better Be Regular
A closed-form analytical expression is derived for the limiting empirical
squared singular value density of a spreading (signature) matrix corresponding
to sparse low-density code-domain (LDCD) non-orthogonal multiple-access (NOMA)
with regular random user-resource allocation. The derivation relies on
associating the spreading matrix with the adjacency matrix of a large
semiregular bipartite graph. For a simple repetition-based sparse spreading
scheme, the result directly follows from a rigorous analysis of spectral
measures of infinite graphs. Turning to random (sparse) binary spreading, we
harness the cavity method from statistical physics, and show that the limiting
spectral density coincides in both cases. Next, we use this density to compute
the normalized input-output mutual information of the underlying vector channel
in the large-system limit. The latter may be interpreted as the achievable
total throughput per dimension with optimum processing in a corresponding
multiple-access channel setting or, alternatively, in a fully-symmetric
broadcast channel setting with full decoding capabilities at each receiver.
Surprisingly, the total throughput of regular LDCD-NOMA is found to be not only
superior to that achieved with irregular user-resource allocation, but also to
the total throughput of dense randomly-spread NOMA, for which optimum
processing is computationally intractable. In contrast, the superior
performance of regular LDCD-NOMA can be potentially achieved with a feasible
message-passing algorithm. This observation may advocate employing regular,
rather than irregular, LDCD-NOMA in 5G cellular physical layer design.Comment: Accepted for publication in the IEEE International Symposium on
Information Theory (ISIT), June 201
Capacity of Complexity-Constrained Noise-Free CDMA
An interference-limited noise-free CDMA downlink channel operating under a
complexity constraint on the receiver is introduced. According to this
paradigm, detected bits, obtained by performing hard decisions directly on the
channel's matched filter output, must be the same as the transmitted binary
inputs. This channel setting, allowing the use of the simplest receiver scheme,
seems to be worthless, making reliable communication at any rate impossible. We
prove, by adopting statistical mechanics notion, that in the large-system limit
such a complexity-constrained CDMA channel gives rise to a non-trivial
Shannon-theoretic capacity, rigorously analyzed and corroborated using
finite-size channel simulations.Comment: To appear in IEEE Communications Letter
Polynomial Linear Programming with Gaussian Belief Propagation
Interior-point methods are state-of-the-art algorithms for solving linear
programming (LP) problems with polynomial complexity. Specifically, the
Karmarkar algorithm typically solves LP problems in time O(n^{3.5}), where
is the number of unknown variables. Karmarkar's celebrated algorithm is known
to be an instance of the log-barrier method using the Newton iteration. The
main computational overhead of this method is in inverting the Hessian matrix
of the Newton iteration. In this contribution, we propose the application of
the Gaussian belief propagation (GaBP) algorithm as part of an efficient and
distributed LP solver that exploits the sparse and symmetric structure of the
Hessian matrix and avoids the need for direct matrix inversion. This approach
shifts the computation from realm of linear algebra to that of probabilistic
inference on graphical models, thus applying GaBP as an efficient inference
engine. Our construction is general and can be used for any interior-point
algorithm which uses the Newton method, including non-linear program solvers.Comment: 7 pages, 1 figure, appeared in the 46th Annual Allerton Conference on
Communication, Control and Computing, Allerton House, Illinois, Sept. 200