20,193 research outputs found

### Partition Information and its Transmission over Boolean Multi-Access Channels

In this paper, we propose a novel partition reservation system to study the
partition information and its transmission over a noise-free Boolean
multi-access channel. The objective of transmission is not message restoration,
but to partition active users into distinct groups so that they can,
subsequently, transmit their messages without collision. We first calculate (by
mutual information) the amount of information needed for the partitioning
without channel effects, and then propose two different coding schemes to
obtain achievable transmission rates over the channel. The first one is the
brute force method, where the codebook design is based on centralized source
coding; the second method uses random coding where the codebook is generated
randomly and optimal Bayesian decoding is employed to reconstruct the
partition. Both methods shed light on the internal structure of the partition
problem. A novel hypergraph formulation is proposed for the random coding
scheme, which intuitively describes the information in terms of a strong
coloring of a hypergraph induced by a sequence of channel operations and
interactions between active users. An extended Fibonacci structure is found for
a simple, but non-trivial, case with two active users. A comparison between
these methods and group testing is conducted to demonstrate the uniqueness of
our problem.Comment: Submitted to IEEE Transactions on Information Theory, major revisio

### On the Linear Convergence of the ADMM in Decentralized Consensus Optimization

In decentralized consensus optimization, a connected network of agents
collaboratively minimize the sum of their local objective functions over a
common decision variable, where their information exchange is restricted
between the neighbors. To this end, one can first obtain a problem
reformulation and then apply the alternating direction method of multipliers
(ADMM). The method applies iterative computation at the individual agents and
information exchange between the neighbors. This approach has been observed to
converge quickly and deemed powerful. This paper establishes its linear
convergence rate for decentralized consensus optimization problem with strongly
convex local objective functions. The theoretical convergence rate is
explicitly given in terms of the network topology, the properties of local
objective functions, and the algorithm parameter. This result is not only a
performance guarantee but also a guideline toward accelerating the ADMM
convergence.Comment: 11 figures, IEEE Transactions on Signal Processing, 201

### Asymptotic Error Free Partitioning over Noisy Boolean Multiaccess Channels

In this paper, we consider the problem of partitioning active users in a
manner that facilitates multi-access without collision. The setting is of a
noisy, synchronous, Boolean, multi-access channel where $K$ active users (out
of a total of $N$ users) seek to access. A solution to the partition problem
places each of the $N$ users in one of $K$ groups (or blocks) such that no two
active nodes are in the same block. We consider a simple, but non-trivial and
illustrative case of $K=2$ active users and study the number of steps $T$ used
to solve the partition problem. By random coding and a suboptimal decoding
scheme, we show that for any $T\geq (C_1 +\xi_1)\log N$, where $C_1$ and
$\xi_1$ are positive constants (independent of $N$), and $\xi_1$ can be
arbitrary small, the partition problem can be solved with error probability
$P_e^{(N)} \to 0$, for large $N$. Under the same scheme, we also bound $T$ from
the other direction, establishing that, for any $T \leq (C_2 - \xi_2) \log N$,
the error probability $P_e^{(N)} \to 1$ for large $N$; again $C_2$ and $\xi_2$
are constants and $\xi_2$ can be arbitrarily small. These bounds on the number
of steps are lower than the tight achievable lower-bound in terms of $T \geq
(C_g +\xi)\log N$ for group testing (in which all active users are identified,
rather than just partitioned). Thus, partitioning may prove to be a more
efficient approach for multi-access than group testing.Comment: This paper was submitted in June 2014 to IEEE Transactions on
Information Theory, and is under review no

### Orientation and Motion of Water Molecules at Air/Water Interface

Analysis of SFG vibrational spectra of OH stretching bands in four
experimental configurations shows that orientational motion of water molecule
at air/water interface is libratory within a limited angular range. This
picture is significantly different from the previous conclusion that the
interfacial water molecule orientation varies over a broad range within the
vibrational relaxation time, the only direct experimental evidence for
ultrafast and broad orientational motion of a liquid interface by Wei et al.
[Phys. Rev. Lett. 86, 4799, (2001)] using single SFG experimental
configuration

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