1,129 research outputs found
Polar Codes: Robustness of the Successive Cancellation Decoder with Respect to Quantization
Polar codes provably achieve the capacity of a wide array of channels under
successive decoding. This assumes infinite precision arithmetic. Given the
successive nature of the decoding algorithm, one might worry about the
sensitivity of the performance to the precision of the computation.
We show that even very coarsely quantized decoding algorithms lead to
excellent performance. More concretely, we show that under successive decoding
with an alphabet of cardinality only three, the decoder still has a threshold
and this threshold is a sizable fraction of capacity. More generally, we show
that if we are willing to transmit at a rate below capacity, then we
need only bits of precision, where is a universal
constant.Comment: In ISIT 201
The Space of Solutions of Coupled XORSAT Formulae
The XOR-satisfiability (XORSAT) problem deals with a system of Boolean
variables and clauses. Each clause is a linear Boolean equation (XOR) of a
subset of the variables. A -clause is a clause involving distinct
variables. In the random -XORSAT problem a formula is created by choosing
-clauses uniformly at random from the set of all possible clauses on
variables. The set of solutions of a random formula exhibits various
geometrical transitions as the ratio varies.
We consider a {\em coupled} -XORSAT ensemble, consisting of a chain of
random XORSAT models that are spatially coupled across a finite window along
the chain direction. We observe that the threshold saturation phenomenon takes
place for this ensemble and we characterize various properties of the space of
solutions of such coupled formulae.Comment: Submitted to ISIT 201
THEORETICAL STUDIES OF BILIPROTEIN CHROMOPHORES AND RELATED BILE PIGMENTS BY MOLECULAR ORBITAL AND RAMACHANDRAN TYPE CALCULATIONS
Ramachandran calculations have been used to gain insight into steric hindrance in bile
pigments related to biliprotein chromophores. The high optical activity of denatured phycocyanin, as
compared to phycoerythrin, has been related to the asymmetric substitution at ring A, which shifts the
equilibrium towards the P-helical form of the chromophore. Geometric effects on the electronic structures
and transitions have then been studied by molecular orbital calculations for several conjugation
systems including the chromophores of phycocyanin. phytochrome P,, cations, cation radicals and
tautomeric forms. For these different chromophores some general trends can be deduced. For instance,
for a given change in the gross shape (e.g. either unfolding of the molecule from a cyclic-helical to a fully
extended geometry, or upon out-of-plane twists of the pyrrole ring A) of the molecules under study, the
predicted absorption spectra all change in a simikar way. Nonetheless, there are characteristic distinctions
between the different n-systems, both in the transition energies and the charge distribution, which
can be related to their known differences in spectroscopic properties and their reactivity
Partitioned List Decoding of Polar Codes: Analysis and Improvement of Finite Length Performance
Polar codes represent one of the major recent breakthroughs in coding theory
and, because of their attractive features, they have been selected for the
incoming 5G standard. As such, a lot of attention has been devoted to the
development of decoding algorithms with good error performance and efficient
hardware implementation. One of the leading candidates in this regard is
represented by successive-cancellation list (SCL) decoding. However, its
hardware implementation requires a large amount of memory. Recently, a
partitioned SCL (PSCL) decoder has been proposed to significantly reduce the
memory consumption. In this paper, we examine the paradigm of PSCL decoding
from both theoretical and practical standpoints: (i) by changing the
construction of the code, we are able to improve the performance at no
additional computational, latency or memory cost, (ii) we present an optimal
scheme to allocate cyclic redundancy checks (CRCs), and (iii) we provide an
upper bound on the list size that allows MAP performance.Comment: 2017 IEEE Global Communications Conference (GLOBECOM
BILIPROTEINS FROM THE BUTTERFLY Pieris brassicae STUDIED BY TIME-RESOLVED FLUORESCENCE AND COHERENT ANTI-STOKES RAMAN SPECTROSCOPY
The fluorescence decay time of the biliverdin IX7 chromophore present in biliproteins isolated from Pieris brassicae is determined to be 44 ± 3 ps. This value suggests a cyclic helical chromophore structure. The vibrational frequencies determined by CARS-spectroscopy are compared with those of model compounds. The data confirm that the chromophore in the protein-bound state adopts a cyclic-helical, flexible conformation
Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release
The intracellular release of calcium from the endoplasmic reticulum is controlled by ion channels. The resulting calcium signals exhibit a rich spatio-temporal signature, which originates at least partly from microscopic fluctuations. While stochasticity in the gating transition of ion channels has been incorporated into many models, the distribution of calcium is usually described by deterministic reaction-diffusion equations. Here we test the validity of the latter modeling approach by using two different models to calculate the frequency of localized calcium signals (calcium puffs) from clustered IP3 receptor channels. The complexity of the full calcium system is here limited to the basic opening mechanism of the ion channels and, in the mathematical reduction simplifies to the calculation of a first passage time. Two models are then studied: (i) a hybrid model, where channel gating is treated stochastically, while calcium concentration is deterministic and (ii) a fully stochastic model with noisy channel gating and Brownian calcium ion motion. The second model utilises the recently developed two-regime method [M. B. Flegg, S. J. Chapman, and R. Erban, âThe two-regime method for optimizing stochastic reaction-diffusion simulations,â J. R. Soc., Interface9, 859â868 (Year: 2012)]10.1098/rsif.2011.0574 in order to simulate a large domain with precision required only near the Ca2+ absorbing channels. The expected time for a first channel opening that results in a calcium puff event is calculated. It is found that for a large diffusion constant, predictions of the interpuff time are significantly overestimated using the model (i) with a deterministic non-spatial calcium variable. It is thus demonstrated that the presence of diffusive noise in local concentrations of intracellular Ca2+ ions can substantially influence the occurrence of calcium signals. The presented approach and results may also be relevant for other cell-physiological first-passage time problems with small ligand concentration and high cooperativity
Finite-Length Scaling of Polar Codes
Consider a binary-input memoryless output-symmetric channel . Such a
channel has a capacity, call it , and for any and strictly
positive constant we know that we can construct a coding scheme
that allows transmission at rate with an error probability not exceeding
. Assume now that we let the rate tend to and we ask how
we have to "scale" the blocklength in order to keep the error probability
fixed to . We refer to this as the "finite-length scaling" behavior.
This question was addressed by Strassen as well as Polyanskiy, Poor and Verdu,
and the result is that must grow at least as the square of the reciprocal
of .
Polar codes are optimal in the sense that they achieve capacity. In this
paper, we are asking to what degree they are also optimal in terms of their
finite-length behavior. Our approach is based on analyzing the dynamics of the
un-polarized channels. The main results of this paper can be summarized as
follows. Consider the sum of Bhattacharyya parameters of sub-channels chosen
(by the polar coding scheme) to transmit information. If we require this sum to
be smaller than a given value , then the required block-length
scales in terms of the rate as , where is a positive
constant that depends on and , and .
Also, we show that with the same requirement on the sum of Bhattacharyya
parameters, the block-length scales in terms of the rate like , where is a constant that
depends on and , and .Comment: In IEEE Transactions on Information Theory, 201
- âŠ