Lossless and near-lossless source coding for multiple access networks

A multiple access source code (MASC) is a source code designed for the following network configuration: a pair of correlated information sequences {X-i}(i=1)(infinity), and {Y-i}(i=1)(infinity) is drawn independent and identically distributed (i.i.d.) according to joint probability mass function (p.m.f.) p(x, y); the encoder for each source operates without knowledge of the other source; the decoder jointly decodes the encoded bit streams from both sources. The work of Slepian and Wolf describes all rates achievable by MASCs of infinite coding dimension (n --> infinity) and asymptotically negligible error probabilities (P-e((n)) --> 0). In this paper, we consider the properties of optimal instantaneous MASCs with finite coding dimension (n 0) performance. The interest in near-lossless codes is inspired by the discontinuity in the limiting rate region at P-e((n)) = 0 and the resulting performance benefits achievable by using near-lossless MASCs as entropy codes within lossy MASCs. Our central results include generalizations of Huffman and arithmetic codes to the MASC framework for arbitrary p(x, y), n, and P-e((n)) and polynomial-time design algorithms that approximate these optimal solutions

Lossless source coding for multiple access networks

A multiple access source code (MASC) is a source code designed for the following network configuration: a pair of jointly distributed information sequences {Xi}i=1∞ and {Yi}i=1∞ is drawn i.i.d. according to joint probability mass function (p.m.f.) p(x,y); the encoder for each source operates without knowledge of the other source; the decoder receives the encoded bit streams of both sources. The rate region for MASCs with arbitrarily small but non-zero error probabilities was studied by Slepian and Wolf. In this paper, we consider the properties of optimal truly lossless MASCs and apply our findings to practical truly lossless and near lossless code design

Optimal code design for lossless and near lossless source coding in multiple access networks

A multiple access source code (MASC) is a source code designed for the following network configuration: a pair of correlated information sequences {Xi}i=1∞ and {Yi }i=1∞ is drawn i.i.d. according to the joint probability mass function (p.m.f.) p(x,y); the encoder for each source operates without knowledge of the other source; the decoder jointly decodes the encoded bit streams from both sources. The work of Slepian and Wolf (1973) describes all rates achievable by MASCs with arbitrarily small but non-zero error probabilities but does not address truly lossless coding or code design. We consider practical code design for lossless and near lossless MASCs. We generalize the Huffman and arithmetic code design algorithms to attain the corresponding optimal MASC codes for arbitrary p.m.f. p(x,y). Experimental results comparing the optimal achievable rate region to the Slepian-Wolf region are included

Broadcast system source codes: a new paradigm for data compression

Broadcast systems play a central role in an enormous variety of network technologies in which one system node must simultaneously send either the same or different information to multiple nodes in the network. Systems incorporating broadcast components include such diverse technologies as wireless communications systems, web servers, distributed computing devices, and video conferencing systems. Currently, the compression algorithms (or source codes) employed in these devices fail to take advantage of the characteristics specific to broadcast systems. Instead, they treat a single node transmitting information to a collection of receivers as a collection of single-transmitter single-receiver communications problems and employ an independent source code on each. This approach is convenient, since it allows direct application of traditional compression techniques in a wide variety of broadcast system applications. Nonetheless, we here argue that the approach is inherently flawed. Our innovation in this paper is to treat the general broadcast system (with an arbitrary number of receivers and both specific and common information) as an inseparable whole and consider the resulting source coding ramifications. The result is a new paradigm for data compression on general broadcast systems. In this work, we describe this broadcast system source coding paradigm and examine the potential gains achievable by moving away from more conventional methods

Uniquely decodable multiple access source codes

The Slepian-Wolf bound raises interest in lossless code design for multiple access networks. Previous work treats instantaneous codes. We generalize the Sardinas and Patterson test and bound the achievable rate region for uniquely decodable codes. The Kraft inequality is generalised to produce the necessary conditions on the codeword lengths for uniquely decodable-side information source code

Rational design of super-alkalis and their role in CO2 activation

Super-alkalis are clusters of atoms. With ionization potentials smaller than those of the alkali atoms, they are playing an increasing role in chemistry as highlighted by recent applications in solar cells as well as in Li-ion batteries. For the past 40 years superalkalis were designed using inorganic elements with the sp orbital character. Here, we show that a large class of superalkalis composed of only simple metal atoms, transition metal complexes as well as organic molecules can be designed by making use of electron counting rules beyond the octet rule. Examples include Al-3(+), Mn(B3N3H6)(2)(+), B9C3H12+, and C5NH6+ which obey the jellium shell closure rule, the 18-electron rule, the Wade-Mingos rule, and Huckel\u27s aromatic rule, respectively. We further show that the ability of superalkalis to transfer an electron easily can be used to activate a CO2 molecule by transforming it from a linear to a bent structure. These results, based on density functional theory with generalized gradient approximation for exchange-correlation potential, open the door to a new class of catalysts for CO2 activation

Systematic study of the singularity mechanism in heavy quarkonium decays

We investigate in detail the role of heavy meson loops in the transition from $J^{PC}=1^{--}$ sources to candidates for QCD "exotics", such as $Z_c(3900)$, $Z_b(10610)$ and $Z_b'(10650)$. We demonstrate that, if a vector state strongly couples to a heavy meson pair in an $S$--wave and this system decays to another heavy meson pair (e.g. via pion emission), again in an $S$-wave, the pertinent diagrams get enhanced significantly, if the intermediate states are (near) on--shell and have small relative momenta. In a limited kinematic range this mechanism generates "singularity regions" that lead to the creation of a large number of low energy heavy meson pairs, providing an ideal environment for the formation of hadron-hadron bound states or resonances. For instance, we predict that the signals for $Z_b$ and $Z_b'$ should be a lot stronger in $\Upsilon(6S)$ decays due to this mechanism, if these states are indeed hadron-hadron resonances. The findings of this work should be valuable for deepening our understanding of the nature of the mentioned states.Comment: 6 pages, 8 eps figures, version to appear in Phys.Lett.

Mean-Variance Asset-Liability Management with State-Dependent Risk Aversion

In this paper, we consider the asset-liability management under the mean-variance criterion. The financial market consists of a risk-free bond and a stock whose price process is modeled by a geometric Brownian motion. The liability of the investor is uncontrollable and is modeled by another geometric Brownian motion. We consider a specific state-dependent risk aversion which depends on a power function of the liability. By solving a flow of FBSDEs with bivariate state process, we obtain the equilibrium strategy among all the open-loop controls for this time-inconsistent control problem. It shows that the equilibrium strategy is a feedback control of the liability.Comment: 12 figure