Jar Decoding: Non-Asymptotic Converse Coding Theorems, Taylor-Type Expansion, and Optimality

Recently, a new decoding rule called jar decoding was proposed; under jar decoding, a non-asymptotic achievable tradeoff between the coding rate and word error probability was also established for any discrete input memoryless channel with discrete or continuous output (DIMC). Along the path of non-asymptotic analysis, in this paper, it is further shown that jar decoding is actually optimal up to the second order coding performance by establishing new non-asymptotic converse coding theorems, and determining the Taylor expansion of the (best) coding rate $R_n (\epsilon)$ of finite block length for any block length $n$ and word error probability $\epsilon$ up to the second order. Finally, based on the Taylor-type expansion and the new converses, two approximation formulas for $R_n (\epsilon)$ (dubbed "SO" and "NEP") are provided; they are further evaluated and compared against some of the best bounds known so far, as well as the normal approximation of $R_n (\epsilon)$ revisited recently in the literature. It turns out that while the normal approximation is all over the map, i.e. sometime below achievable bounds and sometime above converse bounds, the SO approximation is much more reliable as it is always below converses; in the meantime, the NEP approximation is the best among the three and always provides an accurate estimation for $R_n (\epsilon)$. An important implication arising from the Taylor-type expansion of $R_n (\epsilon)$ is that in the practical non-asymptotic regime, the optimal marginal codeword symbol distribution is not necessarily a capacity achieving distribution.Comment: submitted to IEEE Transaction on Information Theory in April, 201

Capacity Analysis of Linear Operator Channels over Finite Fields

Motivated by communication through a network employing linear network coding, capacities of linear operator channels (LOCs) with arbitrarily distributed transfer matrices over finite fields are studied. Both the Shannon capacity $C$ and the subspace coding capacity $C_{\text{SS}}$ are analyzed. By establishing and comparing lower bounds on $C$ and upper bounds on $C_{\text{SS}}$, various necessary conditions and sufficient conditions such that $C=C_{\text{SS}}$ are obtained. A new class of LOCs such that $C=C_{\text{SS}}$ is identified, which includes LOCs with uniform-given-rank transfer matrices as special cases. It is also demonstrated that $C_{\text{SS}}$ is strictly less than $C$ for a broad class of LOCs. In general, an optimal subspace coding scheme is difficult to find because it requires to solve the maximization of a non-concave function. However, for a LOC with a unique subspace degradation, $C_{\text{SS}}$ can be obtained by solving a convex optimization problem over rank distribution. Classes of LOCs with a unique subspace degradation are characterized. Since LOCs with uniform-given-rank transfer matrices have unique subspace degradations, some existing results on LOCs with uniform-given-rank transfer matrices are explained from a more general way.Comment: To appear in IEEE Transactions on Information Theor

Microscopic and self-consistent description for neutron halo in deformed nuclei

A deformed relativistic Hartree-Bogoliubov theory in continuum has been developed for the study of neutron halos in deformed nuclei and the halo phenomenon in deformed weakly bound nuclei is investigated. Magnesium and neon isotopes are studied and some results are presented for the deformed neutron-rich and weakly bound nuclei 44Mg and 36Ne. The core of the former nucleus is prolate, but the halo has a slightly oblate shape. This indicates a decoupling of the halo orbitals from the deformation of the core. The generic conditions for the existence of halos in deformed nuclei and for the occurrence of this decoupling effect are discussed.Comment: 7 pages, 2 figures; invited talk at the XXXV Brazilian Workshop on Nuclear Physics, Sep 2-6, 2012, Maresias, Brazi

Halos in a deformed Relativistic Hartree-Bogoliubov theory in continuum

In this contribution we present some recent results about neutron halos in deformed nuclei. A deformed relativistic Hartree-Bogoliubov theory in continuum has been developed and the halo phenomenon in deformed weakly bound nuclei is investigated. These weakly bound quantum systems present interesting examples for the study of the interdependence between the deformation of the core and the particles in the halo. Magnesium and neon isotopes are studied and detailed results are presented for the deformed neutron-rich and weakly bound nuclei 42Mg. The core of this nucleus is prolate, but the halo has a slightly oblate shape. This indicates a decoupling of the halo orbitals from the deformation of the core. The generic conditions for the existence of halos in deformed nuclei and for the occurrence of this decoupling effect are discussed.Comment: 6 pages, 2 figures; invited talk at the 2nd Int. Conf. on Nuclear Structure & Dynamics (NSD12), Opatija, Croatia, 9-13 July 201

On Linear Operator Channels over Finite Fields

Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver. There are NO constraints on the distribution of the transformation matrix and the field size. Specifically, the optimality of subspace coding over LOCs is investigated. A lower bound on the maximum achievable rate of subspace coding is obtained and it is shown to be tight for some cases. The maximum achievable rate of constant-dimensional subspace coding is characterized and the loss of rate incurred by using constant-dimensional subspace coding is insignificant. The maximum achievable rate of channel training is close to the lower bound on the maximum achievable rate of subspace coding. Two coding approaches based on channel training are proposed and their performances are evaluated. Our first approach makes use of rank-metric codes and its optimality depends on the existence of maximum rank distance codes. Our second approach applies linear coding and it can achieve the maximum achievable rate of channel training. Our code designs require only the knowledge of the expectation of the rank of the transformation matrix. The second scheme can also be realized ratelessly without a priori knowledge of the channel statistics.Comment: 53 pages, 3 figures, submitted to IEEE Transaction on Information Theor

Radioactive Decay of Specific Heavy Elements as an Energy Source for Late-Time Kilonovae and Potential JWST Observations

Revealing the temporal evolution of individual heavy elements synthesized in the merger ejecta from binary neutron star mergers not only improves our understanding of the origin of heavy elements beyond iron but also clarifies the energy sources of kilonovae. In this work, we present a comprehensive analysis of the temporal evolution of the energy fraction of each nuclide based on the $r$-process nucleosynthesis simulations. The heavy elements dominating the kilonova emission within $\sim100$~days are identified, including $^{127}$Sb, $^{128}$Sb, $^{129}$Sb, $^{130}$Sb, $^{129}$Te, $^{132}$I, $^{222}$Rn, $^{223}$Ra, $^{224}$Ra, and $^{225}$Ac. It is found that the late-time kilonova light curve ($t\gtrsim20$~days) is highly sensitive to the presence of the heavy element $^{225}$Ac (with a half-life of 10.0~days). Our analysis shows that the James Webb Space Telescope (JWST), with its high sensitivity in the near-infrared band, is a powerful instrument for the identification of these specific heavy elements.Comment: 7 pages, 8 figures, accepted by MNRA

The effect of Etlingera elatior (Kantan) inflorescene aqueous extract on abberant crypy foci in Sprague dawley rats

This study investigated the effect of Kantan flowers (Etlingera elatior) aqueous extract on aberrant crypt foci (ACF) in Spraque dawley rats. They were divided into 8 groups; four groups each for cancer and normal. The rats were fed with respective concentrations of the flower extractions according to their groups. At the 17th week, the rats were sacrificed. The colons were removed and examined grossly and microscopically followed by scoring of aberrant crypt foci. Result showed no significant difference (p> 0.05) in the body weight increment,colon weight and colon pH among all groups also in the aberrant crypt foci (ACF) scores in proximal colon of cancer groups as well as in distal colon. Besides that, comparison between ACF score of proximal and distal colon using ANOVA and posthoc test revealed no significant differences (p> 0.05) in the ACF numbers between proximal and distal colon of rats. Histological result showed that no abnormal structures were seen in crypts of normal treatment groups Etlingera elatior inflorescence aqueous extract did not have significant effect in reducing aberrant crypt foci formation in Sprague dawley rats