An Upper Bound on the Capacity of non-Binary Deletion Channels

We derive an upper bound on the capacity of non-binary deletion channels. Although binary deletion channels have received significant attention over the years, and many upper and lower bounds on their capacity have been derived, such studies for the non-binary case are largely missing. The state of the art is the following: as a trivial upper bound, capacity of an erasure channel with the same input alphabet as the deletion channel can be used, and as a lower bound the results by Diggavi and Grossglauser are available. In this paper, we derive the first non-trivial non-binary deletion channel capacity upper bound and reduce the gap with the existing achievable rates. To derive the results we first prove an inequality between the capacity of a 2K-ary deletion channel with deletion probability $d$, denoted by $C_{2K}(d)$, and the capacity of the binary deletion channel with the same deletion probability, $C_2(d)$, that is, $C_{2K}(d)\leq C_2(d)+(1-d)\log(K)$. Then by employing some existing upper bounds on the capacity of the binary deletion channel, we obtain upper bounds on the capacity of the 2K-ary deletion channel. We illustrate via examples the use of the new bounds and discuss their asymptotic behavior as $d \rightarrow 0$.Comment: accepted for presentation in ISIT 201

A Note on the Deletion Channel Capacity

Memoryless channels with deletion errors as defined by a stochastic channel matrix allowing for bit drop outs are considered in which transmitted bits are either independently deleted with probability $d$ or unchanged with probability $1-d$. Such channels are information stable, hence their Shannon capacity exists. However, computation of the channel capacity is formidable, and only some upper and lower bounds on the capacity exist. In this paper, we first show a simple result that the parallel concatenation of two different independent deletion channels with deletion probabilities $d_1$ and $d_2$, in which every input bit is either transmitted over the first channel with probability of $\lambda$ or over the second one with probability of $1-\lambda$, is nothing but another deletion channel with deletion probability of $d=\lambda d_1+(1-\lambda)d_2$. We then provide an upper bound on the concatenated deletion channel capacity $C(d)$ in terms of the weighted average of $C(d_1)$, $C(d_2)$ and the parameters of the three channels. An interesting consequence of this bound is that $C(\lambda d_1+(1-\lambda))\leq \lambda C(d_1)$ which enables us to provide an improved upper bound on the capacity of the i.i.d. deletion channels, i.e., $C(d)\leq 0.4143(1-d)$ for $d\geq 0.65$. This generalizes the asymptotic result by Dalai as it remains valid for all $d\geq 0.65$. Using the same approach we are also able to improve upon existing upper bounds on the capacity of the deletion/substitution channel.Comment: Submitted to the IEEE Transactions on Information Theor

Multiwavelength observations of the black hole transient XTE J1752-223 during its 2010 outburst decay

Galactic black hole transients show many interesting phenomena during outburst decays. We present simultaneous X-ray (RXTE, Swift, and INTEGRAL), and optical/near-infrared (O/NIR) observations (SMARTS), of the X-ray transient, XTE J1752-223 during its outburst decay in 2010. The multi- wavelength observations of 150 days in 2010 cover the transition from soft to hard spectral state. The evolution of ATCA/VLBI radio observations are shown to confirm the compact jet appearance. The source shows flares in O/NIR during changes in X-ray and radio properties. One of those flares is bright and long, and starts about 20 days after the transition in timing. Other, smaller flares occur along with the transition in timing and increase in power-law flux, and also right after the detection of the core with VLBI. Furthermore, using the simultaneous broadband X-ray spectra including IN- TEGRAL, we found that a high energy cut-off is necessary with a folding energy at around 250 keV around the time that the compact jet is forming. The broad band spectrum can also be fitted equally well with a Comptonization model. In addition, using photoelectric absorption edges in the XMM– Newton RGS X-ray spectra and the extinction of red clump giants in the direction of the source, we found a lower limit on the distance of > 5 kpc

Complete Multiwavelength Evolution of Galactic Black Hole Transients During Outburst Decay II: Compact Jets and X-ray Variability Properties

We investigated the relation between compact jet emission and X-ray variability properties of all black hole transients with multiwavelength coverage during their outburst decays. We studied the evolution of all power spectral components (including low frequency quasi-periodic oscillations), and related this evolution to changes in jet properties tracked by radio and infrared observations. We grouped sources according to their tracks in radio/X-ray luminosity relation, and show that the standards show stronger broadband X-ray variability than outliers at a given X-ray luminosity when the compact jet turned on. This trend is consistent with the internal shock model and can be important for the understanding of the presence of tracks in the radio/X-ray luminosity relation. We also observed that the total and the QPO rms amplitudes increase together during the earlier part of the outburst decay, but after the compact jet turns either the QPO disappears or its rms amplitude decreases significantly while the total rms amplitudes remain high. We discuss these results with a scenario including a variable corona and a non-variable disk with a mechanism for the QPO separate from the mechanism that create broad components. Finally, we evaluated the timing predictions of the magnetically dominated accretion flow model which can explain the presence of tracks in the radio/X-ray luminosity relation.Comment: Accepted for publication by Ap

On LDPC Codes for Gaussian Interference Channels

In this paper, we focus on the two-user Gaussian interference channel (GIC), and study the Han-Kobayashi (HK) coding/decoding strategy with the objective of designing low-density parity-check (LDPC) codes. A code optimization algorithm is proposed which adopts a random perturbation technique via tracking the average mutual information. The degree distribution optimization and convergence threshold computation are carried out for strong and weak interference channels, employing binary phase-shift keying (BPSK). Under strong interference, it is observed that optimized codes operate close to the capacity boundary. For the case of weak interference, it is shown that via the newly designed codes, a nontrivial rate pair is achievable, which is not attainable by single user codes with time-sharing. Performance of the designed LDPC codes are also studied for finite block lengths through simulations of specific codes picked from the optimized degree distributions.Comment: ISIT 201

A Newman-Penrose Calculator for Instanton Metrics

We present a Maple11+GRTensorII based symbolic calculator for instanton metrics using Newman-Penrose formalism. Gravitational instantons are exact solutions of Einstein's vacuum field equations with Euclidean signature. The Newman-Penrose formalism, which supplies a toolbox for studying the exact solutions of Einstein's field equations, was adopted to the instanton case and our code translates it for the computational use.Comment: 13 pages. Matches the published version. The web page of the codes is changed as https://github.com/tbirkandan/NPInstanto