Adaptive Linear Programming Decoding of Polar Codes

Polar codes are high density parity check codes and hence the sparse factor graph, instead of the parity check matrix, has been used to practically represent an LP polytope for LP decoding. Although LP decoding on this polytope has the ML-certificate property, it performs poorly over a BAWGN channel. In this paper, we propose modifications to adaptive cut generation based LP decoding techniques and apply the modified-adaptive LP decoder to short blocklength polar codes over a BAWGN channel. The proposed decoder provides significant FER performance gain compared to the previously proposed LP decoder and its performance approaches that of ML decoding at high SNRs. We also present an algorithm to obtain a smaller factor graph from the original sparse factor graph of a polar code. This reduced factor graph preserves the small check node degrees needed to represent the LP polytope in practice. We show that the fundamental polytope of the reduced factor graph can be obtained from the projection of the polytope represented by the original sparse factor graph and the frozen bit information. Thus, the LP decoding time complexity is decreased without changing the FER performance by using the reduced factor graph representation.Comment: 5 pages, 8 figures, to be presented at the IEEE Symposium on Information Theory (ISIT) 201

J021659-044920: a relic giant radio galaxy at z ~ 1.3

We report the discovery of a relic Giant Radio Galaxy (GRG) J021659-044920 at redshift $z \sim 1.3$ that exhibits large-scale extended, nearly co-spatial, radio and X-ray emission from radio lobes, but no detection of Active Galactic Nuclei core, jets and hotspots. The total angular extent of the GRG at the observed frame 0.325 GHz, using Giant Metrewave Radio Telescope observations is found to be ${\sim}$ 2.4 arcmin, that corresponds to a total projected linear size of $\sim$ 1.2 Mpc. The integrated radio spectrum between 0.240 and 1.4 GHz shows high spectral curvature (${\alpha}_{\rm 0.610~GHz}^{\rm 1.4~GHz} - {\alpha}_{\rm 0.240~GHz}^{\rm 0.325~GHz}$ $>$ 1.19) with sharp steepening above 0.325 GHz, consistent with relic radio emission that is $\sim$ 8 $\times$ 10$^{6}$ yr old. The radio spectral index map between observed frame 0.325 and 1.4~GHz for the two lobes varies from 1.4 to 2.5 with the steepening trend from outer-end to inner-end, indicating backflow of plasma in the lobes. The extended X-ray emission characterized by an absorbed power-law with photon index $\sim$ 1.86 favours inverse-Compton scattering of the Cosmic Microwave Background (ICCMB) photons as the plausible origin. Using both X-ray and radio fluxes under the assumption of ICCMB we estimate the magnetic field in the lobes to be 3.3 $\mu$G. The magnetic field estimate based on energy equipartition is $\sim$ 3.5 $\mu$G. Our work presents a case study of a rare example of a GRG caught in dying phase in the distant Universe.Comment: 10 pages, 5 figures, 3 tables. Published in MNRAS. Corrected typos and added a referenc

On the nature of infrared-faint radio sources in the SXDF and VLA-VVDS fields

Infrared-Faint Radio Sources (IFRSs) are an unusual class of objects that are relatively bright at radio wavelengths but have faint or undetected infrared counterparts even in deep surveys. We identify and investigate the nature of IFRSs using deep radio (S$_{\rm 1.4~GHz}$ $\sim$ 100 $\mu$Jy beam$^{-1}$ at 5$\sigma$), optical (m$_{\rm r}$ $\sim$ 26 - 27.7 at 5$\sigma$), and near-IR (S$_{\rm 3.6~{\mu}m}$ $\sim$ 1.3 - 2.0 $\mu$Jy beam$^{-1}$ at 5$\sigma$) data available in two deep fields namely the Subaru X-ray Deep Field (SXDF) and the Very Large Array - VIMOS VLT Deep Survey (VLA-VVDS) field. In 1.8 deg$^{2}$ of the two fields we identify a total of nine confirmed and ten candidate IFRSs. We find that our IFRSs are high-redshift radio-loud AGN, with 12/19 sources having redshift estimates in the range of $z$ $\sim$ 1.7 - 4.3, while a limit of $z$ $\geq$ 2.0 is placed for the remaining seven sources. Notably, our study finds, for the first time, IFRSs with measured redshift $>$ 3.0, and also, the redshift estimates for IFRSs in the faintest 3.6 $\mu$m flux regime i.e., S$_{\rm 3.6~{\mu}m}$ $<$ 1.3 ${\mu}$Jy. Radio observations show that our IFRSs exhibit both compact unresolved as well as extended double-lobe morphologies, and have predominantly steep radio spectra between 1.4 GHz and 325 MHz. The non-detection of all but one IFRSs in the X-ray band and the optical-to-MIR colour (m$_{\rm r}$ - m$_{\rm 24~{\mu}m}$) suggest that a significant fraction of IFRSs are likely to be hosted in dusty obscured galaxies.Comment: 20 pages, 8 figures, 4 tables, accepted for publication in MNRA