Correcting Grain-Errors in Magnetic Media

This paper studies new bounds and code constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors. We demonstrate that a permutation of the classical group codes (e.g., Constantin-Rao codes) can correct a single grain-error. In many cases of interest, our results improve upon the currently best known bounds and constructions. Some of the approaches adopted in the context of grain-errors may have application to related channel models

1 Bounds and Constructions for Granular Media Coding

Abstract—Bounds on the rates of grain-correcting codes are presented. The lower bounds are Gilbert–Varshamov-like ones, whereas the upper bounds improve on the previously known result by Mazumdar et al. Constructions of t-grain-correcting codes of length n for certain values of n and t are discussed. Finally, an infinite family of codes of rate approaching 1 that can detect an arbitrary number of grain errors is shown to exist. Index Terms—convex optimization, Gilbert–Varshamov bound, grain-correcting codes, granular media, lower bounds, magnetic recording, Markov chain, upper bounds. I

IRS Scan-mapping of the Wasp-waist Nebula (IRAS 16253–2429). I. Derivation of Shock Conditions from H_2 Emission and Discovery of 11.3 μm PAH Absorption

The outflow driven by the Class 0 protostar, IRAS 16253–2429, is associated with bipolar cavities visible in scattered mid-infrared light, which we refer to as the Wasp-Waist Nebula. InfraRed Spectometer (IRS) scan mapping with the Spitzer Space Telescope of a ~1' × 2' area centered on the protostar was carried out. The outflow is imaged in six pure rotational (0-0 S(2) through 0-0 S(7)) H_2 lines, revealing a distinct, S-shaped morphology in all maps. A source map in the 11.3 μm polycyclic aromatic hydrocarbon (PAH) feature is presented in which the protostellar envelope appears in absorption. This is the first detection of absorption in the 11.3 μm PAH feature. Spatially resolved excitation analysis of positions in the blue- and redshifted outflow lobes, with extinction-corrections determined from archival Spitzer 8 μm imaging, shows remarkably constant temperatures of ~1000 K in the shocked gas. The radiated luminosity in the observed H_2 transitions is found to be 1.94 ± 0.05 × 10^(–5) L_⊙ in the redshifted lobe and 1.86 ± 0.04 × 10^(–5) L_⊙ in the blueshifted lobe. These values are comparable to the mechanical luminosity of the flow. By contrast, the mass of hot (T ~ 1000 K) H_2 gas is 7.95 ± 0.19 × 10^(–7) M_⊙ in the redshifted lobe and 5.78 ± 0.17 × 10^(–7) M_⊙ in the blueshifted lobe. This is just a tiny fraction, of order 10^(–3), of the gas in the cold (30 K), swept-up gas mass derived from millimeter CO observations. The H_2 ortho/para ratio of 3:1 found at all mapped points in this flow suggests previous passages of shocks through the gas. Comparison of the H_2 data with detailed shock models of Wilgenbus et al. shows the emitting gas is passing through Jump (J-type) shocks. Pre-shock densities of 10^4 cm^(–3)≤ n _H ≤ 10^5 cm^(–3) are inferred for the redshifted lobe and n _H ≤ 10^3 cm^(–3) for the blueshifted lobe. Shock velocities are 5 km s^(–1) ≤ v_s ≤ 10 km s^(–1) for the redshifted gas and v_s = 10 km s^(–1) for the blueshifted gas. Initial transverse (to the shock) magnetic field strengths for the redshifted lobe are in the range 10-32 μG, and just 3 μG for the blueshifted lobe. A cookbook for using the CUBISM contributed software for IRS spectral mapping data is presented in the Appendix

Publications of the Jet Propulsion Laboratory, July 1964 through June 1965

JPL publications bibliography with abstracts - reports on DSIF, Mariner program, Ranger project, Surveyor project, and other space programs, and space science

On Coding and Detection Techniques for Two-Dimensional Magnetic Recording

Edited version embargoed until 15.04.2020 Full version: Access restricted permanently due to 3rd party copyright restrictions. Restriction set on 15/04/2019 by AS, Doctoral CollegeThe areal density growth of magnetic recording systems is fast approaching the superparamagnetic limit for conventional magnetic disks. This is due to the increasing demand for high data storage capacity. Two-dimensional Magnetic Recording (TDMR) is a new technology aimed at increasing the areal density of magnetic recording systems beyond the limit of current disk technology using conventional disk media. However, it relies on advanced coding and signal processing techniques to achieve areal density gains. Current state of the art signal processing for TDMR channel employed iterative decoding with Low Density Parity Check (LDPC) codes, coupled with 2D equalisers and full 2D Maximum Likelihood (ML) detectors. The shortcoming of these algorithms is their computation complexity especially with regards to the ML detectors which is exponential with respect to the number of bits involved. Therefore, robust low-complexity coding, equalisation and detection algorithms are crucial for successful future deployment of the TDMR scheme. This present work is aimed at finding efficient and low-complexity coding, equalisation, detection and decoding techniques for improving the performance of TDMR channel and magnetic recording channel in general. A forward error correction (FEC) scheme of two concatenated single parity bit systems along track separated by an interleaver has been presented for channel with perpendicular magnetic recording (PMR) media. Joint detection decoding algorithm using constrained MAP detector for simultaneous detection and decoding of data with single parity bit system has been proposed. It is shown that using the proposed FEC scheme with the constrained MAP detector/decoder can achieve a gain of up to 3dB over un-coded MAP decoder for 1D interference channel. A further gain of 1.5 dB was achieved by concatenating two interleavers with extra parity bit when data density along track is high. The use of single bit parity code as a run length limited code as well as an error correction code is demonstrated to simplify detection complexity and improve system performance. A low-complexity 2D detection technique for TDMR system with Shingled Magnetic Recording Media (SMR) was also proposed. The technique used the concatenation of 2D MAP detector along track with regular MAP detector across tracks to reduce the complexity order of using full 2D detection from exponential to linear. It is shown that using this technique can improve track density with limited complexity. Two methods of FEC for TDMR channel using two single parity bit systems have been discussed. One using two concatenated single parity bits along track only, separated by a Dithered Relative Prime (DRP) interleaver and the other use the single parity bits in both directions without the DRP interleaver. Consequent to the FEC coding on the channel, a 2D multi-track MAP joint detector decoder has been proposed for simultaneous detection and decoding of the coded single parity bit data. A gain of up to 5dB was achieved using the FEC scheme with the 2D multi-track MAP joint detector decoder over un-coded 2D multi-track MAP detector in TDMR channel. In a situation with high density in both directions, it is shown that FEC coding using two concatenated single parity bits along track separated by DRP interleaver performed better than when the single parity bits are used in both directions without the DRP interleaver.9mobile Nigeri

Astrophysical Shrapnel: Discriminating Among Near-Earth Stellar Explosion Sources of Live Radioactive Isotopes

We consider the production and deposition on Earth of isotopes with half-lives in the range 10$^{5}$ to 10$^{8}$ years that might provide signatures of nearby stellar explosions, extending previous analyses of Core-Collapse Supernovae (CCSNe) to include Electron-Capture Supernovae (ECSNe), Super-Asymptotic Giant Branch (SAGBs) stars, Thermonuclear/Type Ia Supernovae (TNSNe), and Kilonovae/Neutron Star Mergers (KNe). We revisit previous estimates of the $^{60}$Fe and $^{26}$Al signatures, and extend these estimates to include $^{244}$Pu and $^{53}$Mn. We discuss interpretations of the $^{60}$Fe signals in terrestrial and lunar reservoirs in terms of a nearby stellar ejection ~2.2 Myr ago, showing that (i) the $^{60}$Fe yield rules out the TNSN and KN interpretations, (ii) the $^{60}$Fe signals highly constrain a SAGB interpretation but do not completely them rule out, (iii) are consistent with a CCSN origin, and (iv) are highly compatible with an ECSN interpretation. Future measurements could resolve the radioisotope deposition over time, and we use the Sedov blast wave solution to illustrate possible time-resolved profiles. Measuring such profiles would independently probe the blast properties including distance, and would provide additional constraints the nature of the explosion.Comment: 38 pages, 6 figures. Comments welcom