Optimal Threshold-Based Multi-Trial Error/Erasure Decoding with the Guruswami-Sudan Algorithm

Traditionally, multi-trial error/erasure decoding of Reed-Solomon (RS) codes is based on Bounded Minimum Distance (BMD) decoders with an erasure option. Such decoders have error/erasure tradeoff factor L=2, which means that an error is twice as expensive as an erasure in terms of the code's minimum distance. The Guruswami-Sudan (GS) list decoder can be considered as state of the art in algebraic decoding of RS codes. Besides an erasure option, it allows to adjust L to values in the range 1<L<=2. Based on previous work, we provide formulae which allow to optimally (in terms of residual codeword error probability) exploit the erasure option of decoders with arbitrary L, if the decoder can be used z>=1 times. We show that BMD decoders with z_BMD decoding trials can result in lower residual codeword error probability than GS decoders with z_GS trials, if z_BMD is only slightly larger than z_GS. This is of practical interest since BMD decoders generally have lower computational complexity than GS decoders.Comment: Accepted for the 2011 IEEE International Symposium on Information Theory, St. Petersburg, Russia, July 31 - August 05, 2011. 5 pages, 2 figure

Optimal Thresholds for GMD Decoding with (L+1)/L-extended Bounded Distance Decoders

We investigate threshold-based multi-trial decoding of concatenated codes with an inner Maximum-Likelihood decoder and an outer error/erasure (L+1)/L-extended Bounded Distance decoder, i.e. a decoder which corrects e errors and t erasures if e(L+1)/L + t <= d - 1, where d is the minimum distance of the outer code and L is a positive integer. This is a generalization of Forney's GMD decoding, which was considered only for L = 1, i.e. outer Bounded Minimum Distance decoding. One important example for (L+1)/L-extended Bounded Distance decoders is decoding of L-Interleaved Reed-Solomon codes. Our main contribution is a threshold location formula, which allows to optimally erase unreliable inner decoding results, for a given number of decoding trials and parameter L. Thereby, the term optimal means that the residual codeword error probability of the concatenated code is minimized. We give an estimation of this probability for any number of decoding trials.Comment: Accepted for the 2010 IEEE International Symposium on Information Theory, Austin, TX, USA, June 13 - 18, 2010. 5 pages, 2 figure

Decoding Generalized Concatenated Codes Using Interleaved Reed-Solomon Codes

Generalized Concatenated codes are a code construction consisting of a number of outer codes whose code symbols are protected by an inner code. As outer codes, we assume the most frequently used Reed-Solomon codes; as inner code, we assume some linear block code which can be decoded up to half its minimum distance. Decoding up to half the minimum distance of Generalized Concatenated codes is classically achieved by the Blokh-Zyablov-Dumer algorithm, which iteratively decodes by first using the inner decoder to get an estimate of the outer code words and then using an outer error/erasure decoder with a varying number of erasures determined by a set of pre-calculated thresholds. In this paper, a modified version of the Blokh-Zyablov-Dumer algorithm is proposed, which exploits the fact that a number of outer Reed-Solomon codes with average minimum distance d can be grouped into one single Interleaved Reed-Solomon code which can be decoded beyond d/2. This allows to skip a number of decoding iterations on the one hand and to reduce the complexity of each decoding iteration significantly - while maintaining the decoding performance - on the other.Comment: Proceedings of the 2008 IEEE International Symposium on Information Theory, Toronto, ON, Canada, July 6 - 11, 2008. 5 pages, 2 figure

Adjuvant radiotherapy improves progression-free survival in intracranial atypical meningioma

BACKGROUND: Meningiomas are the most common primary tumors of the central nervous system. In patients with WHO grade I meningiomas no adjuvant therapy is recommended after resection. In case of anaplastic meningiomas (WHO grade III), adjuvant fractionated radiotherapy is generally recommended, regardless of the extent of surgical resection. For atypical meningiomas (WHO grade II) optimal postoperative management has not been clearly defined yet. METHODS: We conducted a retrospective analysis of patients treated for intracranial atypical meningioma at Charité Universitätsmedizin Berlin from March 1999 to October 2018. Considering the individual circumstances (risk of recurrence, anatomical location, etc.), patients were either advised to follow a wait-and-see approach or to undergo adjuvant radiotherapy. Primary endpoint was progression-free survival (PFS). RESULTS: This analysis included 99 patients with atypical meningioma (WHO grade II). Nineteen patients received adjuvant RT after primary tumor resection (intervention group). The remaining 80 patients did not receive any further adjuvant therapy after surgical resection (control group). Median follow-up was 37 months. Median PFS after primary resection was significantly longer in the intervention group than in the control group (64 m vs. 37 m, p = 0.009, HR = 0.204, 95% CI = 0.062-0.668). The influence of adjuvant RT was confirmed in multivariable analysis (p = 0.041, HR = 0.192, 95% CI = 0.039-0.932). CONCLUSIONS: Our study adds to the evidence that RT can improve PFS in patients with atypical meningioma

The Geometry of the Catalytic Active Site in [FeFe]-hydrogenases is Determined by Hydrogen Bonding and Proton Transfer

[FeFe]-hydrogenases are efficient metalloenzymes that catalyze the oxidation and evolution of molecular hydrogen, H2. They serve as a blueprint for the design of synthetic H2-forming catalysts. [FeFe]-hydrogenases harbor a six-iron cofactor that comprises a [4Fe-4S] cluster and a unique diiron site with cyanide, carbonyl, and hydride ligands. To address the ligand dynamics in catalytic turnover and upon carbon monoxide (CO) inhibition, we replaced the native aminodithiolate group of the diiron site by synthetic dithiolates, inserted into wild-type and amino acid variants of the [FeFe]-hydrogenase HYDA1 from Chlamydomonas reinhardtii. The reactivity with H2 and CO was characterized using in situ and transient infrared spectroscopy, protein crystallography, quantum chemical calculations, and kinetic simulations. All cofactor variants adopted characteristic populations of reduced species in the presence of H2 and showed significant changes in CO inhibition and reactivation kinetics. Differences were attributed to varying interactions between polar ligands and the dithiolate head group and/or the environment of the cofactor (i.e., amino acid residues and water molecules). The presented results show how catalytically relevant intermediates are stabilized by inner-sphere hydrogen bonding suggesting that the role of the aminodithiolate group must not be restricted to proton transfer. These concepts may inspire the design of improved enzymes and biomimetic H2-forming catalysts

Antikaon Production in Proton-Nucleus Reactions and the K−K^- properties in nuclear matter

We calculate the momentum-dependent potentials for $K^+$ and $K^-$ mesons in a dispersion approach at nuclear density $\rho_0$ using the information from the vacuum $K^+ N$ and $K^- N$ scattering amplitudes, however, leaving out the resonance contributions for the in-medium analysis. Whereas the $K^+$ potential is found to be repulsive ($\approx$ + 30 MeV) and to show only a moderate momentum dependence, the $K^-$ selfenergy at normal nuclear matter density turns out to be $\approx$ - 200 MeV at zero momentum in line with kaon atomic data, however, decreases rapidly in magnitude for higher momenta. The antikaon production in p + A reactions is calculated within a coupled transport approach and compared to the data at KEK including different assumptions for the antikaon potentials. Furthermore, detailed predictions are made for $p + ^{12}C$ and $p + ^{207}Pb$ reactions at 2.5 GeV in order to determine the momentum dependent antikaon potential experimentally.Comment: 27 pages, LaTeX, including 14 ps-figures, UGI-98-1

Bridging hydride at reduced H-cluster species in [FeFe]-hydrogenases revealed by infrared spectroscopy, isotope editing, and quantum chemistry

[FeFe]-Hydrogenases contain a H2-converting cofactor (H-cluster) in which a canonical [4Fe–4S] cluster is linked to a unique diiron site with three carbon monoxide (CO) and two cyanide (CN–) ligands (e.g., in the oxidized state, Hox). There has been much debate whether reduction and hydrogen binding may result in alternative rotamer structures of the diiron site in a single (Hred) or double (Hsred) reduced H-cluster species. We employed infrared spectro-electrochemistry and site-selective isotope editing to monitor the CO/CN– stretching vibrations in [FeFe]-hydrogenase HYDA1 from Chlamydomonas reinhardtii. Density functional theory calculations yielded vibrational modes of the diatomic ligands for conceivable H-cluster structures. Correlation analysis of experimental and computational IR spectra has facilitated an assignment of Hred and Hsred to structures with a bridging hydride at the diiron site. Pronounced ligand rotation during μH binding seems to exclude Hred and Hsred as catalytic intermediates. Only states with a conservative H-cluster geometry featuring a μCO ligand are likely involved in rapid H2 turnover