Quantum Error Correction via Codes over GF(2)

It is well known that n-length stabilizer quantum error correcting codes (QECCs) can be obtained via n-length classical error correction codes (CECCs) over GF(4), that are additive and self-orthogonal with respect to the trace Hermitian inner product. But, most of the CECCs have been studied with respect to the Euclidean inner product. In this paper, it is shown that n-length stabilizer QECCs can be constructed via 371 length linear CECCs over GF(2) that are self-orthogonal with respect to the Euclidean inner product. This facilitates usage of the widely studied self-orthogonal CECCs to construct stabilizer QECCs. Moreover, classical, binary, self-orthogonal cyclic codes have been used to obtain stabilizer QECCs with guaranteed quantum error correcting capability. This is facilitated by the fact that (i) self-orthogonal, binary cyclic codes are easily identified using transform approach and (ii) for such codes lower bounds on the minimum Hamming distance are known. Several explicit codes are constructed including two pure MDS QECCs.

Low-Complexity Near-ML Decoding of Large Non-Orthogonal STBCs using Reactive Tabu Search

Non-orthogonal space-time block codes (STBC) with large dimensions are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) as well as full transmit diversity. Decoding of non-orthogonal STBCs with large dimensions has been a challenge. In this paper, we present a reactive tabu search (RTS) based algorithm for decoding non-orthogonal STBCs from cyclic division algebras (CDA) having largedimensions. Under i.i.d fading and perfect channel state information at the receiver (CSIR), our simulation results show that RTS based decoding of 12 X 12 STBC from CDA and 4-QAM with 288 real dimensions achieves i) 10(-3) uncoded BER at an SNR of just 0.5 dB away from SISO AWGN performance, and ii) a coded BER performance close to within about 5 dB of the theoretical MIMO capacity, using rate-3/4 turbo code at a spectral efficiency of 18 bps/Hz. RTS is shown to achieve near SISO AWGN performance with less number of dimensions than with LAS algorithm (which we reported recently) at some extra complexity than LAS. We also report good BER performance of RTS when i.i.d fading and perfect CSIR assumptions are relaxed by considering a spatially correlated MIMO channel model, and by using a training based iterative RTS decoding/channel estimation scheme.

Low-Complexity Near-MAP Decoding of Large Non-Orthogonal STBCs Using PDA

Non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) are attractive because they can simultaneously achieve both high spectral efficiencies (same spectral efficiency as in V-BLAST for a given number of transmit antennas) as well as full transmit diversity. Decoding of non-orthogonal STBCs with hundreds of dimensions has been a challenge. In this paper, we present a probabilistic data association (PDA) based algorithm for decoding non-orthogonal STBCs with large dimensions. Our simulation results show that the proposed PDA-based algorithm achieves near SISO AWGN uncoded BER as well as near-capacity coded BER (within 5 dB of the theoretical capacity) for large non-orthogonal STBCs from CDA. We study the effect of spatial correlation on the BER, and show that the performance loss due to spatial correlation can be alleviated by providing more receive spatial dimensions. We report good BER performance when a training-based iterative decoding/channel estimation is used (instead of assuming perfect channel knowledge) in channels with large coherence times. A comparison of the performances of the PDA algorithm and the likelihood ascent search (LAS) algorithm (reported in our recent work) is also presented.

Belief Propagation Based Decoding of Large Non-Orthogonal STBCs

In this paper,we present a belief propagation (BP) based algorithm for decoding non-orthogonal space-time block codes (STBC) from cyclic division algebras (CDA) having large dimensions. The proposed approachinvolves message passing on Markov random field (MRF) representation of the STBC MIMO system. Adoption of BP approach to decode non-orthogonal STBCs of large dimensions has not been reported so far. Our simulation results show that the proposed BP-based decoding achieves increasingly closer to SISO AWGN performance for increased number of dimensions. In addition, it also achieves near-capacity turbo coded BER performance; for e.g., with BP decoding of 24 x 24 STBC from CDA using BPSK (i.e.,n576 real dimensions) and rate-1/2 turbo code (i.e., 12 bps/Hz spectral efficiency), coded BER performance close to within just about 2.5 dB from the theoretical MIMO capacity is achieved.

Ideal Structure of the Silver Code

The Silver code has captured a lot of attention in the recent past,because of its nice structure and fast decodability. In their recent paper, Hollanti et al. show that the Silver code forms a subset of the natural order of a particular cyclic division algebra (CDA). In this paper, the algebraic structure of this subset is characterized. It is shown that the Silver code is not an ideal in the natural order but a right ideal generated by two elements in a particular order of this CDA. The exact minimum determinant of the normalized Silver code is computed using the ideal structure of the code. The construction of Silver code is then extended to CDAs over other number fields.

Steric effects on the ultraviolet absorption of 1,2-enedioic and related systems

1,2-Enedioic systems, being sterically perturbed from planarity do not show the effect of the extended conjugation expected of a (formal) trienic entity. In the absence of a model which approximates to a uniplanar situation, the strategy of replacing an ester group in the enedioates by a cyano (for which less stringent steric demand may be presumed) and noting the correction concomitant to this replacement was adopted to arrive at a notional figure for the position of maximal absorption in the planar enedioates. From this the conclusion, subject to substantiation by molecular mechanical or quantum chemical calculations, was drawn that even the E-isomeric and comparatively less substituted enedioates are highly sterically perturbed. An alternative to an earlier explanation of the bathochromic shift of absorption maxima encountered in the 5-cyclic ene-ester and ene-nitrile, relative to the 6-cyclic analogues (observed also with the enedioates and cyanovinyl ester systems), seen later to have been based on unwarranted premises, has been advanced. A comment on the absorption characteristics of enedioic anhydrides has been appended.

Geometry changes induced by negative hyperconjugative interactions involving carbonyl and thiocarbonyl groups

MNDO geometry optimizations have been carried out on a series of acyclic and cyclic unsymmetrically disubstituted carbonyl and thiocarbonyl compounds. The C=X unit shows a consistent and often sizeable tilt towards one of the substituents, following the order O > Snot, vert, similarN > C > B. Reference ab initio calculations and available experimental results support the MNDO results. The effect, which is particularly dramatic in small rings, is attributed primarily to favorable negative hyperconjugative interaction between the lone pair on X and a low lying adjacent σ* orbital. Such an interaction can lead to highly distorted structures, including perhaps to a planar molecule with an inverted sp2 carbon center.

cAMP-regulated Protein Lysine Acetylases in Mycobacteria

Cyclic AMP synthesized by Mycobacterium tuberculosis has been shown to play a role in pathogenesis. However, the high levels of intracellularcAMP found in both pathogenic and nonpathogenic mycobacteria suggest that additional and important biological processes are regulated by characterization of novel cAMP-binding proteins in M. smegmatis and M. tuberculosis (MSMEG_5458 and Rv0998, respectively) that contain a cyclic nucleotide binding domain fused to a domain that shows similarity to the GNAT family of acetyltransferases. We detect protein lysine acetylation in mycobacteria and identify a universal stress protein (USP) as a substrate of MSMEG_5458. Acetylation of a lysine residue in USP is regulated by cAMP, and using a strain deleted for MSMEG_5458, we show that USP is indeed an in vivo substrate for MSMEG_5458. The Rv0998 protein shows a strict cAMP-dependent acetylation of USP, despite a lower affinity for cAMP than MSMEG_5458. Thus, this report not only represents the first demonstration of protein lysine acetylation in mycobacteria but also describes a unique functional interplay between a cyclic nucleotide binding domain and a protein acetyltransferase.

Ferrocene-Promoted Photoactivated DNA Cleavage and Anticancer Activity of Terpyridyl Copper(II) Phenanthroline Complexes

Ferrocene-appended copper(II) complexes [Cu( Fc-tpy)(B)](ClO4)(2) (1-3) and [Cu(Ph-tpy)(dppz)](ClO4)(2) (4) as control, where Fc-tpy is 4'-ferroceny1-2,2':6',2 ''-terpyridine, Ph-tpy is 4'-pheny1-2,2':6',2 ''-terpyridine, and B is a phenanthroline base, viz., 1,10-phenanthroline (phen, 1), dipyridoquinoxaline (dpq, 2), and dipyridophenazine (dppz, 3), were prepared and structurally characterized, and their DNA binding, photoactivated DNA cleavage activity, and cytotoxic properties were studied [Fe = (eta(5)-C5H4)Fe-11(eta(5)-C5H5)]. Complexes 1 and 3 as hexafluorophosphate salts were structurally characterized by X-ray crystallography. Molecular structures of [Cu(Fc-tpy)(phen)](PF6)(2) (1a) and [Cu(Fc-tpy)(dppz)](PF6)(2)center dot MeCN (3a center dot MeCN) show a distorted square-pyramidal geometry at copper(II), with the Fc-tpy ligand and the phenanthroline base showing respective tridentate and bidentate binding modes. The phenanthroline base exhibits axial-equatorial bonding, while the Fc-tpy ligand binds at the basal plane. The complexes showed quasi-reversible cyclic voltammetric responses near 0.45 and -0.3 V vs SCE in aqueous DMF-0.1 M KCl assignable to the Fc(+)-Fc and Cu(II) Cu(1) redox couples, respectively. The complexes bind to DNA, giving K-b values of 1.4 x 10(4) to 5.6 x 10(5) M-1 in the order 4 similar to 3 > 2 > 1. Thermal denaturation and viscometric titration data suggest groove and/or partial intercalative mode of DNA binding of the complexes. The complexes showed chemical nuclease activity in the presence of 3-mercaptopropionic acid (0.5 mM) or H2O2 (0.25 mM). Complexes 2-4 showed plasmid DNA cleavage activity in visible light, forming (OH)-O-center dot radicals. The Fc-tpy complex 3 showed better DNA photocleavage activity than its Ph-tpy analogue. The ferrocene moiety in the dppz complex 3 makes it more photocytotoxic than the Ph-tpy analogue 4 in HeLa cells.

Tetrathiomolybdate Mediated Rearrangement of Aziridinemethanol Tosylates: A Thia-Aza-Payne Rearrangement

Aziridinemethanol sulfonate esters react with tetrathiomolybdate 1 to give thiirane derivatives as the major product and cyclic disulfides as minor product under mild reaction conditions via an unprecedented thia-aza-Payne-type rearrangement. Interestingly, when the reaction of I was carried out with 2-aziridino-cyclohexanol derivatives it resulted in the formation of thia-bicyclo[3.1.1]heptane or dithia-bicyclo[3.2.1]octane derivatives.

A Training-Based Iterative Detection/Channel Estimation Scheme for Large Non-Orthogonal STBC MIMO Systems

In this paper, we propose a training-based channel estimation scheme for large non-orthogonal space-time block coded (STBC) MIMO systems.The proposed scheme employs a block transmission strategy where an N-t x N-t pilot matrix is sent (for training purposes) followed by several N-t x N-t square data STBC matrices, where Nt is the number of transmit antennas. At the receiver, we iterate between channel estimation (using an MMSE estimator) and detection (using a low-complexity likelihood ascent search (LAS) detector) till convergence or for a fixed number of iterations. Our simulation results show that excellent bit error rate and nearness-to-capacity performance are achieved by the proposed scheme at low complexities. The fact that we could show such good results for large STBCs (e.g., 16 x 16 STBC from cyclic division algebras) operating at spectral efficiencies in excess of 20 bps/Hz (even after accounting for the overheads meant for pilot-based channel estimation and turbo coding) establishes the effectiveness of the proposed scheme.