Poincare invariant quantum field theories with twisted internal symmetries

Following up the work of 1] on deformed algebras, we present a class of Poincare invariant quantum field theories with particles having deformed internal symmetries. The twisted quantum fields discussed in this work satisfy commutation relations different from the usual bosonic/fermionic commutation relations. Such twisted fields by construction are nonlocal in nature. Despite this nonlocality we show that it is possible to construct interaction Hamiltonians which satisfy cluster decomposition principle and are Lorentz invariant. We further illustrate these ideas by considering global SU(N) symmetries. Specifically we show that twisted internal symmetries can provide a natural-framework for the discussion of the marginal deformations (beta-deformations) of the N = 4 SUSY theories.

Structured Dispersion Matrices From Division Algebra Codes for Space-Time Shift Keying

We propose a novel method of constructing Dispersion Matrices (DM) for Coherent Space-Time Shift Keying (CSTSK) relying on arbitrary PSK signal sets by exploiting codes from division algebras. We show that classic codes from Cyclic Division Algebras (CDA) may be interpreted as DMs conceived for PSK signal sets. Hence various benefits of CDA codes such as their ability to achieve full diversity are inherited by CSTSK. We demonstrate that the proposed CDA based DMs are capable of achieving a lower symbol error ratio than the existing DMs generated using the capacity as their optimization objective function for both perfect and imperfect channel estimation.

Generalized distributive law for ML decoding of space-time block codes

The problem of designing good space-time block codes (STBCs) with low maximum-likelihood (ML) decoding complexity has gathered much attention in the literature. All the known low ML decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast-decodable (conditionally multigroup decodable) structure of a code. We refer to this well-known technique of decoding STBCs as conditional ML (CML) decoding. In this paper, we introduce a new framework to construct ML decoders for STBCs based on the generalized distributive law (GDL) and the factor-graph-based sum-product algorithm. We say that an STBC is fast GDL decodable if the order of GDL decoding complexity of the code, with respect to the constellation size, is strictly less than M-lambda, where lambda is the number of independent symbols in the STBC. We give sufficient conditions for an STBC to admit fast GDL decoding, and show that both multigroup and conditionally multigroup decodable codes are fast GDL decodable. For any STBC, whether fast GDL decodable or not, we show that the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from cyclic division algebras which is not multigroup or conditionally multigroup decodable, the GDL decoder provides about 12 times reduction in complexity compared to the CML decoder. Similarly, for the Golden code, which is conditionally multigroup decodable, the GDL decoder is only half as complex as the CML decoder.

Black holes in higher spin supergravity

We study black hole solutions in Chern-Simons higher spin supergravity based on the superalgebra sl(3 vertical bar 2). These black hole solutions have a U(1) gauge field and a spin 2 hair in addition to the spin 3 hair. These additional fields correspond to the R-symmetry charges of the supergroup sl(3 vertical bar 2). Using the relation between the bulk field equations and the Ward identities of a CFT with N = 2 super-W-3 symmetry, we identify the bulk charges and chemical potentials with those of the boundary CFT. From these identifications we see that a suitable set of variables to study this black hole is in terms of the charges present in three decoupled bosonic sub-algebras of the N = 2 super-W-3 algebra. The entropy and the partition function of these R-charged black holes are then evaluated in terms of the charges of the bulk theory as well as in terms of its chemical potentials. We then compute the partition function in the dual CFT and find exact agreement with the bulk partition function.

Generalized distributive law for ML decoding of STBCs: further results

The problem of designing good Space-Time Block Codes (STBCs) with low maximum-likelihood (ML) decoding complexity has gathered much attention in the literature. All the known low ML decoding complexity techniques utilize the same approach of exploiting either the multigroup decodable or the fast-decodable (conditionally multigroup decodable) structure of a code. We refer to this well known technique of decoding STBCs as Conditional ML (CML) decoding. In [1], we introduced a framework to construct ML decoders for STBCs based on the Generalized Distributive Law (GDL) and the Factor-graph based Sum-Product Algorithm, and showed that for two specific families of STBCs, the Toepltiz codes and the Overlapped Alamouti Codes (OACs), the GDL based ML decoders have strictly less complexity than the CML decoders. In this paper, we introduce a `traceback' step to the GDL decoding algorithm of STBCs, which enables roughly 4 times reduction in the complexity of the GDL decoders proposed in [1]. Utilizing this complexity reduction from `traceback', we then show that for any STBC (not just the Toeplitz and Overlapped Alamouti Codes), the GDL decoding complexity is strictly less than the CML decoding complexity. For instance, for any STBC obtained from Cyclic Division Algebras that is not multigroup or conditionally multigroup decodable, the GDL decoder provides approximately 12 times reduction in complexity compared to the CML decoder. Similarly, for the Golden code, which is conditionally multigroup decodable, the GDL decoder is only about half as complex as the CML decoder.

Construction of Block Orthogonal STBCs and Reducing Their Sphere Decoding Complexity

Construction of high rate Space Time Block Codes (STBCs) with low decoding complexity has been studied widely using techniques such as sphere decoding and non Maximum-Likelihood (ML) decoders such as the QR decomposition decoder with M paths (QRDM decoder). Recently Ren et al., presented a new class of STBCs known as the block orthogonal STBCs (BOSTBCs), which could be exploited by the QRDM decoders to achieve significant decoding complexity reduction without performance loss. The block orthogonal property of the codes constructed was however only shown via simulations. In this paper, we give analytical proofs for the block orthogonal structure of various existing codes in literature including the codes constructed in the paper by Ren et al. We show that codes formed as the sum of Clifford Unitary Weight Designs (CUWDs) or Coordinate Interleaved Orthogonal Designs (CIODs) exhibit block orthogonal structure. We also provide new construction of block orthogonal codes from Cyclic Division Algebras (CDAs) and Crossed-Product Algebras (CPAs). In addition, we show how the block orthogonal property of the STBCs can be exploited to reduce the decoding complexity of a sphere decoder using a depth first search approach. Simulation results of the decoding complexity show a 30% reduction in the number of floating point operations (FLOPS) of BOSTBCs as compared to STBCs without the block orthogonal structure.