Weighing matrices and spherical codes

Mutually unbiased weighing matrices (MUWM) are closely related to an antipodal spherical code with 4 angles. In the present paper, we clarify the relationship between MUWM and the spherical sets, and give the complete solution about the maximum size of a set of MUWM of weight 4 for any order. Moreover we describe some natural generalization of a set of MUWM from the viewpoint of spherical codes, and determine several maximum sizes of the generalized sets. They include an affirmative answer of the problem of Best, Kharaghani, and Ramp.Comment: Title is changed from "Association schemes related to weighing matrices

Compute-and-Forward on a Multi-User Multi-Relay Channel

In this paper, we consider a system in which multiple users communicate with a destination with the help of multiple half-duplex relays. Based on the compute-and-forward scheme, each relay, instead of decoding the users' messages, decodes an integer-valued linear combination that relates the transmitted messages. Then, it forwards the linear combination towards the destination. Given these linear combinations, the destination may or may not recover the transmitted messages since the linear combinations are not always full rank. Therefore, we propose an algorithm where we optimize the precoding factor at the users such that the probability that the equations are full rank is increased and that the transmission rate is maximized. We show, through some numerical examples, the effectiveness of our algorithm and the advantage of performing precoding allocation at the users. Also, we show that this scheme can outperform standard relaying techniques in certain regimes

Peak-to-Mean Power Control in OFDM, Golay Complementary Sequences, and Reed–Muller Codes

We present a range of coding schemes for OFDM transmission using binary, quaternary, octary, and higher order modulation that give high code rates for moderate numbers of carriers. These schemes have tightly bounded peak-to-mean envelope power ratio (PMEPR) and simultaneously have good error correction capability. The key theoretical result is a previously unrecognized connection between Golay complementary sequences and second-order Reed–Muller codes over alphabets ℤ2h. We obtain additional flexibility in trading off code rate, PMEPR, and error correction capability by partitioning the second-order Reed–Muller code into cosets such that codewords with large values of PMEPR are isolated. For all the proposed schemes we show that encoding is straightforward and give an efficient decoding algorithm involving multiple fast Hadamard transforms. Since the coding schemes are all based on the same formal generator matrix we can deal adaptively with varying channel constraints and evolving system requirements

New York City Zoning -- 1961-1991: Turning Back The Clock -- But With An Up-To-The-Minute Social Agenda

Since the last update over 30 years ago, there is a need to once again change our zoning laws. Over the years, societal concerns and priorities have fluctuated with the times and, as a result, exceptions have been made to the zoning regulations which reflect these changing social interests. The result is a Zoning Resolution which stands at 806 pages (and still counting). It is an ad-hoc, convoluted, chaotic non-plan for the City, held together by binders rather than a common vision. This essay examines the zoning history of New York City and concludes that a new Comprehensive Reassessment, which will guide future development in accordance with the needs and values of today\u27s society, is needed to unify the goals of city planning and to reinvigorate the potential effectiveness of zoning in New York City

Peak-to-mean power control and error correction for OFDM transmission using Golay sequences and Reed-Muller codes

A coding scheme for OFDM transmission is proposed, exploiting a previously unrecognised connection between pairs of Golay complementary sequences and second-order Reed-Muller codes. The scheme solves the notorious problem of power control in OFDM systems by maintaining a peak-to-mean envelope power ratio of at most 3dB while allowing simple encoding and decoding at high code rates for binary, quaternary or higher-phase signalling together with good error correction

redMaGiC: selecting luminous red galaxies from the DES Science Verification data

We introduce redMaGiC, an automated algorithm for selecting luminous red galaxies (LRGs). The algorithm was specifically developed to minimize photometric redshift uncertainties in photometric large-scale structure studies. redMaGiC achieves this by self-training the colour cuts necessary to produce a luminosity-thresholded LRG sample of constant comoving density. We demonstrate that redMaGiC photo-zs are very nearly as accurate as the best machine learning-based methods, yet they require minimal spectroscopic training, do not suffer from extrapolation biases, and are very nearly Gaussian. We apply our algorithm to Dark Energy Survey (DES) Science Verification (SV) data to produce a redMaGiC catalogue sampling the redshift range z ∈ [0.2, 0.8]. Our fiducial sample has a comoving space density of 10-3 (h-1 Mpc)-3, and a median photo-z bias (zspec - zphoto) and scatter (sigmaz/(1 + z)) of 0.005 and 0.017, respectively. The corresponding 5sigma outlier fraction is 1.4 per cent. We also test our algorithm with Sloan Digital Sky Survey Data Release 8 and Stripe 82 data, and discuss how spectroscopic training can be used to control photo-z biases at the 0.1 per cent level

Multi-user interference mitigation under limited feedback requirements for WCDMA systems with base station cooperation

One of the techniques that has been recently identified for dealing with multi-user interference (MUI) in future communications systems is base station (BS) cooperation or joint processing. However, perfect MUI cancellation with this technique demands severe synchronization requirements, perfect and global channel state information (CSI), and an increased backhaul and signaling overhead. In this paper, we consider a more realistic layout with the aim of mitigating the MUI, where only local CSI is available at the BSs. Due to synchronization inaccuracies and errors in the channel estimation, the system becomes partially asynchronous. In the downlink of wideband code division multiple access based systems, this asynchronism stands for the loss of the orthogonality of the spreading codes allocated to users and thus, for an increase in the MUI level of the system. In this contribution, we propose a framework for mitigating the MUI which builds in three main steps: definition of a cooperation area based on the channel characteristics, statistical modeling of the average MUI power experienced by each user and a specific spreading code allocation scheme for users served with joint processing. This code allocation assigns spreading codes to users in such a way that minimum average cross-correlation between active users can be achieved. Interestingly, these steps can be performed with a limited amount of extra feedback from the user's side