Four-dimensional modulation and coding: An alternate to frequency-reuse

Four dimensional modulation as a means of improving communication efficiency on the band-limited Gaussian channel, with the four dimensions of signal space constituted by phase orthogonal carriers (cos omega sub c t and sin omega sub c t) simultaneously on space orthogonal electromagnetic waves are discussed. "Frequency reuse' techniques use such polarization orthogonality to reuse the same frequency slot, but the modulation is not treated as four dimensional, rather a product of two-d modulations, e.g., QPSK. It is well known that, higher dimensionality signalling affords possible improvements in the power bandwidth sense. Four-D modulations based upon subsets of lattice-packings in four-D, which afford simplification of encoding and decoding are described. Sets of up to 1024 signals are constructed in four-D, providing a (Nyquist) spectral efficiency of up to 10 bps/Hz. Energy gains over the reuse technique are in the one to three dB range t equal bandwidth

Errorless Robust JPEG Steganography using Outputs of JPEG Coders

Robust steganography is a technique of hiding secret messages in images so that the message can be recovered after additional image processing. One of the most popular processing operations is JPEG recompression. Unfortunately, most of today's steganographic methods addressing this issue only provide a probabilistic guarantee of recovering the secret and are consequently not errorless. That is unacceptable since even a single unexpected change can make the whole message unreadable if it is encrypted. We propose to create a robust set of DCT coefficients by inspecting their behavior during recompression, which requires access to the targeted JPEG compressor. This is done by dividing the DCT coefficients into 64 non-overlapping lattices because one embedding change can potentially affect many other coefficients from the same DCT block during recompression. The robustness is then combined with standard steganographic costs creating a lattice embedding scheme robust against JPEG recompression. Through experiments, we show that the size of the robust set and the scheme's security depends on the ordering of lattices during embedding. We verify the validity of the proposed method with three typical JPEG compressors and benchmark its security for various embedding payloads, three different ways of ordering the lattices, and a range of Quality Factors. Finally, this method is errorless by construction, meaning the embedded message will always be readable.Comment: 10 pages, 11 figures, 1 table, submitted to IEEE Transactions on Dependable and Secure Computin

Integer-Forcing MIMO Linear Receivers Based on Lattice Reduction

A new architecture called integer-forcing (IF) linear receiver has been recently proposed for multiple-input multiple-output (MIMO) fading channels, wherein an appropriate integer linear combination of the received symbols has to be computed as a part of the decoding process. In this paper, we propose a method based on Hermite-Korkine-Zolotareff (HKZ) and Minkowski lattice basis reduction algorithms to obtain the integer coefficients for the IF receiver. We show that the proposed method provides a lower bound on the ergodic rate, and achieves the full receive diversity. Suitability of complex Lenstra-Lenstra-Lovasz (LLL) lattice reduction algorithm (CLLL) to solve the problem is also investigated. Furthermore, we establish the connection between the proposed IF linear receivers and lattice reduction-aided MIMO detectors (with equivalent complexity), and point out the advantages of the former class of receivers over the latter. For the $2 \times 2$ and $4\times 4$ MIMO channels, we compare the coded-block error rate and bit error rate of the proposed approach with that of other linear receivers. Simulation results show that the proposed approach outperforms the zero-forcing (ZF) receiver, minimum mean square error (MMSE) receiver, and the lattice reduction-aided MIMO detectors.Comment: 9 figures and 11 pages. Modified the title, abstract and some parts of the paper. Major change from v1: Added new results on applicability of the CLLL reductio