Martin Tomlinson

Magnitude modulation for small satellite Earth terminals using QPSK and OQPSK

This paper investigates the design and application of data magnitude modulation to reduce power amplifier back-off for QPSK and OQPSK modulations for small satellite Earth stations. The coefficients for data magnitude modulation are obtained by using an iterative design loop. The parameters of this loop are tuned to obtain maximum gain. Roll-off factors from 10% to 100% are considered, with emphasis on small roll-off values for increased bandwidth efficiency. It is shown that a gain of almost 6 dB can ideally be obtained for a roll-off factor of 10%. Error correction coding is used to compensate for the increased sensitivity to noise of the magnitude modulated data. The loss due to this increased sensitivity is reduced from almost 5.5 dB to 1.2 dB for a roll-off factor of 10% by using high rate product codes, thus giving an overall gain of 4.8 dB. Trade offs between spectral regrowth and implementation are addressed.

Addendum to “An Efficient Algorithm to Find All Small-Size Stopping Sets of Low-Density Parity-Check Matrices”

In an earlier transactions paper, Rosnes and Ytrehus presented an efficient algorithm for determining all stopping sets of low-density parity-check (LDPC) codes, up to a specified weight, and also gave results for a number of well-known codes including the family of IEEE 802.16e LDPC codes, commonly referred to as the WiMax codes. It is the purpose of this short paper to review the algorithm for determining the initial part of the stopping set weight spectrum (which includes the codeword weight spectrum), and to provide some improvements to the algorithm. As a consequence, complete stopping set weight spectra up to weight 32 (for selected IEEE 802.16e LDPC codes) can be provided, while in previous work only stopping set weights up to 28 are reported. In the published standard for the IEEE 802.16e codes there are two methods of construction presented, depending upon the code rate and the code length. We compare the stopping sets of the resulting codes and provide complete stopping set weight spectra (up to five terms) for all IEEE 802.16e LDPC codes using both construction methods.

Power efficient back-off reduction through polyphase filtering magnitude modulation

A multistage polyphase magnitude modulation (MPMM) technique is proposed for single carrier (SC) modulations, to efficiently reduce the peak-to-average power ratio (PAPR) of the bandwidth limited signal resulting from root-raised cosine (RRC) filtering. We show that the application of back-off to the transmitter high-power amplifier (HPA), in order to avoid nonlinear distortion and thus spectral regrowth, can be almost eliminated, even at very low roll-off values, leading to systemiquests high power efficiency. We also show that noise sensitivity due to MPMM is considerably minimized by improving the initial receivers soft-decoding estimates, based on the average positions of the MPMM constellation symbols.

Efficient M-QAM Transmission Using Compacted Magnitude Modulation Tables

Magnitude Modulation is a technique proposed with success for QPSK and OQPSK in order to maximize power and bandwidth of small satellite earth stations, by reducing PAPR of the modulated signal at the HPA input. To meet the ever growing demand for higher data rates, higher order modulations have been considered. This paper shows that it is possible to use the magnitude modulation concept for the M-QAM case, even considering the huge number of symbol combinations. The constellation and RRC symmetries are explored, allowing considerable reduction on look-up table computation complexity and storage requirements. Experimental results show considerable gains (>2dB) in PAPR and back-off reduction for 16-QAM with negligible BER losses.

Combating geometrical attacks in a DWT based blind video watermarking system

This paper describes a high capacity blind video watermarking system invariant to geometrical attacks such as shift, rotation, scaling and cropping. A spatial domain reference watermark is used to obtain invariance to geometric attacks by employing image registration techniques to determine and invert the attacks. A second, high capacity watermark, which carries the data payload, is embedded in the wavelet domain according to a human visual system (HVS) model. This is protected by a state-of-the-art error correction code (turbo code). The proposed system is invariant to scaling up to 180%, rotation up to 70/spl deg/ and arbitrary aspect ratio changes up to 200% on both axes. Furthermore, the system is virtually invariant to any shifting, cropping, or combined shifting and cropping.

On the Minimum/Stopping Distance of Array Low-Density Parity-Check Codes

In this paper, we study the minimum/stopping distance of array low-density parity-check (LDPC) codes. An array LDPC code is a quasi-cyclic LDPC code specified by two integers q and m, where q is an odd prime and m q. In the literature, the minimum/stopping distance of these codes (denoted by d(q, m) and h(q, m), respectively) has been thoroughly studied for m 5. Both exact results, for small values of q and m, and general (i.e., independent of q) bounds have been established. For m = 6, the best known minimum distance upper bound, derived by Mittelholzer, is d(q, 6) 32. In this paper, we derive an improved upper bound of d(q, 6) 20 and a new upper bound d(q, 7) 24 by using the concept of a template support matrix of a codeword/stopping set. The bounds are tight with high probability in the sense that we have not been able to find codewords of strictly lower weight for several values of q using a minimum distance probabilistic algorithm. Finally, we provide new specific minimum/stopping distance results for m 7 and low-to-moderate values of q ≤79.

Direct digital frequency synthesizer for a FH spread spectrum system: analysis and design

A complete characterization of direct digital frequency synthesizers; (DDFSs) is made, deducing exact expressions and general properties of these synthesizers. As an application example of the derived expression for the power spectrum density with phase quantization, an extremely simple algorithm is described that sequentially computes the frequency and magnitude of each component and gives exactly the, same result as an FFT. Expressions for the signal-to-noise ratio, including phase and amplitude quantization, and general design rules are also presented. An ECL (emitter coupled logic) hardware prototype was built, and its performance is shown to be in good agreement with both theoretical and simulation results.<<ETX>>

Analysis of the distribution of the number of erasures correctable by a binary linear code and the link to low-weight codewords

The number and weight of low-weight codewords of a binary linear code determine the erasure channel performance. Analysis is given of the probability density function of the number of erasures correctable by the code in terms of the weight enumerator polynomial. For finite-length codes, zero erasure decoder error rate is impossible, even with maximum-distance-separable (MDS) codes and maximum-likelihood decoding. However, for codes that have binomial weight spectra, for example BCH, Goppa and double-circulant codes, the erasure correction performance is close to that of MDS codes. One surprising result is that, for many (n, k) codes, the average number of correctable erasures is almost equal to n-k, which is significantly larger than d min -1. For the class of iteratively decodable codes (LDPC and turbo codes), the erasure performance is poor in comparison to algebraic codes designed for maximum d min . It is also shown that the turbo codes that have optimised d min have significantly better performance than LDPC codes. A probabilistic method, which has considerably smaller search space than that of the generator matrix-based methods, is presented to determine the d min of a linear code using random erasure patterns. Using this approach, it is shown that there are (168, 84, 24) and (216, 108, 24) quadratic double-circulant codes

Magnitude modulation for VSAT's low back-off transmission

This paper addresses the problem of controlling the envelopes power peak of single carrier modulated signals, band limited by root-raised cosine (RRC) pulse shaping filters, in order to reduce power amplifier back-off for very small aperture terminals ground stations. Magnitude modulation (MM) is presented as a very efficient solution to the peak-to-average power ratio problem. This paper gives a detailed description of the MM concept and its recent evolutions. It starts by extending the look-up-table (LUT) based approach of the MM concept to M-ary constellations with M ≤ 16. The constellation and RRC symmetries are explored, allowing considerable reduction on LUT computation complexity and storage requirements. An effective multistage polyphase (MPMM) approach for the MM concept is then proposed. As opposed to traditional LUT-MM solutions, MM coefficients are computed in real-time by a low complexity multirate filter system. The back-off from high-power amplifier saturation is almost eliminated (reduction is greater than 95%) with just a 2-stage MPMM system even for very demanding roll-off cases (e.g., α = 0.1). Also, the MPMM is independent of modulation in use, allowing its easy application to constellations with M > 16.

Some Results on the Weight Distributions of the Binary Double-Circulant Codes Based on Primes

This paper presents a more efficient algorithm to count codewords of given weights in self-dual double-circulant and formally self-dual quadratic double-circulant codes over GF(2). A method of deducing the modular congruence of the weight distributions of the binary quadratic double-circulant codes is proposed. This method is based on that proposed by Mykkeltveit, Lam and McEliece, JPL. Tech. Rep., 1972, which was applied to the extended quadratic-residue codes. A useful application of this modular congruence method is to provide independent verification of the weight distributions of the extended quadratic-residue and quadratic double-circulant codes. Using this method in conjunction with the proposed efficient codeword counting algorithm, we are able i) to give the previously unpublished weight distributions of the [76, 38,12] and [124, 62, 20] binary quadratic double-circulant codes; ii) to provide corrections to the published results on the weight distributions of the binary extended quadratic-residue code of prime 151, and the number of codewords of weights 30 and 32 of the binary extended quadratic-residue code of prime 137; and iii) to prove that the [168, 84, 24] extended quadratic-residue and quadratic double-circulant codes are inequivalent