Huffman Sequences Research Articles

A Novel Approach to Construct Huffman Sequences with Low PAPR

A Novel Approach to Construct Huffman Sequences with Low PAPR

Pilot Design for BEM-Based Channel Estimation in Doubly Selective Channel

This paper investigates pilot design for enhanced channel estimation in single carrier communication systems over doubly-selective channels (DSC). Our contribution is twofold: first, we propose to use Huffman sequences as pilot clusters with low peak-to-average power ratio (PAPR), yet with good channel estimation performance when periodic pilot placement is adopted; second, we propose a low-complexity pilot placement strategy based on the analysis of the complex-exponential basis expansion model (CE-BEM) of the DSC. The latter leads to improved channel estimation performance with useful insights for pilot placement.

Sharp Computational Images From Diffuse Beams: Factorization of the Discrete Delta Function

Discrete delta functions define the limits of attainable spatial resolution for all imaging systems. Here we construct broad, multi-dimensional discrete functions that replicate closely the action of a Dirac delta function under aperiodic convolution. These arrays spread the energy of a sharp probe beam to simultaneously sample multiple points across the volume of a large object, without losing image sharpness. A diffuse point-spread function applied in any imaging system can reveal the underlying structure of objects less intrusively and with equal or better signal-to-noise ratio. These multi-dimensional arrays are related to previously known, but relatively rarely employed, one-dimensional integer Huffman sequences. Practical point-spread functions can now be made sufficiently large to span the size of the object under measure. Such large arrays can be applied to ghost imaging, which has demonstrated potential to greatly improve signal-to-noise ratios and reduce the total dose required for tomographic imaging. The discrete arrays built here parallel the continuum self-adjoint or Hermitian functions that underpin wave theory and quantum mechanics.

BER Performance of SS System Using a Huffman Sequence against CW Jamming

BER Performance of SS System Using a Huffman Sequence against CW Jamming

Design and performance of Huffman sequences in medical ultrasound coded excitation

This paper deals with coded-excitation techniques for ultrasound medical echography. Specifically, linear Huffman coding is proposed as an alternative approach to other widely established techniques, such as complementary Golay coding and linear frequency modulation. The code design is guided by an optimization procedure that boosts the signal-to-noise ratio gain (GSNR) and, interestingly, also makes the code robust in pulsed-Doppler applications. The paper capitalizes on a thorough analytical model that can be used to design any linear coded-excitation system. This model highlights that the performance in frequency-dependent attenuating media mostly depends on the pulse-shaping waveform when the codes are characterized by almost ideal (i.e., Kronecker delta) autocorrelation. In this framework, different pulse shapers and different code lengths are considered to identify coded signals that optimize the contrast resolution at the output of the receiver pulse compression. Computer simulations confirm that the proposed Huffman codes are particularly effective, and that there are scenarios in which they may be preferable to the other established approaches, both in attenuating and non-attenuating media. Specifically, for a single scatterer at 150 mm in a 0.7-dB/(MHz·cm) attenuating medium, the proposed Huffman design achieves a main-to-side lobe ratio (MSR) equal to 65 dB, whereas tapered linear frequency modulation and classical complementary Golay codes achieve 35 and 45 dB, respectively.

Orthogonal and ZCZ Sets of Real-Valued Periodic Orthogonal Sequences from Huffman Sequences

This paper presents a method of generating sets of orthogonal and zero-correlation zone (ZCZ) periodic real-valued sequences of period 2n, n ≥ 1. The sequences admit a fast correlation algorithm and the sets of sequences achieve the upper bound on family size. A periodic orthogonal sequence has the periodic autocorrelation function with zero sidelobes, and a set with orthogonal sequences whose mutual periodic crosscorrelation function at zero shift is zero. Similarly, a ZCZ set is the set of the sequences with zero-correlation zone. In this paper, we derive the real-valued periodic orthogonal sequences of period 2n from a real-valued Huffman sequence of length 2ν + 1, ν being a positive integer and ν ≥ n, whose aperiodic autocorrelation function has zero sidelobes except possibly at the left and right shift-ends. The orthogonal and ZCZ sets of real-valued periodic orthogonal sequences are useful in various systems, such as synchronous code division multiple access (CDMA) systems, quasi-synchronous CDMA systems and digital watermarkings.

Computing and estimating the number of [formula omitted]-ary Huffman sequences of a specified length

An n -ary Huffman sequence of length q is the list, in non-decreasing order, of the lengths of the code words in a prefix-free replacement code for a q -letter source alphabet over an n -letter code alphabet, optimal with respect to some probability (relative frequency) distribution over the source alphabet, meaning that the code minimizes the average number of code letters per source letter. Here we extend a theorem in [E. Norwood, The number of different possible compact codes, IEEE Trans. Inform. Theory (October) (1967) 613–616] about the case n = 2 to arbitrary n ≥ 2 . The theorem permits the recursive computation of the number, h ( q , n ) , of different n -ary Huffman sequences of length q , and the estimation of h ( q , n ) , which turns out to grow geometrically with q , for each n ≥ 2 . Upper and lower estimates of h ( q , n ) are given for 2 ≤ n ≤ 6 . For instance, c 1 ( 1.75488 ) q ≤ h ( q , 2 ) ≤ c 2 ( 1.83929 ) q for some constants c 1 , c 2 ; this result significantly tightens the estimates of h ( q , 2 ) in [J. Burkert, Simple bounds on the numbers of binary Huffman sequences, Bull. Inst. Combin. Appl. 58 (2010) 79–82].

Orthogonal Set of Huffman Sequences and Its Application to Suppressed-Interference Quasi-Synchronous CDMA System

A Huffman sequence has a zero-sidelobe aperiodic autocorrelation function except at both shift ends. This paper presents orthogonal sets of the zero correlation zone (ZCZ) Huffman sequences and the application to a quasi-synchronous CDMA system with interferences suppressed. The sequences with low or large peak values are constructed on the basis of sequence spectra corresponding to multiple convolution of elementary sequences, and include the ZCZ sequences. The CDMA system is constructed from the ZCZ sequences, and suppresses intersymbol and interchannel interferences.

Generating Huffman sequences

An easy algorithm is described a special case of which will generate a list of all n-ary Huffman sequences of length m, for any given integers m⩾1, n⩾2.

An account of monaural phase sensitivity.

Listeners can detect phase differences between the envelopes of sounds occupying remote frequency regions, and between the fine structures of partials that interact within a single auditory filter. They are insensitive to phase differences between partials that differ sufficiently in frequency to preclude within-channel interactions. A new model is proposed that can account for all three of these findings, and which, unlike currently popular approaches, does not discard across-channel timing information. Sensitivity is predicted quantitatively by analyzing the output of a cochlear model using a spectro-temporal decomposition inspired by responses of neurons in the auditory cortex, and by computing a distance metric between the responses to two stimuli to be discriminated. Discriminations successfully modeled include phase differences between pairs of bandpass filtered harmonic complexes, and between pairs of sinusoidally amplitude modulated tones, discrimination between amplitude and frequency modulation, and discrimination of transient signals differing only in their phase spectra ("Huffman sequences").

A new account of monaural phase sensitivity

Phase differences between partials of complex tones are detectable only when they interact within an auditory filter. This is consistent with auditory models whereby across-channel timing information is explicitly discarded. However, these models (e.g., the autocorrelogram) fail to account for listeners’ ability to detect across-channel phase differences for some sounds. For example, when two groups of unresolved harmonics are filtered into different frequency regions and presented concurrently, listeners can detect a 1- to 2-ms ‘‘pitch pulse asynchrony’’ between the peaks of the waveforms of the two groups. We attribute phase insensitivity for resolved partials to the rapid phase transition near the peak of the traveling wave, causing auditory neurons responding to each partial to do so at a variety of phases. In contrast, a group of unresolved harmonics does not produce a sharp traveling-wave peak, and all neurons responding do so synchronously. We propose a model whereby ‘‘auditory spectrograms’’ are processed by cortical filters tuned to characteristic frequency, modulation rate, and spectral ‘‘scale.’’ The model accounts quantitatively for detection of envelope phase disparities between AM tones, discrimination of AM from QFM, and discrimination of Huffman sequences. We argue that auditory models should not discard all across-channel phase information.

Phase reflection diffusers design using Huffman sequences

Phase reflection diffusers based on integer sequences are, unfortunately, limited in their frequency response. The purpose of this paper is to present an alternative form of diffusion structure using noninteger sequence based phase reflection gratings. This paper will present a new method of generating such diffusers based on Huffman sequences. The theory, design, advantages, and limitations of these structures will be discussed and simulation results of their performance will be presented. In particular, their independence from the frequency response effects typical of integer based sequences. Methods of extending and improving their performance will also be suggested. Methods of construction will also be discussed. The paper will show that it is possible to develop diffusing structures which have a better frequency performance than conventional phase reflecting structures.

Spreading sequences for multicarrier CDMA systems

The paper contains an analysis of the basic criteria for the selection of spreading sequences for the multicarrier CDMA (MC-CDMA) systems with spectrum spreading in the frequency domain. It is shown that the time-domain crosscorrelation function between the spreading sequences is not a proper interference measure for the asynchronous MC-CDMA users. Therefore, the spectral correlation function is introduced and, together with the crest factor and the dynamic range of the corresponding multicarrier waveforms, is used for the evaluation of MC-CDMA sequences. Some well-known classes of sequences, such as Walsh, Gold, orthogonal Gold, and Zadoff-Chu sequences, as well as Legandre and Golay complementary sequences, are evaluated with respect to the aforementioned basic criteria. It is also shown that the crest factors of the multicarrier spread spectrum waveforms based on the multilevel Huffman sequences are very close to or even lower than the crest factor of a single sine wave.

Huffman sequences with uniform time energy distribution

Abstract In this work, the generation of Huffman sequences with a given length and uniform time energy distribution is analyzed and a systematic method for designing the sequence is presented. The comparative analysis with a uniformly distributed pseudorandom signal shows the advantages of the proposed Huffman sequence.

Complementary Huffman sequences

The theories of complementary and Huffman sequences have been two distinct areas. It is shown that each Huffman sequence has its complementary pair. In radar applications, these pairs can be used, in the same way as other binary and nonbinary complementary sequences. They have the added advantage of zero autocorrelation sidelobes at all time shifts except the largest one. Even these sidelobes are cancelled if the autocorrelation functions are summed because of the complementarity.

Minimax sidelobe reduction filtering for Huffman sequence autocorrelation function type signals

A solution is presented for the impulse response of an FIR sidelobe reduction filter, intended for signals consisting of a main lobe and two symmetrically spaced side-lobes, i.e. for signals of the Huffman sequence autocorrelation function type. The filter minimizes the output main-lobe level subject to a constraint on the maximum sidelobe level. It is shown that for those input signals with sidelobe levels that do not exceed half of the main-lobe level, the filter required can be represented uniquely as a parallel combination of zero-forcing filters. The tradeoff between the reduction of sidelobe level and the degradation of signal-to-noise ratio is examined. >

Some integer Huffman sequences (Corresp.)

A class of real integer Huffman sequences is presented. The zero pattern of the z -transform of these sequences indicates a general method for their synthesis.

Finite-Length Test Sequences in System Identification Techniques

A scheme is presented for the rapid measurement of weighting sequences of in-operation linear systems. Finite duration sequences are used as test signals to the system under test, whose response to the sequences is processed by an appropriate digital filter. The test sequences are here required to have high energy ratio and low sidelobes in their auto-correlation function. It is shown that sequences having desirable properties can be obtained by clipping Huffman sequences. Results of computer simulation tests performed in different systems and using different sequences are also given.

Huffman sequences with approximately uniform envelopes or cross-correlation functions (Corresp.)

The question of whether uniform Huffman (impulse equivalent) sequences exist is discussed, and some necessary conditions for a Huffman sequence to be uniform are mentioned. A comprehensive search revealed that no uniform Huffman sequences exist from lengths 4 to 17, inclusive. A procedure is described for synthesizing pairs of Huffman sequences whose cross-correlations are approximately uniform and, incidentally, are also themselves Huffman sequences.

Modified Barker and Huffman Sequences in Combination Codes

lt is possible that usable combination codes can be obtained if Barker and Huffman sequences are chosen as the inner and outer codes. lt is shown that an improvement in either energy efficiency or time sidelobe structure will result either from a modification of a Huffman sequence or from a modification of a Barker sequence. Results are given for a combination code of length 91, with inner and outer codes of length 7 and 13.