Related papers: Sets of Low Correlation Sequences from Cyclotomy
Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared to random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation…
Various problems in engineering and natural science demand binary sequences that do not resemble translates of themselves, that is, the sequences must have small aperiodic autocorrelation at every nonzero shift. If $f$ is a sequence, then…
Sequences with low aperiodic autocorrelation are used in communications and remote sensing for synchronization and ranging. The autocorrelation demerit factor of a sequence is the sum of the squared magnitudes of its autocorrelation values…
Sequences with a low correlation have very important applications in communications, cryptography, and compressed sensing. In the literature, many efforts have been made to construct good sequences with various lengths where binary…
Low autocorrelation binary sequences (LABS) are very important for communication applications. And it is a notoriously difficult computational problem to find binary sequences with low aperiodic autocorrelations. The problem can also be…
The subject of this paper is transmission over a general class of binary-input memoryless symmetric channels using error correcting codes based on sparse graphs, namely low-density generator-matrix and low-density parity-check codes. The…
Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in…
The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or -1, called binary sequences, and sequences…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
In a distributed information application an encoder compresses an arbitrary vector while a similar reference vector is available to the decoder as side information. For the Hamming-distance similarity measure, and when guaranteed perfect…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
In the realm of modern digital communication, cryptography, and signal processing, binary sequences with a low correlation properties play a pivotal role. In the literature, considerable efforts have been dedicated to constructing good…
Cyclic codes are the most studied subclass of linear codes and widely used in data storage and communication systems. Many cyclic codes have optimal parameters or the best parameters known. They are divided into simple-root cyclic codes and…
Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of…
Sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. Among the known sequences, cyclotomic families have the optimal autocorrelation property. In this paper, we…
Computable Information Density (CID), the ratio of the length of a losslessly compressed data file to that of the uncompressed file, is a measure of order and correlation in both equilibrium and nonequilibrium systems. Here we show that…
This paper considers three kinds of length sequences of the complete genome. Detrended fluctuation analysis, spectral analysis, and the mean distance spanned within time $L$ are used to discuss the correlation property of these sequences.…
Unimodular sequences with low autocorrelations are desired in many applications, especially in the area of radar and code-division multiple access (CDMA). In this paper, we propose a new algorithm to design unimodular sequences with low…
Certain applications require the use of signals that combine both the capability to operate with low signal-to-noise ratios and the ability to support multiple users without interference. In the case where many users have very different…
Due to wide applications of binary sequences with low correlation to communications, various constructions of such sequences have been proposed in literature. However, most of the known constructions via finite fields make use of the…