Udaya Parampalli

New Classes of Frequency-Hopping Sequences With Optimal Partial Correlation

In this paper, the partial Hamming correlation properties of frequency-hopping sequences (FHSs) are discussed. The Peng-Fan bounds on sets of FHSs are generalized to the case of partial correlation. Both individual FHSs with optimal partial autocorrelation and sets of FHSs with optimal partial correlation are presented. The former has more new parameters compared with the known individual FHSs with optimal partial autocorrelation, while the later is obtained in the literature for the first time.

New Constructions for Optimal Sets of Frequency-Hopping Sequences

In this paper, two generic constructions of optimal frequency-hopping sequence (FHS) sets employing d-form functions with difference-balanced property are presented. They generalize the previous constructions of optimal FHS sets using m-sequences and produce new optimal FHS sets that cannot be produced by the earlier constructions. By choosing appropriate d-form functions with difference-balanced property, both constructions lead to FHSs with large linear complexity. In addition, one of the proposed constructions gives new optimal parameters of FHS sets.

Nonbinary sequences with perfect and nearly perfect autocorrelations

The design of pseudorandom sequences with optimal correlation properties forms a crucial part of communications and radar engineering. Perfect autocorrelation sequences are however exceedingly rare. We discuss a technique that yields examples of such designs over enlarged PSK (PSK+) alphabets. We also design nearly perfect autocorrelation sequences over enlarged QAM (QAM+) alphabets, compatible with contemporary wireless transmission standards.

A Framework of Constructions of Minimal Storage Regenerating Codes With the Optimal Access/Update Property

In this paper, we present a generic framework for constructing systematic minimum storage regenerating codes with two parity nodes based on the invariant subspace technique. Codes constructed in our framework not only contain some best known codes as special cases, but also include some new codes with key properties, such as the optimal access property and the optimal update property. In particular, for a given storage capacity of an individual node, one of the new codes has the largest number of systematic nodes and two of the new codes have the largest number of systematic nodes with the optimal update property.

New Bound on Frequency Hopping Sequence Sets and Its Optimal Constructions

In this paper, we derive a new bound on maximum nontrivial Hamming correlation of frequency hopping (FH) sequences from the Singleton bound in error correcting code literature, and we discuss the relation between the new bound and the known ones on FH sequences. Further, we construct two classes of FH sequences from punctured Reed-Solomon codes and one class of FH sequences from polynomial functions, which meet the new bound.

New Complete Complementary Codes for Peak-to-Mean Power Control in Multi-Carrier CDMA

Owing to the zero non-trivial aperiodic correlation sum properties, complete complementary codes (CCC) have been applied to asynchronous multi-carrier code-division multiple-access (MC-CDMA) communications in order to provide zero interference performance. When each complementary code is arranged to be a matrix, the peak-to-mean envelope power ratio (PMEPR) of the CCC-MC-CDMA system is determined by the column sequences of the complementary matrices. The existing CCC have the column sequence PMEPR of M, where M denotes the number of subcarriers in a CCC-MC-CDMA system. In practice, M is generally large and a PMEPR approaching this value is unacceptable. To solve this problem, a new class of CCC using generalized Boolean functions and with a column sequence PMEPR of at most 2 is proposed in this paper.

Optimal variable-weight optical orthogonal codes via cyclic difference families

Variable-weight optical orthogonal code (OOC) was introduced by G-C Yang for multimedia optical CDMA systems with multiple quality of service (QoS) requirement. In this paper, a construction for optimal variable-weight OOCs via cyclic difference families is given. Several new constructions for cyclic difference families are also given. By using these constructions, new optimal (n, W, 1, Q)-OOCs for 2 ¿ |W| ¿ 4 are constructed.

A blind digital watermarking scheme based on complete complementary codes

Complete complementary code can be applied to digital watermarking technologies as well as communication systems like approximately synchronized CDMA because of its good correlation properties. In this paper, we propose a blind watermarking algorithm which does not need to refer any original data in the watermark extraction process. We also discuss the analogy between the proposed watermarking scheme and CT-CDMA communication systems based on complete complementary codes. In addition, some extensions of the proposed watermarking method and future problems are discussed in the paper.

Optimal odd-length binary Z-complementary pairs

A pair of sequences is called a Golay complementary pair (GCP) if their aperiodic autocorrelation sums are zero for all out-of-phase time shifts. Existing known binary GCPs only have even-lengths in the form of 2α 10β 26γ (where \(α, β, γ) are nonnegative integers). To fill the gap left by the odd-lengths, we investigate the optimal odd-length binary (OB) pairs, which display the closest correlation property to that of GCPs. Our criteria of closeness is that each pair has the maximum possible zero-correlation zone (ZCZ) width and minimum possible out-of-zone aperiodic autocorrelation sums. Such optimal pairs are called optimal OB Z-complementary pairs (OB-ZCP) in this paper. We show that each optimal OB-ZCP has maximum ZCZ width of (N+1)/2, and minimum out-of-zone aperiodic sum magnitude of 2, where N denotes the sequence length (odd). Systematic constructions of such optimal OP-ZCPs are proposed by insertion and deletion of certain binary GCPs, which settle the 2011 Li-Fan-Tang-Tu open problem positively. The proposed optimal OB-ZCPs may serve as a replacement for GCPs in many engineering applications, where odd sequence lengths are preferred. In addition, they give rise to a new family of base-two almost difference families, which are useful in studying partially balanced incomplete block design.

BEHAVIORAL MODELS OVER RINGS MINIMAL REPRESENTATIONS AND APPLICATIONS TO CODING AND SEQUENCES

Abstract In this paper we consider polynomial kernel representations for behaviors. For behaviors over fields it is well-known that minimal representations, i.e. representations with minimal row degrees, are exactly those representations for which the polynomial matrix is row reduced. In this paper we consider behaviors over a particular type of ring, namely ℤ p r , where p is a prime number and r is a positive integer. As a starting point in this investigation we focus on minimal partial realizations. These are equivalent to shortest linear recurrence relations. We present an algorithm that computes a parametrization of all shortest linear recurrence relations for a finite sequence in ℤ p r . For this we extend well-known techniques developed by Reeds and Sloane in the 80s with methods from the theory of behavioral modeling.