arXiv subjects

Gobinda Ghosh

Publications and source records attributed to Gobinda Ghosh.

6 recordsLinked to original sources

arXiv2026

Kernel-Type Fractional Extensions of Reverse Callebaut, Rogers H\"older and Cauchy Schwarz Inequalities on Time Scales

In this paper, we establish kernel-type fractional extensions of reverse Callebaut, Rogers--H\"older and Cauchy--Schwarz inequalities on time scales. The proposed results are formulated by means of a nonnegative kernel operator associated with the diamond-$\alpha$ integral, which enables the inclusion of memory effects within the framework of dynamic inequalities. By choosing particular kernels and time scales, the obtained inequalities reduce to their continuous, discrete and quantum counterparts. Moreover, when the kernel is taken as the identity kernel, the results recover the corresponding classical diamond-$\alpha$ dynamic inequalities. Several consequences are derived as special cases, including fractional reverse Cauchy--Schwarz inequalities and weighted reverse Rogers--H\"older inequalities. The results provide a unified approach for studying reverse inequalities in continuous, discrete, quantum and fractional dynamic settings and may be applied to obtain a priori estimates for Volterra-type and delay dynamic equations.

math.OC↗

arXiv2024

Construction of CCC and ZCCS Through Additive Characters Over Galois Field

The rapid progression in wireless communication technologies, especially in multicarrier code-division multiple access (MC-CDMA), there is a need of advanced code construction methods. Traditional approaches, mainly based on generalized Boolean functions, have limitations in code length versatility. This paper introduces a novel approach to constructing complete complementary codes (CCC) and Z-complementary code sets (ZCCS), for reducing interference in MC-CDMA systems. The proposed construction, distinct from Boolean function-based approaches, employs additive characters over Galois fields GF($p^{r}$), where $p$ is prime and $r$ is a positive integer. First, we develop CCCs with lengths of $p^{r}$, which are then extended to construct ZCCS with both unreported lengths and sizes of $np^{r}$, where $n$ are arbitrary positive integers. The versatility of this method is further highlighted as it includes the lengths of ZCCS reported in prior studies as special cases, underscoring the method's comprehensive nature and superiority.

cs.IT↗

arXiv2024

A Direct Construction of 2D-CCC with Arbitrary Array Size and Flexible Set Size Using Multivariable Function

Recently, two-dimensional (2D) array codes have been found to have applications in wireless communication.In this paper, we propose direct construction of 2D complete complementary codes (2D-CCCs) with arbitrary array size and flexible set size using multivariable functions (MVF). The Peak-to-mean envelope power ratio (PMEPR) properties of row and column sequences of the constructed 2D-CCC arrays are investigated. The proposed construction generalizes many of the existing state-of-the-art such as Golay complementary pair (GCP), one-dimensional (1D)-CCC, 2D Golay complementary array set (2D-GCAS), and 2D-CCC with better parameters compared to the existing work.

cs.IT↗

arXiv2023

Construction of Optimal Binary Z-Complementary Code Sets with New Lengths

Z-complementary code sets (ZCCSs) are used in multicarrier code-division multiple access (MC-CDMA) systems, for interference-free communication over multiuser and quasi-asynchronous environments. In this letter, we propose three new constructions of optimal binary $\left(R2^{k+1},2^{k+1}, Rγ,γ\right)$-ZCCS, $\left(R2^{k+1},2^{k+1}, R2^{m_{2}},2^{m_{2}}\right)$-ZCCS and $\left(2^{k+1},2^{k+1},3γ,2γ\right)$-ZCCS based on generalized Boolean functions (GBFs), where $γ=2^{m_{1}-1}+2^{m_{1}-3}, m_{1}\geq 5, k\geq 1,m_{2}\geq 1$ and $R$ is any even number. The proposed ZCCSs cover many unreported lengths and large set sizes.

cs.IT↗

arXiv2023

A Direct Construction of Optimal 2D-ZCACS with Flexible Array Size and Large Set Size

In this paper, we propose a direct construction of optimal two-dimensional Z-complementary array code sets (2D-ZCACS) using multivariable functions (MVFs). In contrast to earlier works, the proposed construction allows for a flexible array size and a large set size. Additionally, the proposed design can be transformed into a one-dimensional Z-complementary code set (1D-ZCCS). Many of the 1D-ZCCS described in the literature appeared to be special cases of this proposed construction. At last, we compare our work with the current state of the art and then draw our conclusions.

cs.IT↗

arXiv2021

Direct Construction of Optimal Z-Complementary Code Sets for all Possible Even Length by Using Pseudo-Boolean Functions

Z-complementary code set (ZCCS) are well known to be used in multicarrier code-division multiple access (MCCDMA) system to provide a interference free environment. Based on the existing literature, the direct construction of optimal ZCCSs are limited to its length. In this paper, we are interested in constructing optimal ZCCSs of all possible even lengths using Pseudo-Boolean functions. The maximum column sequence peakto-man envelop power ratio (PMEPR) of the proposed ZCCSs is upper-bounded by two, which may give an extra benefit in managing PMEPR in an ZCCS based MC-CDMA system, as well as the ability to handle a large number of users.

cs.IT↗