arXiv subjects

Palash Sarkar

Publications and source records attributed to Palash Sarkar.

29 records · Page 2Linked to original sources

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↗

arXiv2021

Pseudo-Boolean Functions for Optimal Z-Complementary Code Sets with Flexible Lengths

This paper aims to construct optimal Z-complementary code set (ZCCS) with non-power-of-two (NPT) lengths to enable interference-free multicarrier code-division multiple access (MC-CDMA) systems. The existing ZCCSs with NPT lengths, which are constructed from generalized Boolean functions (GBFs), are sub-optimal only with respect to the set size upper bound. For the first time in the literature, we advocate the use of pseudo-Boolean functions (PBFs) (each of which transforms a number of binary variables to a real number as a natural generalization of GBF) for direct constructions of optimal ZCCSs with NPT lengths.

cs.IT↗

arXiv2020

Separation Results for Boolean Function Classes

We show (almost) separation between certain important classes of Boolean functions. The technique that we use is to show that the total influence of functions in one class is less than the total influence of functions in the other class. In particular, we show (almost) separation of several classes of Boolean functions which have been studied in the coding theory and cryptography from classes which have been studied in combinatorics and complexity theory.

cs.CC↗

arXiv2020

A Direct and Generalized Construction of Polyphase Complementary Set with Low PMEPR and High Code-Rate for OFDM System

A major drawback of orthogonal frequency division multiplexing (OFDM) systems is their high peak-to-mean envelope power ratio (PMEPR). The PMEPR problem can be solved by adopting large codebooks consisting of complementary sequences with low PMEPR. In this paper, we present a new construction of polyphase complementary sets (CSs) using generalized Boolean functions (GBFs), which generalizes Schmidt's construction in 2007, Paterson's construction in 2000 and Golay complementary pairs (GCPs) given by Davis and Jedwab in 1999. Compared with Schmidt's approach, our proposed CSs lead to lower PMEPR with higher code-rate for sequences constructed from higher-order ($\geq 3$) GBFs. We obtain polyphase complementary sequences with maximum PMEPR of $2^{k+1}$ and $2^{k+2}-2M$ where $k,M$ are non-negative integers that can be easily derived from the GBF associated with the CS.

cs.IT↗

arXiv2020

Can Efficient Detection and Isolation Control an Epidemic?

The World Health Organisation (WHO) has very strongly recommended testing and isolation as a strategy for controlling the ongoing COVID-19 pandemic. The goal of this paper is to quantify the effects of detection and isolation in formal models of epidemics of varying complexity. A key parameter of such models is the basic reproduction ratio. We show that an effective detection and isolation strategy leads to a reduction of the basic reproduction ratio and can even lead to this ratio becoming lower than one.

q-bio.PE↗

arXiv2019

Optimal Z-complementary Code Set From Generalized Reed-Muller Codes

Z-complementary code set (ZCCS), an extension of perfect complementary codes (CCs), refers to a set of two-dimensional matrices having zero correlation zone properties. ZCCS can be used in various multi-channel systems to support, for example, quasi-synchronous interference-free multicarrier code-division multiple access communication and optimal channel estimation in multiple-input multiple-output systems. Traditional constructions of ZCCS heavily rely on a series of sequence operations which may not be feasible for rapid hardware generation particularly for long ZCCSs. In this paper, we propose a direct construction of ZCCS using second-order Reed-Muller codes with efficient graphical representation. Our proposed construction, valid for any number of isolated vertices present in the graph, is capable of generating optimal ZCCS meeting the set size upper bound.

cs.IT↗

arXiv2019

A Direct Construction of Optimal ZCCS With Maximum Column Sequence PMEPR Two for MC-CDMA System

Multicarrier code-division multiple-access (MC-CDMA) combines an orthogonal frequency division multiplexing (OFDM) modulation and a code-division multiple-access (CDMA) scheme to exploits the benefits of both the technologies. The high peak-to-mean envelope power ratio (PMEPR) is a considerable problem in MC-CDMA system. However, the problem can be addressed by utilizing complete complementary codes (CCCs) in MC-CDMA system. But the set size upper bound of CCC does not allow the system to support large number of users for a given number of subcarriers in the system. In a CCC and Z-complementary code set (ZCCS) based asynchronous MC-CDMA system, the PMEPR is determined by column sequence PMEPR of the codes. In order to support a large number of users with low column sequence PMEPR, in this paper, we have proposed a new optimal ZCCS with larger set size. The code is constructed using Boolean function approach, i.e., by a direct construction method. The number of constituent sequences in ZCCS is the same as the number of subcarriers in MC-CDMA. So, large size ZCCS for large number of users in MC-CDMA can be constructed through a rapid hardware generation. The proposed ZCCS has maximum column sequence PMEPR of 2 and it achieves the theoretical upper bound of optimality. Our proposed construction can also generate inter-group complementary (IGC) code set for MC-CDMA with the same PMEPR. This work also establishes a link from ZCCS and IGC code set to higher-order ($\geq 2$) Reed-Muller (RM) code.

cs.IT↗

arXiv2019

A Direct Construction of Z-Complementary Pairs Using Generalized Boolean Functions

The zero correlation zone (ZCZ) ratio, i.e., the ratio of the width of the ZCZ and the length of the sequence plays a major role in reducing interference in an asynchronous environment of communication systems. However, to the best of the author's knowledge, the highest ZCZ ratio for even-length binary Z-complementary pairs (EB-ZCPs) which are directly constructed using generalized Boolean functions (GBFs), is $\frac{2}{3}$. In this research, we present a direct construction of EB-ZCPs through GBFs, which can achieve a ZCZ ratio of $\frac{3}{4}$. In general, the constructed EB-ZCPs are of length $2^{m-1}+2$, having a ZCZ width of $2^{m-2}+2^{π(m-3)}+1$ where pi is a permutation over $m-2$ variables.

math.CO↗

arXiv2016

On Irreducible Polynomials of the Form $b(x^d)$

Let $p$ be a prime and $b(x)$ be an irreducible polynomial of degree $k$ over $\mathbb{F}_p$. Let $d\geq 1$ be an integer. Consider the following question: Is $b(x^d)$ irreducible? We derive necessary conditions for $b(x^d)$ to be irreducible. Further, when the necessary conditions are satisfied, we obtain the probability for $b(x^d)$ to be irreducible.

math.NT↗

arXiv2008

Colliding Message Pairs for 23 and 24-step SHA-512

Recently, Indesteege et al. [1] had described attacks against 23 and 24-step SHA-512 at SAC '08. Their attacks are based on the differential path by Nikolic and Biryukov [2]. The reported complexities are $2^{44.9}$ and $2^{53}$ calls to the respective step reduced SHA-512 hash function. They provided colliding message pairs for 23-step SHA-512 but did not provide a colliding message pair for 24-step SHA-512. In this note we provide a colliding message pair for 23-step SHA-512 and the first colliding message pair for 24-step SHA-512. Our attacks use the differential path first described by Sanadhya and Sarkar at ACISP '08 [3]. The complexities of our attacks are $2^{16.5}$ and $2^{34.5}$ calls to the respective step reduced SHA-512 hash function. Complete details of the attacks will be provided in an extended version of this note.

cs.CR↗

arXiv2008

22-Step Collisions for SHA-2

In this note, we provide the first 22-step collisions for SHA-256 and SHA-512. Detailed technique of generating these collisions will be provided in the next revision of this note.

cs.CR↗