arXiv subjects

Sudhan Majhi

Publications and source records attributed to Sudhan Majhi.

29 records · Page 2Linked to original sources

arXiv2022

A Direct Construction of GCP and Binary CCC of Length Non Power of Two

Golay complementary pairs (GCPs) and complete complementary codes (CCCs) have found a wide range of practical applications in coding, signal processing and wireless communication due to their ideal correlation properties. In fact, binary CCCs have special advantages in spread spectrum communication due to their simple modulo-2 arithmetic operation, modulation and correlation simplicity, but they are limited in length. In this paper, we present a direct construction of GCPs, mutually orthogonal complementary sets (MOCSs) and binary CCCs of non-power of two lengths to widen their application in the recent field. First, a generalised Boolean function (GBF) based truncation technique has been used to construct GCPs of non-power of two lengths. Then Complementary sets (CSs) and MOCSs of lengths of the form $2^{m-1}+2^{m-3}$ ($m \geq 5$) and $2^{m-1}+2^{m-2}+2^{m-4}$ ($m \geq 6$) are generated by GBFs. Finally, binary CCCs with desired lengths are constructed using the union of MOCSs. The row and column sequence peak to mean envelope power ratio (PMEPR) has been investigated and compared with existing work. The column sequence PMEPR of resultant CCCs can be effectively upper bounded by $2$.

cs.IT↗

arXiv2021

Q-Learning Based Energy-Efficient Network Planning in IP-over-EON

During network planning phase, optimal network planning implemented through efficient resource allocation and static traffic demand provisioning in IP-over-elastic optical network (IP-over-EON) is significantly challenging compared with the fixed-grid wavelength division multiplexing (WDM) network due to increased flexibility in IP-over-EON. Mathematical optimization models used for this purpose may not provide solution for large networks due to large computational complexity. In this regard, a greedy heuristic may be used that intuitively selects traffic elements in sequence from static traffic demand matrix and attempts to find the best solution. However, in general, such greedy heuristics offer suboptimal solutions, since appropriate traffic sequence offering the optimal performance is rarely selected. In this regard, we propose a reinforcement learning technique (in particular a Q-learning method), combined with an auxiliary graph (AG)-based energy efficient greedy method to be used for large network planning. The Q-learning method is used to decide the suitable sequence of traffic allocation such that the overall power consumption in the network reduces. In the proposed heuristic, each traffic from the given static traffic demand matrix is successively selected using the Q-learning technique and provisioned using the AG-based greedy method.

cs.NI↗

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

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↗

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

New Sets of Optimal Odd-length Binary Z-Complementary Pairs

A pair of sequences is called a Z-complementary pair (ZCP) if it has zero aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region, called zero correlation zone (ZCZ). Optimal odd-length binary ZCPs (OB-ZCPs) display closest correlation properties to Golay complementary pairs (GCPs) in that each OB-ZCP achieves maximum ZCZ of width (N+1)/2 (where N is the sequence length) and every out-of-zone AACSs reaches the minimum magnitude value, i.e. 2. Till date, systematic constructions of optimal OB-ZCPs exist only for lengths $2^α \pm 1$, where $α$ is a positive integer. In this paper, we construct optimal OB-ZCPs of generic lengths $2^α10^β26^γ+1$ (where $α,~ β, ~ γ$ are non-negative integers and $α\geq 1$) from inserted versions of binary GCPs. The key leading to the proposed constructions is several newly identified structure properties of binary GCPs obtained from Turyn's method. This key also allows us to construct OB-ZCPs with possible ZCZ widths of $4 \times 10^{β-1} +1$, $12 \times 26^{γ-1}+1$ and $12 \times 10^β26^{γ-1}+1$ through proper insertions of GCPs of lengths $10^β,~ 26^γ, \text{and } 10^β26^γ$, respectively. Our proposed OB-ZCPs have applications in communications and radar (as an alternative to GCPs).

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↗

arXiv2019

New Optimal $Z$-Complementary Code Sets from Matrices of Polynomials

The concept of paraunitary (PU) matrices arose in the early 1990s in the study of multi-rate filter banks. So far, these matrices have found wide applications in cryptography, digital signal processing, and wireless communications. Existing PU matrices are subject to certain constraints on their existence and hence their availability is not guaranteed in practice. Motivated by this, for the first time, we introduce a novel concept, called $Z$-paraunitary (ZPU) matrix, whose orthogonality is defined over a matrix of polynomials with identical degree not necessarily taking the maximum value. We show that there exists an equivalence between a ZPU matrix and a $Z$-complementary code set when the latter is expressed as a matrix with polynomial entries. Furthermore, we investigate some important properties of ZPU matrices, which are useful for the extension of matrix sizes and sequence lengths. Finally, we propose a unifying construction framework for optimal ZPU matrices which includes existing PU matrices as a special case.

cs.IT↗

arXiv2016

Two-Level Spatial Multiplexing using Hybrid Beamforming Antenna Arrays for mmWave Communications

In this work, we consider a two-level hierarchical MIMO antenna array system, where each antenna of the upper level is made up of a subarray on the lower one. The concept of spatial multiplexing is applied twice in this situation: Firstly, the spatial multiplexing of a Line-of-Sight (LoS) MIMO system is exploited. It is based on appropriate (sub-)array distances and achieves multiplexing gain due to phase differences among the signals at the receive (sub-)arrays. Secondly, one or more additional reflected paths of different angles (separated from the LoS path by different spatial beams at the subarrays) are used to exploit spatial multiplexing between paths. By exploiting the above two multiplexing kinds simultaneously, a high dimensional system with maximum spatial multiplexing is proposed by jointly using 'phase differences' within paths and 'angular differences' between paths. The system includes an advanced hybrid beamforming architecture with large subarray separation, which could occur in millimeter wave backhaul scenarios. The possible gains of the system w.r.t. a pure LOS MIMO system are illustrated by evaluating the capacities with total transmit power constraints.

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