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

## TL;DR

This paper presents a direct construction method for optimal ZCCS with maximum column sequence PMEPR of 2, enabling large user support in MC-CDMA systems with efficient hardware implementation.

## Contribution

It introduces a new direct Boolean function-based construction of large ZCCS with maximum PMEPR of 2, supporting more users in MC-CDMA systems and linking to Reed-Muller codes.

## Key findings

- Constructed ZCCS achieves maximum PMEPR of 2.
- Supports large number of users with rapid hardware generation.
- Establishes connection between ZCCS, IGC codes, and Reed-Muller codes.

## Abstract

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.