Construction of Binary Odd Shift Complementary Pairs of All Lengths
Piyush Priyanshu, Indian Institute of Technology, Patna, Bihar, India, India; Sudhan Majhi, Indian Institute of Science, Bengaluru, Karnataka, India, India; Subhabrata Paul, Indian Institute of Technology, Patna, Bihar, India, India
Session:
Combinatorics and Information Theory 1
Track:
21: Other topics
Location:
VIP
Presentation Time:
Wed, 10 Jul, 10:30 - 10:50
Session Chair:
Chaoping Xing, Shanghai Jiaotong University
Abstract
In orthogonal frequency division multiplexing (OFDM), peak-to-mean envelope power ratio (PMEPR) plays a vital role in the system's performance. In binary Golay complementary pair (GCP), PMEPR is less than or equal to $2$. However, the binary GCPs are limited in length. This paper proposes a novel construction of a new family of binary complementary pairs, named an odd shift complementary pair (OSCP), having all possible lengths. The PMEPR depends on the function we choose. However, we have calculated the PMEPR of OSCP having a length of $2^m-1$, where the function is a second-order Boolean function and asymptotically bounded by $4$. OSCP is the pair of two complex-valued sequences having their sum of aperiodic auto-correlation function (AACF) zero at every odd time shift.