Multicarrier transmission system such as Orthogonal Frequency Division Multiplexing (OFDM) is a promising technique for high bit rate transmission in wireless communication systems. OFDM is a spectrally efficient modulation technique that can achieve high speed data transmission over multipath fading channels without the need for powerful equalization techniques. A major drawback of OFDM is the...

Binary Golay sequence pairs exist for lengths 2, 10 and 26 and, by Turyn’s product construction, for all lengths of the form 21026 where a, b, c are non-negative integers. Computer search has shown that all inequivalent binary Golay sequence pairs of length less than 100 can be constructed from five “seed” pairs, of length 2, 10, 10, 20 and 26. We give the first complete explanation of the orig...

Controlling the peak-to-mean envelope power ratio (PMEPR) of Orthogonal Frequency Division Multiplexed (OFDM) transmissions is a notoriously di cult problem, though one which is of vital importance for the practical application of OFDM in low-cost applications. The utility of Golay complementary sequences in solving this problem has been recognised for some time. In this paper, a powerful theor...

OFDM is a powerful multicarrier transmission technique used extensively for wireless applications. High PAPR is one of the deleterious problems of OFDM. This paper reviews basic OFDM system and PAPR problem associated with it. Also, the construction of M-QAM particularly 16-QAM sequences using QPSK Golay sequences over 4  is conferred. It is elucidated that a 16-QAM constellation can be writte...

The Savitzky–Golay smoothing and differentiation filter optimally fits a set of data points to a polynomial in the least-squares sense. The Savitzky–Golay filter has been developed and generalized well in the literatures. However, the data subset is subject to an odd number ð2m þ 1Þ: In this communication, the Savitzky–Golay filter is extended for even number data. Simulations are performed to ...

We discuss a specific type of error-control coding using Golay codes. First we introduce the basics of coding. Then we discuss the Golay code in binary form, extended binary form, and ternary form.

We give a new construction of the extended binary Golay code. The construction is carried out by taking the Gray image of a self-dual linear code over the ring R = F2+uF2+vF2+uvF2 of length 6 and size 212. Writing a typical generating matrix of the form [I3|A], with A being a 3× 3 matrix over R, and finding some dependencies among the entries of A, we are able to set a general form for the gene...

This study concerns the development and investigation of a new composing method of short coded sequences and their transmission based on well-known Golay complementary codes and applied compression technique allowing to increase the signal-to-noise ratio (SNR) and penetration. This new method can potentially play important role in examination of superficial structures, e.g. dermatology, ophthal...

Golay complementary sequences, often referred to as Golay pairs, are characterised by the property that the sum of their aperiodic autocorrelation functions equals to zero, except for the zero shift. Because of this property, Golay complementary sequences can be utilised to construct Hadamard matrices defining sets of orthogonal spreading sequences for DS CDMA systems of the lengths not necessa...