We present a range of coding schemes for OFDM transmission using binary, quaternary, octary, and higher order modulation that give high code rates for moderate numbers of carriers. These schemes have tightly bounded peak-to-mean envelope power ratio (PMEPR) and simultaneously have good error correction capability. The key theoretical result is a previously unrecognized connection between Golay complementary sequences and second-order Reed-Muller codes over alphabets Z/sub 2/h. We obtain additional flexibility in trading off code rate, PMEPR, and error correction capability by partitioning the second-order Reed-Muller code into cosets such that codewords with large values of PMEPR are isolated. For all the proposed schemes we show that encoding is straightforward and give an efficient decoding algorithm involving multiple fast Hadamard transforms. Since the coding schemes are all based on the same formal generator matrix we can deal adaptively with varying channel constraints and evolving system requirements.

/pdf/peak-to-mean-power-control-in-ofdm-golay-complementary-384pix8yoa.pdf

Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes

We have developed a simple, wide-optical-bandwidth, high-resolution system for performing rapid optical frequency domain reflectometry measurements and applied it to multidimensional tomographic imaging. The source is a grating-tuned external cavity semiconductor laser with a tuning capability of 25 nm in 100 ms. We discuss system performance and show a two-dimensional optical coherence tomography image of a thin glass sandwich structure as a preliminary demonstration of the systems depth and resolution capabilities.

Optical coherence tomography using a frequency-tunable optical source

We demonstrate a high-speed, frequency swept, 1300 nm laser source for frequency domain reflectometry and OCT with Fourier domain/swept-source detection. The laser uses a fiber coupled, semiconductor amplifier and a tunable fiber Fabry-Perot filter. We present scaling principles which predict the maximum frequency sweep speed and trade offs in output power, noise and instantaneous linewidth performance. The use of an amplification stage for increasing output power and for spectral shaping is discussed in detail. The laser generates ~45 mW instantaneous peak power at 20 kHz sweep rates with a tuning range of ~120 nm full width. In frequency domain reflectometry and OCT applications the frequency swept laser achieves 108 dB sensitivity and ~10 mum axial resolution in tissue. We also present a fast algorithm for real time calibration of the fringe signal to equally spaced sampling in frequency for high speed OCT image preview.

Amplified, Frequency Swept Lasers for Frequency Domain Reflectometry and OCT Imaging : Design and Scaling Principles

This paper gives an introduction to optical coherence tomography (OCT), explains its basic principles, and
discusses the information content of OCT images. Various interferometric techniques used in OCT are reviewed
and a short survey of results obtained so far in different fields of application and possible future
developments are presented.

https://www.spiedigitallibrary.org/journals/Journal-of-Biomedical-Optics/volume-1/issue-02/0000/Optical-coherence-tomography/10.1117/12.231361.pdf

Optical coherence tomography.

Controlling the peak-to-mean envelope power ratio (PMEPR) of orthogonal frequency-division multiplexed (OFDM) transmissions is a notoriously difficult 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 recognized for some time In this paper, a powerful theory linking Golay complementary sets of polyphase sequences and Reed-Muller codes is developed Our main result shows that any second-order coset of a q-ary generalization of the first order Reed-Muller code can be partitioned into Golay complementary sets whose size depends only on a single parameter that is easily computed from a graph associated with the coset As a first consequence, recent results of Davis and Jedwab (see Electron Lett, vol33, p267-8, 1997) on Golay pairs, as well as earlier constructions of Golay (1949, 1951, 1961), Budisin (1990) and Sivaswamy (1978) are shown to arise as special cases of a unified theory for Golay complementary sets As a second consequence, the main result directly yields bounds on the PMEPRs of codes formed from selected cosets of the generalized first order Reed-Muller code These codes enjoy efficient encoding, good error-correcting capability, and tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using small numbers of carriers

https://www.hpl.hp.com/techreports/98/HPL-98-57R1.pdf

Generalised Reed-Muller codes and power control in OFDM modulation

The improved performance of an optical time-domain reflectometer (OTDR) through the application of a correlation technique using codes with complementary autocorrelation properties is discussed. The theoretical foundations of the method are presented along with experimental results exhibiting the best one-way range reported to date for a practical long-haul, long-wavelength OTDR system. >

Real-time long range complementary correlation optical time domain reflectometer

A general rigorous theory of optical heterodyne and homodyne measurements is presented. The power spectrum of the photocurrent resulting from two uncorrelated optical beams mixing on a photodetector is derived. In particular, a rigorous analysis is presented for the delayed self-homodyne method which is used to characterize laser source linewidth by a Mach-Zehnder interferometer with a delay exceeding the source coherence length. Existing treatments are generalized to address non-Lorentzian laser sources of arbitrary lineshape. The analysis is further generalized to cover the case of modulated nonstationary sources. An example of the application of this theory is given. It is shown how the theory may be used to interpret an experimental result obtained using the gated delayed self-homodyne technique for characterizing the frequency chirp of laser sources under modulation. >

Spectral analysis of optical mixing measurements

A long-coherence-length, diode-pumped, monolithic Nd:YAG laser operating at 1.32 mu m is used to perform coherent FMCW (frequency-modulated continuous wave) reflectometry measurements. Compared with semiconductor-based lasers, the low phase noise of the Nd:YAG source offers greatly increased distance range combined with increased sensitivity to optical reflections. Measurement of Rayleigh backscatter from 50 km of fiber is demonstrated with over 60 dB of two-way optical dynamic range. Two-point spatial resolution is demonstrated to be better than 10 cm. This source and coherent measurement technique may have potential for both short and long-haul reflectometry applications. >

Coherent FMCW reflectometry using a temperature tuned Nd:YAG ring laser

Optical low-coherence reflectometry is used to investigate the internal structure and optical properties of human scalp hair. Regardless of hair color, the refractive index of the cortical region remains within the range of 1.56-1.59. The amplitude of the backscattered infrared light coupled into different-colored hair confirms the relative melanin content. Discontinuities in the refractive index permit identification of distinct structural layers within the hair shaft.

/pdf/characterization-of-human-scalp-hairs-by-optical-low-n2rtz7yuhu.pdf

Characterization of human scalp hairs by optical low-coherence reflectometry.

Optical filtering of amplified spontaneous emission improves measurement dynamic range for frequency response measurements of optoelectronic receivers. For high bandwidth receivers, a novel periodically filtered intensity noise technique is proposed. Response measurements using these techniques on a 1 GHz and 30 GHz receiver are demonstrated. >

Steven A. Newton

Papers

Real-time long range complementary correlation optical time domain reflectometer

Spectral analysis of optical mixing measurements

Coherent FMCW reflectometry using a temperature tuned Nd:YAG ring laser

Characterization of human scalp hairs by optical low-coherence reflectometry.

High-frequency photodiode characterization using a filtered intensity noise technique