Ivan J. Fair

Guided scrambling: a new line coding technique for high bit rate fiber optic transmission systems

The technique introduced has relatively simple encoding and decoding procedures which can be implemented at the high bit rates used in optical fiber communication systems. Because it is similar to the established technique of self-synchronizing scrambling but is also capable of guiding the scrambling process to produce a balanced encoded bit stream, the technique is called guided scrambling, (GS). The concept of GS coding is explained, and design parameters which ensure good line code characteristics are discussed. The performance of a number of guided scrambling configurations is reported in terms of maximum consecutive like-encoded bits, encoded stream disparity, decoder error extension, and power spectral density of the encoded signal. Comparison of guided scrambling with conventional line code techniques indicates a performance which approaches that of alphabetic lookup table codes with an implementation complexity similar to that of current nonalphabetic coding techniques. >

PAPR reduction of OFDM signals using partial transmit sequence: an optimal approach using sphere decoding

Partial transmit sequence (PTS) is a promising technique for peak-to-average-power ratio (PAPR) reduction in orthogonal frequency division multiplexing (OFDM) systems. Computation of optimal PTS weight factors via exhaustive search requires exponential complexity in the number of subblocks; consequently, many suboptimal strategies have been developed to date. In this letter, we introduce an efficient algorithm for computing the optimal PTS weights that has lower complexity than exhaustive search.

Techniques for early stopping and error detection in turbo decoding

In this letter, we present three new criteria for early stopping and error detection in turbo decoding. The approaches are based on monitoring the mean of the absolute values of the log-likelihood ratio of the decoded bits, which we show to be directly related to the variance of the metachannel. We demonstrate that this mean value increases as the number of errors in a frame decreases, and as a result, propose the simple mean-estimate criterion. We show that the systematic component of a terminated recursive systematic convolutional encoder used in turbo codes provides a built-in cyclic redundancy check (CRC). To further improve the performance, we also propose the mean-sign-change (MSC) criterion and the MSC-CRCeb criterion, in which a short external CRC code and the built-in CRC are concatenated with the MSC criterion.

Density Evolution for Nonbinary LDPC Codes Under Gaussian Approximation

This paper extends the work on density evolution for binary low-density parity-check (LDPC) codes with Gaussian approximation to LDPC codes over GF(q) . We first generalize the definition of channel symmetry for nonbinary inputs to include q-ary phase-shift keying (PSK) modulated channels for prime q and binary-modulated channels for q that is a power of 2. For the well-defined q-ary-input symmetric-output channel, we prove that under the Gaussian assumption, the density distribution for messages undergoing decoding is fully characterized by (q-1) quantities. Assuming uniform edge weights, we further show that the density of messages computed by the check node decoder (CND) is fully defined by a single number. We then present the approximate density evolution for regular and irregular LDPC codes, and show that the (q-1) -dimensional integration involved can be simplified using a dimensionality reduction algorithm for the important case of q=2p. Through application of approximate density evolution and linear programming, we optimize the degree distribution of LDPC codes over GF(3) and GF(4). The optimized irregular LDPC codes demonstrate performance close to the Shannon capacity for long codewords. We also design GF(q) codes for high-order modulation by using the idea of a channel adapter. We find that codes designed in this fashion outperform those optimized specifically for the binary additive white Gaussian noise (AWGN) channel for a short codewords and a spectral efficiency of 2 bits per channel use (b/cu).

Analysis of Four-Wave Mixing Suppression in Fiber-Optic OFDM Transmission Systems With an Optical Phase Conjugation Module

Coherent optical orthogonal frequency-division multiplexed (OFDM) systems must be carefully designed to minimize the detrimental impact of fiber nonlinearity manifested through four-wave mixing (FWM). Because of the small subcarrier spacing associated with OFDM, a significant fraction of FWM processes is well matched, resulting in a rapid buildup of FWM light with propagation distance. In this paper, we consider optical phase conjugation (OPC) as an approach to suppress such well-matched FWM processes. An analytical formula accurately predicting the degree of suppression is derived and discussed. It is shown that when combined with the methods previously proposed in the literature, the application of OPC can dramatically reduce the overall FWM power accumulated within the link for a wide range of crucial design parameters.

On Four-Wave Mixing Suppression in Dispersion-Managed Fiber-Optic OFDM Systems With an Optical Phase Conjugation Module

Coherent optical orthogonal frequency-division multiplexed (OFDM) systems with uniform chromatic dispersion can efficaciously combat both fiber dispersion by utilizing the properties of the cyclic prefix and four-wave mixing (FWM) among the individual subcarriers via the phased-array effect in dispersive fiber links. Such excellent performance, however, often implies appreciable sacrifices in data rate, since a long cyclic prefix is required to compensate for the dispersion accumulated at the receiver. The spectral efficiency of such OFDM systems may be substantially improved by dispersion management. Dispersion-compensating fibers placed periodically along the transmission line can significantly shorten the channel memory thereby allowing a reduction in the cyclic prefix overhead. However, the FWM tolerance of such dispersion-managed (DM) links may suffer considerably. In this work, the application of optical phase conjugation (OPC) to DM OFDM systems is investigated. Several systems set-ups are considered, and the degrees of inter-subcarrier FWM suppression are estimated analytically for arbitrary dispersion map parameters. A comparison is also made against links with uniform chromatic dispersion. Despite their inherently inferior FWM tolerance properties, DM OFDM systems can be made quite competitive with the application of OPC.

Error-control selective mapping coding for PAPR reduction in OFDM systems

In this paper, we present a new selective mapping (SLM) approach that integrates peak-to-average power ratio (PAPR) reduction with error control (EC) in OFDM systems. We call this new scheme EC-SLM coding. EC-SLM coding has a simple coding structure and does not require transmission of side information. Several well-known linear EC codes such as convolutional codes, turbo codes, and LDPC codes can be included in EC-SLM coding. Performance of EC-SLM coding is evaluated.

Peak-to-average power ratio reduction of an OFDM signal using guided scrambling coding

Selective mapping (SLM) and partial transmit sequences (PTS) are two approaches that significantly improve the statistics of the peak-to-average power ratio of an orthogonal frequency-division multiplexing signal. Guided scrambling (GS) is a multimode coding technique that is used to constrain the characteristics of encoded sequences in digital transmission and recording systems. We demonstrate the similarity of these techniques, and integrate GS coding with SLM and PTS. Our proposed GS-SLM and GS-PTS techniques result in very good PAPR performance with little error extension, and do not require transmission of side information.

A performance metric for codes with a high-order spectral null at zero frequency

Sum-variance is a well-known metric for assessing the performance of dc-free codes (first-order spectral-null codes), however, as we show in this paper, it is unsuitable for comparing the magnitude of spectral components of high-order spectral-null (HOSN) codes at low frequencies. In this paper, we introduce a new performance metric for evaluating the spectrum compression of arbitrarily HOSN codes around zero frequency; we call this metric the low-frequency spectrum weight (LFSW). We show that the asymptotic low-frequency spectral components of Kth-order spectral-null codes (K/spl ges/1) are exclusively determined by the order K and the LFSW, and that the LFSW equals the zero-frequency value in the spectrum of the corresponding sequence of Kth-order running digital sum values. We derive this result for symbol-by-symbol encoding, and then extend it to block HOSN codes. We then derive a closed-form expression for the LFSW of HOSN codes constructed through state-independent encoding. Closed-form expressions for LFSW of first-order zero-disparity codes and for the asymptotic LSFW of maxentropic dc-free sequences are also given.

Low-density parity-check codes for space-time wireless transmission

Irregular low-density parity-check (LDPC) codes have shown exceptionally good performance for single antenna systems over a wide class of channels. In this paper, we investigate their application to multiple antenna systems in flat Rayleigh fading channels. For small transmit arrays, we focus mainly on space-time coding with 2/sup p/-ary LDPC codes, where p equals the number of encoded bits transmitted by the transmit antenna array during each signaling interval. For large transmit arrays, we study a layered space-time architecture using binary LDPC codes as component codes of each layer: We show through simulation that, when applied to multiple antenna systems with high diversity order, LDPC codes of quasi-regular construction are able to achieve higher coding gain and/or diversity gain than previously proposed space-time trellis codes, space-time turbo codes, and convolutional codes in a number of fading conditions. Extending the work of density evolution with Gaussian approximation, we study 2/sup p/-ary LDPC codes on multiple antenna fading channels, and search for the optimum 2/sup p/-ary quasi-regular codes in quasi-static fading. We also show that on fast fading channels, 2/sup p/-ary irregular LDPC codes, though designed for static channels, have superior performance to nonbinary quasiregular codes and binary irregular codes specifically designed for fast fading channels.