Knud J. Larsen

Short convolutional codes with maximal free distance for rates 1/2, 1/3, and 1/4 (Corresp.)

A combined threshing and harvesting machine, particularly for rice, has a separator for separating grain from waste. The seaparator includes an endless movable screen to which the grain and waste are carried in a stream of air. The waste is carried from the separator in a stream of air and the screen conveys the grain away for discharge from the separator.

Construction and decoding of a class of algebraic geometry codes

A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH decoder codes. >

Fast decoding of codes from algebraic plane curves

Improvement to an earlier decoding algorithm for codes from algebraic geometry is presented. For codes from an arbitrary regular plane curve the authors correct up to d*/2-m/sup 2//8+m/4-9/8 errors, where d* is the designed distance of the code and m is the degree of the curve. The complexity of finding the error locator is O(n/sup 7/3/), where n is the length of the code. For codes from Hermitian curves the complexity of finding the error values, given the error locator, is O(n/sup 2/), and the same complexity can be obtained in the general case if only d*/2-m/sup 2//2 errors are corrected. >

High-Speed 1550 nm VCSEL Data Transmission Link Employing 25 GBd 4-PAM Modulation and Hard Decision Forward Error Correction

Current short-range optical interconnects capacity is moving from 100 to 400 Gb/s and beyond. Direct modulation of several laser sources is used to minimize bandwidth limitations of current optical and electrical components. This total capacity is provided either by wavelength division multiplexing or parallel optics; it is important to investigate on the ultimate transmission capabilities of each laser source to facilitate current capacity standards and allow for future demands. High-speed four-level pulse amplitude modulation at 25 GBd of a 1.5 μ m vertical-cavity surface-emitting laser (VCSEL) is presented in this paper. The 20 GHz 3 dB-bandwidth laser is, at the time of submission, the largest bandwidth of a 1.5 μ m VCSEL ever reported. Forward error correction (FEC) is implemented to achieve transmission over 100 m virtually error free after FEC decoding. Line rate of 100 Gb/s is achieved by emulation polarization multiplexing using 50 Gb/s signal obtained from a single VCSEL.

Comments on "An efficient algorithm for computing free distance" by Bahl, L., et al.

In the above paper, ^1 Bahl et aL described a bidirectional search algorithm for computing the free distance of convolutional codes. There are some flaws in that algorithm. This correspondence contains a corrected version of the algorithm together with a proof that the corrected version always computes the free distance for noncatastrophic codes.

Error correcting coding for OTN

Forward error correction codes for 100 Gb/s optical transmission are currently receiving much attention from transport network operators and technology providers. We discuss the performance of hard decision decoding using product type codes that cover a single OTN frame or a small number of such frames. In particular we argue that a three-error correcting BCH is the best choice for the component code in such systems.

Rate-adaptive constellation shaping for near-capacity achieving turbo coded BICM

In this paper the problem of constellation shaping is considered. Mapping functions are designed for a many-to-one signal shaping strategy, combined with a turbo coded Bit-interleaved Coded Modulation (BICM), based on symmetric Huffman codes with binary reflected Gray-like properties. An algorithm is derived for finding the Huffman code with such properties for a variety of alphabet sizes, and near-capacity performance is achieved for a wide SNR region by dynamically choosing the optimal code rate, constellation size and mapping function based on the operating SNR point and assuming perfect channel quality estimation. Gains of more than 1dB are observed for high SNR compared to conventional turbo coded BICM, and it is shown that the mapping functions designed here significantly outperform current state of the art Turbo-Trellis Coded Modulation and other existing constellation shaping methods.

Turbo Equalization for Digital Coherent Receivers

High order modulation formats allow to reach higher spectral efficiency and data rate. However, their practical implementation is limited by their reduced tolerance to noise and to the optical signal power that can be launched into the fiber without generating excessive nonlinear signal distortions. In this paper, it is demonstrated that Turbo Equalization routines can be used to mitigate performance degradations stemming from optical fiber propagation effects both in optical fiber dispersion managed and unmanaged coherent detection links. The effectiveness of this solution is analyzed both numerically and experimentally for different transmission systems.

Reconfigurable Forward Error Correction Decoder for Beyond 100 Gbps High Speed Optical Links

In this paper we propose a reconfigurable forward error correction decoder for beyond 100 Gbps high speed optical links. The decoders for product codes can be configured to support the applications at a rate of a multiple of 100 Gbps, which provides the flexibility and scalability.

Turbo equalization techniques toward robust PDM 16-QAM optical fiber transmission

In this paper, we show numerically and experimentally that turbo equalization (TE) is an efficient technique to mitigate performance degradations stemming from optical fiber propagation effects in both optical fiber dispersion managed and unmanaged coherent detection links. The effectiveness of the proposed solution can be appreciated in both linear and nonlinear regimes for either scenario. We report on a system employing a polarization division multiplexing (PDM) 16-quadrature amplitude modulation (QAM) format for which we accomplish an increment in tolerance to link input power of up to 3 dB that represents a substantial improvement margin. The best bit error rate (BER) performances will therefore be guaranteed in a larger window, 6 dB, of link input power thanks to the implemented TE scheme. Moreover, our proposed approach is also proven to effectively mitigate interchannel impairments from surrounding amplitude shift-keying interfering channels in a dispersion managed link achieving also in this case an increment in power tolerance of 3 dB. Furthermore, in terms of BER performances, our proposed TE approach guarantees a gain of about a half order of magnitude at the best operational point. As TE can be included in the current coherent detection transceiver technologies and complement other equalization techniques, it has prospects for application in next-generation high-capacity and long-reach optical transmission links.