FPGA-Implemented Fractal Decoder with Forward Error Correction in Short-Reach Optical Interconnects

Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on a positional number system. In this work, we evaluated the indivisible code using the average probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This study researched a fractal decoder device for additional error control, implemented in field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10% to 30% for different n while receiving the reciprocal of the golden ratio.     

Interaction of a transient cylindrical acoustic wave with a multimode cylindrical piezoelectric transducer

The interaction between a transient cylindrical acoustic wave and a cylindrical piezoelectric transducer with sectioned electrodes is considered. The solution is obtained using the integral Laplace transform with respect to time (in the form of natural-mode series). In going to the space of originals, the problem is reduced to integral Volterra equations. The results of calculation are presented for various angular dimensions of the electrode sections and various distances from the wave source to the piezoelectric transducer. Translated from Prikladnaya Mekhanika, Vol. 35, No. 10, pp. 37–45, October, 1999.     

A Nonlinear Model of Age-Dependent Population Dynamics

We consider a mathematical model of age-dependent population dynamics that is a generalization of the Gurtin–MacCamy model. We study the existence and uniqueness of solutions of an initial boundary-value problem and the existence and stability of stationary age distributions.     

Transient oscillations of a multimode cylidrical piezoelectric transducer with a disconnected electrode section

The transient excitation of a cylindrical piezoelectric transducer with sectional electrodes is considered. A signal is supplied to one of the electrode sections while the electrodes of the other section are disconnected. The problem is solved by applying the Laplace integral time transform and representing the functions to be determined in the form of a series in natural oscillation modes. Calculation results are given for some transient signal profiles and different electrode-section sizes. Institute of Pulse Processes and Technology, National Academy of Sciences of Ukraine, Nikolaev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 4, pp. 73–79, April, 1999.