Journal of Engineering

Volume 2016, Article ID 2385372, 10 pages

http://dx.doi.org/10.1155/2016/2385372

## Possibilities for Advanced Encoding Techniques at Signal Transmission in the Optical Transmission Medium

Institute of Telecommunications, Slovak University of Technology in Bratislava, Ilkovičova 3, 812 19 Bratislava, Slovakia

Received 25 November 2015; Accepted 13 March 2016

Academic Editor: A. S. Madhukumar

Copyright © 2016 Filip Čertík and Rastislav Róka. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents a possible simulation of negative effects in the optical transmission medium and an analysis for the utilization of different signal processing techniques at the optical signal transmission. An attention is focused on the high data rate signal transmission in the optical fiber influenced by linear and nonlinear environmental effects presented by the prepared simulation model. The analysis includes possible utilization of OOK, BPSK, DBPSK, BFSK, QPSK, DQPSK, 8PSK, and 16QAM modulation techniques together with RS, BCH, and LDPC encoding techniques for the signal transmission in the optical fiber. Moreover, the prepared simulation model is compared with real optical transmission systems. In the final part, a comparison of the selected modulation techniques with different encoding techniques and their implementation in real transmission systems is shown.

#### 1. Introduction

Nowadays, an interest in the signal transmission through optical fibers is rapidly increasing due to the transmission bandwidth. Creating new optical transmission paths can be time consuming and expensive [1–4]. Therefore, more effective approaches are appearing to satisfy increased customer requests. In both electric and optical domains, utilizing new advanced signal processing techniques can lead to increasing of the transmission capacity. Such solutions can be easily integrated. With increasing of modulation rates, negative influences on the transmitted optical signals are growing and so additional bit errors in information flows are emergent. Therefore, it is important to design and analyze a performance of advanced signal processing techniques utilized in the optical transmission medium with respect to its environmental influences. The simulation can determine transmission boundaries of each advanced signal processing technique for the designed optical system and allow comparing all possible solutions before their practical deployment. The simulation allows evaluating possible increasing of data rates and transmission ranges in deployed optical transmission systems using advanced signal processing techniques and designing new optical transmission systems with advanced optical components and fibers.

First, basic parameters of the optical fiber and principles of selected encoding techniques are introduced. In this paper, the simulation studies are restricted to the block codes. Convolutional codes with different rates and constraint lengths can later be considered along with the assumed modulation techniques. Then, a comparison of the prepared simulation model with real optical transmission systems measured by the Ciena system is presented. Moreover, a specific application of the optical transmission system with advanced optical signal processing techniques can also be represented in this case. A main attention of the contribution is focused on the analysis of different modulation and encoding techniques at the signal transmission in the optical transmission medium and their possible implementation in real transmission systems. From proposed, realized, and presented signal modulations, only some of them are considered for enhanced analysis, evaluation, and comparison purposes. In the final part, selected modulation and encoding techniques implemented on real transmission systems are analyzed for the high data rate signal transmissions.

##### 1.1. Characteristics of the Optical Fiber

Each optical fiber represents a transmission system, which is frequency dependent. A pulse propagation inside this transmission system can be described by the nonlinear Schrödinger equation (NLSE), which is derivate from Maxwell’s equations. From the NLSE equation, we can express effects in optical fibers that are classified as [5, 6](a)linear effects, which are wavelength dependent,(b)nonlinear effects, which are intensity (power) dependent.

*Linear Effects*. Major impairments of optical signals transmitted via the optical fiber environment are mainly caused by linear effects, the dispersion and the attenuation. The attenuation limits a power of optical signals and represents transmission losses. Nowadays, optical transmission systems are able to minimize impact of the attenuation by deploying all-optical amplifiers. Another source of the linear effect represents the dispersion causing broadening of optical pulses in time and signal phase shifting at the fiber end. There are three main dispersion types [5–8]:(i)The modal dispersion caused by the different propagation velocity of optical modes propagating in multimode fibers.(ii)The chromatic dispersion caused by the different propagation velocity of wavelengths generated in laser sources propagating in the optical fiber. It consists of material, profile, and waveguide dispersions.(iii)The polarization mode dispersion caused by the birefringence effect due to a nonsymmetry and imperfections of optical fibers.

*Nonlinear Effects*. These effects play an important role at the long haul optical signal transmission. Nonlinear effects can be classified as follows:(i)*Kerr nonlinearities* are self-induced effects, where the phase velocity of the pulse depends on the pulse’s own intensity. The Kerr effect describes a change in the fiber refractive index due to electrical perturbations. Due to the Kerr effect, following effects are possible to describe:(a)Self-phase modulation (SPM) is an effect that changes the refractive index of the transmission medium caused by the pulse intensity [9, 10].(b)Four-wave mixing (FWM) is an effect where the fourth wave can be arisen by mixing of three optical waves and this one can appear in the same wavelength as one of mixed waves [9].(c)Cross-phase effect (XPM) is an effect that causes a spectral broadening where the optical pulse can change the phase of another pulse with different wavelengths [9–11].(ii)*Scattering nonlinearities* occur due to a photon inelastic scattering to lower energy photons. The pulse energy is transferred to another wave with a different wavelength. Two such effects appear in the optical fiber:(a)Stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) are effects that change a variance of light wave into different waves when the intensity reaches a certain threshold [9–11].

##### 1.2. Principles of Selected Encoding Techniques

Forward error correction (FEC) techniques represent a system where additional data are inserted into a data message so that it can be recovered by a receiver even when a number of errors due to transmission is emergent. These FEC codes are widely used in systems where a data retransmission is not an option such as broadcasting and high haul optical transmission systems [12, 13]. FEC codes are usually divided into convolutional and block codes:(i)Convolutional codes are processed on a bit-by-bit basis.(ii)Block codes are processed on a block-by-block basis.

Convolutional codes are based on the encoding signal with a final impulse response. This type of coding does not require division of bits into the blocks. The convolution codes may be decoded using the Viterbi algorithm, which is a method of decoding with maximum reliability. This method is based on finding the most appropriate way forward through the possible states of transition. The complexity of the Viterbi algorithm increases with the number of states in decoding. Therefore, it is advisable to use codes that use a small amount of redundancy. Convolutional codes have lower resistance against noise than the linear block codes and not using the minimal trellis like linear blocks [13, 14].

For analysis, block codes, especially cyclic block codes, are considered. Cyclic block codes are widely used in data communication because their structure makes encoder and decoder circuitry simple. Cyclic block codes are defined as the cyclic code if is a linear code of the length over a finite field and if any cyclic shift of a codeword is also a codeword as shown in

The information data with the length are coded with the polynomial using (1). Considerwhere represents the polynomial of degree , is the information polynomial of degree , and the generator polynomial must be of degree .

The Reed-Solomon (RS) codes that belong to cyclic block codes are widely used in many communication fields [13, 14]. The RS codes are related to BCH codes and can be defined as a primitive BCH code of the length , where

RS codes are specified as or , where represent the code length, represents the information length, and is the Hamming distance. Let be a number of errors that can be corrected; then correction () or detection () abilities are specified for the code. There exist two encoding types for RS codes:(i)Nonsystematic.(ii)Systematic.

The decoding for RS codes is based on syndrome equations:where is the locator th error and represents its value (detection of location and value). More information about RS encoding techniques can be found in [13].

The Bose Chaudhuri Hocquenghem (BCH) code is a cyclic polynomial code over a finite field with chosen polynomial generator. BCH codes are -error correcting codes defined over finite fields , where . The advantage of BCH codes is using syndrome to decode errors in which there exist good decoding algorithms that correct multiple errors [14].

The generating of a binary BCH code over an extension field is easy to construct. The polynomial generator is needed to obtain a cyclic code [12–16]. For any integer and , there exists a primitive BCH code with parameters , , and . The generator polynomial of -error correcting primitive BCH codes of the length is given bywhere LCM represents the Least Common Multiple. Then the code is generated using (2).

BCH codes are decoded with various algorithm based on calculation of syndromes values for the received codeword.

Low Density Parity Check (LDPC) codes belong to linear encoding techniques that can transmit data close to the Shannon theorem (the channel capacity). The main disadvantage of the LDPC code is the time consumption of the code algorithm, which often limits its utilization in high data rate optical transmission systems. However, it is possible to encode more low data rate signals and then merge them into one high data rate signal. The high data rate signal can be transmitted via the optical transmission system.

The LDPC coding is defined by the LDPC matrix. Assuming the length of information bits* K*, the length of encoded bits , and the average weigh column (weight vectors represent the sum of nonzero components of the vector), then is the sum of the parity check in code. The LDPC matrix is composed of rows and columns. The generation matrix is necessary to encode coding sequence [14, 15].

Prepared block schemes of mentioned encoding techniques in the simulation model are shown in Figures 1 and 2. Figure 3 shows the schematic block diagram of LDPC source signal. Blocks are initiated using a Bernoulli generator that generates random binary bits representation of the information signal. The signal is then coded with an adequate encoding technique. The output signal is filtered with a Gaussian filter for representation of the real signal. The LDPC block is created by using 10 Bernoulli generators, each encoded with the LDPC code and merged into the high data rate signal [16, 17].