Procedimiento para la Gestión del Turismo de Eventos e Incentivos

This section is a brief introduction to the theory of FEC. The understanding of coding and its limitations requires some awareness of information theory and how it would help with a digital communication system. Here, information refers to a physical quantity which can be measured, transformed, stored, and moved from place to place [202]. Figure 5.1 illustrates a fairly general framework for a sink-to- sink digital communication link, which contains key features to perform physical actions on information. It is clear that the data message from the source is encoded and modulated for communication over the channel. After the channel, the message is demodulated, decoded and sent to the destination or receiver. According to information theory, all the elements in this link have mathematical descriptions and principles which govern their performance. The source of information can be analogue (e.g. audio or video signal) which is stored in the form of a wave signal, or digital (e.g. a data file) which is stored in the form of bits. The signal produced by the source is converted if necessary into a digital signal which is made up of ‘1’s and ‘0’s, by the source encoder. The number of bits to represent the data may exceed the number of bits of actual information content. Shannon’s Source Coding Theorem [63] ensures that a particular source of data can be compressed without any loss of information (lossless compression). When compressing a data stream, a source encoder thus removes redundancy present in the data. Generally, the source encoder

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employs specific types of codes to achieve compression, called collectively source codes or data compression codes [202], including Huffman coding, run-length coding, arithmetic coding and Lempel-Ziv coding. In short, source encoding is the process of efficiently converting the output of either an analogue or a digital source into a sequence of binary digits. The information sequence is then passed through the channel encoder, with the purpose of introducing controlled redundancy in the binary information sequence via channel codes that can be used at the receiver to overcome the effects of noise and interference encountered in the transmission through the channel. The redundancy removed by the source encoder, which typically depends on the source in an unstructured way, is unstructured. In contrast, the appended redundancy for the channel encoder is structured and able to provide both uniform protection to all the information in the stream and indications of the error occurrences plus the way to correct them. In other words, the appended redundancy bits help to increase the channel reliability and improve the fidelity of the received signal. The channel encoder is the first step in the error correction or error detection process. Often, this operates by accepting a block of input symbols and producing a block of ϖ (> ) symbols at the output. The input to the channel encoder is referred to as the message symbols or information symbols (or bits, for binary codes). The binary sequence at the output of the channel encoder is passed to a digital modulator, serving as the interface to the communication channel. The modulator converts the channel encoded symbol sequences into signals appropriate for transmission over the channel, since specific channel-conforming representations are required in many channels. For example, in some cases, the channel requires the signal be sent as a continuous-time voltage, or an electromagnetic waveform in a specified frequency band. The most fundamental digital modulation techniques are

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based on keying, including PSK (phase-shift keying), FSK (frequency-shift keying), ASK (amplitude-shift keying), and QAM (quadrature amplitude modulation). In the case of this thesis, it has been stated in Chapter 4 that the signal is represented by the concentration of molecules. Thus, simple ASK or OOK modulation is applied, which means that the emission of molecules represents a binary ‘1’, whilst no release represents a binary ‘0’. Generally, the communication channel is the physical medium over which the information is conveyed between two distinct places. Common examples of channels include telephone lines, fibre-optic lines, microwave radio channels, internet cables and underwater acoustic channels. Whatever the physical medium used for transmission of the information, the essential feature is that the transmitted signal can be corrupted in a random manner by a variety of possible mechanisms. For example, some noise may be added to the signal or it may suffer from time delay, time jitter, attenuation due to the transmission distance or carrier offset, or inadvertent interference from other channels. Moreover, interference among symbols may occur if the signal is filtered by the channel response [202]. For the purpose of analysis, channels are always characterized by specific mathematical models, which are sufficiently accurate to represent the attributes of the communication scenario. For example, the bacterial communication channel proposed in this work is represented by a BAC channel, the detailed properties of which have been stated in Chapter 4. After the transmission across the channel, the demodulator or equalizer receives the signal and converts it into a sequence of symbols that represents estimates of the transmitted data symbols. This sequence of symbols then passes through the channel decoder which attempts to reconstruct the original information sequence from the channel encoding algorithm used by the channel encoder and the redundancy contained in the received data. Then

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the source decoder provides an uncompressed representation of the data according to the source encoding algorithm, which is finally received by the destination. It should be noted that in this chapter, the source encoder and decoder, modulation and demodulation are not considered. Instead, the focus will be on channel encoding and decoding methods. (error protection) Source Source Encoder Channel Encoder Modulation Channel Source Source Decoder Channel Decoder Demodulation/ equalization (data Compression) (transmission waveform generation) Sometimes combined coding/modulation(e.g. TCM) Sometimes combined/iterative decoding and modulation

Figure 5.1 A general framework for digital communications [202].

To summarise, FEC attempts to control data transmission errors over unreliable or noisy communication channels by transmitting sufficient redundant data to allow the receiver to recover from errors unaided, i.e. without sender retransmissions. Redundant bits are formed using functions of the original message bits, which may be present in an unmodified form in the encoded output (systematic codes) or not (non-systematic codes) [202]. Therefore, FEC allows the receiver to correct errors without the need for a reverse channel to request data retransmission but at the expense of a fixed and a larger forward channel bandwidth. It is therefore applied in cases where retransmissions are either very expensive or almost impossible, such as

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one-way communication links and when broadcasting to different receivers in multicast scenarios [203]. The FEC information is sparsely used in modems and generally stored in receiver mass storage devices so as to be able to recover the corrupted data. Different FEC codes are chosen for different conditions. Specifically, the code rate and the type of coding used determine the number of errors that can be corrected using FEC. A simple example is to send ‘000’ (‘111’ correspondingly) instead of sending only one ‘0’ (‘1’ correspondingly) to the channel. Due to noise in the channel, the received bits may become ‘001’. However, either ‘000’ or ‘111’ could have been sent but a maximum likelihood (ML) decoding scheme will decode the message correctly as ‘000’ and therefore ‘0’. The error correction capability of the code is dependent upon many factors, but is usually improved by increasing the amount of redundancy added to the message. The drawback to adding a lot of redundancy is that either the transmission rate is decreased as the link must be shared among the significant data information as well as the redundant bits or the bit rate must increase on the link. The benefit, however, is that the receiver has a better chance of correcting the errors without having to request a retransmission of the message. The major established categories of FEC codes are:

 Block codes (such as linear block codes, cyclic codes)  Convolutional codes

 Modern codes (such as Turbo codes)

Block codes operate on fixed-size blocks (packets) and their decoding is generally performed in polynomial time. There are many different types of block codes, such as linear block codes (e.g. Hamming codes), and cyclic codes (e.g. RS, Golay and BCH codes). Convolutional codes operate on bit or symbol streams of arbitrary length and are usually decoded using the Viterbi algorithm but their decoding may

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become extremely complex [204]. In recent years, codes such as Turbo codes have been discovered that offer performance close to the Shannon theoretical limit [205].