Abstract
This chapter is devoted to digital communications in a smart world. The author examines turbo codes that are currently introduced in many international standards and implemented in numerous advanced communication systems, applied in a smart world, and evaluate the process of extrinsic information transfer (EXIT). The convergence properties of the iterative decoding process, associated with a given turbo-coding scheme, are estimated using the analysis technique based on so-called EXIT charts. This approach provides a possibility to predict the bit-error rate (BER) of a turbo code system with only the extrinsic information transfer chart. The idea is to consider the associated soft-input soft-output (SISO) stages as information processors, which map input a priori log likelihood ratios (LLRs) onto output extrinsic LLRs. Compared with other methods, the suggested approach provides insight into the iterative behavior of linear turbo systems with substantial reduction in numerical complexity.
TopIntroduction
Digital communications (or, data communication) is defined as data transfer over a communication channel. In a smart world, digital communications support a wide range of multimedia applications, such as audio, video and computer data that differ significantly in their traffic characteristics and performance requirements (Lokshina, 2011a, 2011b; Lokshina, Durkin, & Lanting, 2017; Lokshina & Zhong, 2017, 2019; Sklar, 2002).
Turbo codes have been adopted for providing error correction in several advanced communication systems, such as the 3rd-Generation Wideband Code Division Multiple Access (3G WCDMA) and 4th-generation Long Term Evolution (4G LTE) systems (ETSI TS 136 212 LTE, 2013; Maunder, 2015; Ngo, Maunder, & Hanzo, 2015). Turbo codes comprise a parallel concatenation of two constituent convolutional codes. By iteratively exchanging information between the two corresponding constituent decoders, turbo codes facilitate reliable communication at transmission throughputs that approach the channel capacity (Berrou, Glavieu, & Thitimajshima, 1993; Brink, 2001; Colavolpe, Ferrari, & Raheli, 2001; Hanzo, Liew, Yeap, Tee, & Ng, 2010; Lokshina, 2011a, 2011b; Lokshina & Zhong, 2017, 2019; Maunder, Wang, Ng, Yang, & Hanzo, 2008; Ngo, Maunder, & Hanzo, 2015).
Turbo codes represent a great advancement in the coding theory. Their excellent performance, especially at low and medium signal-to-noise ratios, has attracted an enormous interest for applications in digital communications. Historically, turbo codes were first deployed for satellite links and deep-space missions, where they offered impressive Bit-Error Rate (BER) performance beyond existing levels with no additional power requirement (a premium resource for satellites). Since then, they have made their way in the 3rd-generation wireless phones, Digital Video Broadcasting (DVB) systems, Wireless Metropolitan Area Networks (WMAN) and Wi-Fi networks.
Currently in a smart world, even if several research issues are still open, the success of turbo codes is growing, and their introduction in many international standards is in progress; the 3rd-Generation Partnership Project (3G PP) Universal Mobile Telecommunications System (UMTS) standard for 3rd-Generation Personal Communications and the European Telecommunications Standards Institute (ETSI) Digital Video Broadcasting – Terrestrial (DVB-T) standard for terrestrial digital video broadcasting are among them (Auer, Kryvinska, & Strauss, 2009; Bashah, Kryvinska, & Do, 2012; Brink, 2001; Iliev, Lokshina, & Radev, 2009; Kryvinska, Auer, Zinterhof, & Strauss, 2008; Kryvinska, Strauss, Collini‐Nocker, & Zinterhof, 2011; Lokshina, 2011a; Lokshina & Zhong, 2017, 2019).
In turbo processes the channel decoder and the demodulator at the receiver exchange extrinsic information. Such turbo processes are frequently analyzed using Extrinsic Information Transfer (EXIT) charts (Brink, 2000; Divsalar, Dolinar, & Pollara, 2000; Iliev, 2007; Iliev et al., 2009; Lokshina, 2011a, 2011b; Lokshina & Zhong, 2017, 2019; Ngo et al., 2015). This approach provides a possibility to predict the bit-error rate of a turbo code system using only the extrinsic information transfer chart (Lokshina, 2011b; Lokshina & Zhong, 2017; Lokshina & Zhong, 2019).
Key Terms in this Chapter
Extrinsic Information Transfer (EXIT) Chart: A technique to support the construction of good iteratively-decoded error-correcting codes (in particular, turbo codes).
Error Control: A technique that enables reliable delivery of digital data over unreliable communication channels.
Wireless Channel: A logical connection over a multiplexed medium such a radio channel. A channel is used to convey an information signal from one or several senders (or, transmitters) to one or several receivers.
Digital Communications: A concept of computer communications that is capable of very high speeds, suitable for transmission of images, voice, video, as well as data.
Bit-Error Ratio (BER): The number of bit errors per unit time. The bit-error ratio (also BER) is the number of bit errors divided by the total number of transferred bits during a studied time interval. Bit error ratio is a unitless performance measure, often expressed as a percentage.
Smart World: A concept of a digital world that evolves from the definition of ubiquitous computing and promotes the ideas of a physical world that is richly and invisibly interwoven with sensors, actuators, displays, and computational elements, embedded seamlessly in the everyday objects of our lives, and connected through a continuous network.
Turbo Code: A class of high-performance forward error correction (FEC) codes. The first practical codes to closely approach the channel capacity, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level.
Signal-to-Noise Ratio: A measure of how much useful information there is in a system, such as the internet, as a proportion of the entire contents. The ratio of the strength of an electrical or other signal carrying information to that of interference, generally expressed in decibels.
Communications System: A collection of individual communications networks, transmission systems, relay stations, tributary stations, and data terminal equipment (DTE) capable of interconnection and interoperation to form an integrated whole.
Network Performance: The analysis and review of collective network statistics, to define the quality of services offered by the underlying computer network. It is a qualitative and quantitative process that measures and defines the performance level of a given network.