History

In 1993, turbo codes were introduced by Berrou

Claude Berrou

Claude Berrou is a French professor in electrical engineering at École Nationale Supérieure des Télécommunications de Bretagne, now Telecom-Bretagne...

, Glavieux

Alain Glavieux

Alain Glavieux , was a French professor in electrical engineering at École Nationale Supérieure des Télécommunications de Bretagne...

, and Thitimajshima

Punya Thitimajshima

Punya Thitimajshima , a Thai professor in the department of telecommunications engineering at King Mongkut's Institute of Technology at Ladkrabang, is the co-inventor with Claude Berrou and Alain Glavieux of a groundbreaking coding scheme called turbo codes.Thitimajshima was educated at King...

. In 1995, the turbo principle, which was developed for turbo codes, was applied to an equalizer by Douillard, Jézéquel, and Berrou

Claude Berrou

Claude Berrou is a French professor in electrical engineering at École Nationale Supérieure des Télécommunications de Bretagne, now Telecom-Bretagne...

. They formulated the ISI receiver problem as a turbo code decoding problem, where the channel is thought of as a rate 1 convolutional code and the error correction coding is the second code. In 1997, Glavieux

Alain Glavieux

Alain Glavieux , was a French professor in electrical engineering at École Nationale Supérieure des Télécommunications de Bretagne...

, Laot, and Labat demonstrated that a linear equalizer could be used in a turbo equalizer framework. This discovery made turbo equalization computationally efficient enough to be applied to a wide range of applications.

Standard Communication System Overview

Before discussing turbo equalizers, it is necessary to understand the basic receiver in the context of a communication system. This is the topic of this section.

At the transmitter

Transmitter

In electronics and telecommunications a transmitter or radio transmitter is an electronic device which, with the aid of an antenna, produces radio waves. The transmitter itself generates a radio frequency alternating current, which is applied to the antenna. When excited by this alternating...

, information bits

Bit

A bit is the basic unit of information in computing and telecommunications; it is the amount of information stored by a digital device or other physical system that exists in one of two possible distinct states...

 are encoded

Code

A code is a rule for converting a piece of information into another form or representation , not necessarily of the same type....

. Encoding adds redundancy by mapping the information bits to a longer bit vector – the code bit vector . The encoded bits are then interleaved

Interleaving

In computer science and telecommunication, interleaving is a way to arrange data in a non-contiguous way to increase performance.It is typically used:* In error-correction coding, particularly within data transmission, disk storage, and computer memory....

. Interleaving permutes the order of the code bits resulting in bits . The main reason for doing this is to insulate the information bits from bursty noise. Next, the symbol mapper maps the bits into complex symbols

Modulation

In electronics and telecommunications, modulation is the process of varying one or more properties of a high-frequency periodic waveform, called the carrier signal, with a modulating signal which typically contains information to be transmitted...

 . These digital symbols are then converted into analog symbols with an D/A converter

Digital-to-analog converter

In electronics, a digital-to-analog converter is a device that converts a digital code to an analog signal . An analog-to-digital converter performs the reverse operation...

. Typically the signal is then up-converted to pass band frequencies by mixing it with a carrier

Carrier wave

In telecommunications, a carrier wave or carrier is a waveform that is modulated with an input signal for the purpose of conveying information. This carrier wave is usually a much higher frequency than the input signal...

 signal. This is a necessary step for complex symbols. The signal is then ready to be transmitted through the channel

Channel (communications)

In telecommunications and computer networking, a communication channel, or channel, refers either to a physical transmission medium such as a wire, or to a logical connection over a multiplexed medium such as a radio channel...

.

At the receiver

Receiver (Information Theory)

The receiver in information theory is the receiving end of a communication channel. It receives decoded messages/information from the sender, who first encoded them. Sometimes the receiver is modeled so as to include the decoder. Real-world receivers like radio receivers or telephones can not be...

, the operations performed by the transmitter are reversed to recover , an estimate of the information bits. The down-converter

Digital down converter

In digital signal processing, a digital down-converter converts a digitized real signal centered at an intermediate frequency to a basebanded complex signal centered at zero frequency...

 mixes the signal back down to baseband. The A/D converter

Analog-to-digital converter

An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...

 then samples the analog signal, making it digital. At this point, is recovered. The signal is what would be received if were transmitted through the digital baseband

Baseband

In telecommunications and signal processing, baseband is an adjective that describes signals and systems whose range of frequencies is measured from close to 0 hertz to a cut-off frequency, a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies...

 equivalent of the channel plus noise

Noise (electronics)

Electronic noise is a random fluctuation in an electrical signal, a characteristic of all electronic circuits. Noise generated by electronic devices varies greatly, as it can be produced by several different effects...

. The signal is then equalized

Equalizer (communications)

In telecommunication, the equalizer is a device that attempts to reverse the distortion incurred by a signal transmitted through a channel.- Digital communications :...

. The equalizer attempts to unravel the ISI

Intersymbol interference

In telecommunication, intersymbol interference is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have similar effect as noise, thus making the communication less reliable...

 in the received signal to recover the transmitted symbols. It then outputs the bits associated with those symbols. The vector may represent hard decisions on the bits or soft decisions. If the equalizer makes soft decisions, it outputs information relating to the probability of the bit being a 0 or a 1. If the equalizer makes hard decisions on the bits, it quantizes the soft bit decisions and outputs either a 0 or a 1. Next, the signal is deinterleaved which is a simple permutation transformation that undoes the transformation the interleaver executed. Finally, the bits are decoded by the decoder. The decoder

Decoder

A decoder is a device which does the reverse operation of an encoder, undoing the encoding so that the original information can be retrieved. The same method used to encode is usually just reversed in order to decode...

estimates from .

A diagram of the communication system is shown below. In this diagram, the channel is the equivalent baseband channel, meaning that it encompasses the D/A, the up converter, the channel, the down converter, and the A/D.

Turbo Equalizer Overview

The block diagram of a communication system employing a turbo equalizer is shown below. The turbo equalizer encompasses the equalizer, the decoder, and the blocks in between.

The difference between a turbo equalizer and a standard equalizer is the feedback loop from the decoder to the equalizer. Due to the structure of the code, the decoder not only estimates the information bits , but it also discovers new information about the coded bits . The decoder is therefore able to output extrinsic information, about the likelihood that a certain code bit stream was transmitted. Extrinsic information is new information that is not derived from information input to the block. This extrinsic information is then mapped back into information about the transmitted symbols for use in the equalizer. These extrinsic symbol likelihoods, , are fed into the equalizer as a priori symbol probabilities. The equalizer uses this a priori information as well as the input signal to estimate extrinsic probability information about the transmitted symbols. The a priori information fed to the equalizer is initialized to 0, meaning that the initial estimate made by the turbo equalizer is identical to the estimate made by the standard receiver. The information is then mapped back into information about for use by the decoder. The turbo equalizer repeats this iterative process until a stopping criterion is reached.

External links

• Turbo Equalization Resources includes an annotated bibliography, interactive block diagram, and turbo equalization simulation code.
• Turbo Equalization a Signal Processing Magazine primer on turbo equalization. Since it was written for the signal processing community in general, it is relatively accessible.
• Turbo Equalization: Principles and New Results an IEEE Transactions on Communications journal article that offers a detailed, clear explanation of turbo equalization.