Source Coding And Channel Coding

Published Date: 02 Nov 2017

Introduction

1.1 Objective

The high demand for multimedia services provided by wireless transmission systems has made the limited resources that are available to digital wireless communication systems even more significant. The emerging requirements for these services need bandwidth for reliable and high rate data communications; and enough power for efficient transmission. The limited accessibility of these resources; and their dependence on the channel conditions are the constraints in the design of a reliable and efficient communication system. Hence there arises a need to optimize these resources using adaptive methods to meet the potential requirements. Power adaptation has been effective approach for justifying the effect of communication channels on the quality of signal transmission. The available power can be adapted to the transmitted binary symbols according to the channel conditions, which lead to optimized transmit power and also an increase in data rate. Optimization of transmitted power according to the channel conditions is a well known initiative in wireless systems.

A communication system typically involves a mechanism of measuring the quality of the channel seen by the receiver and providing such information to the transmitter to adjust the amount of transmitted power. Less power is used if the channel is good and more power when the channel is bad. Few modifications to this approach have been proposed such as to send higher data rates rather than reducing the power if the channel is good, or not to send at all if the channel is bad. These systems are considered as opportunistic systems since they take advantage of the information about the channel to optimize the communication process. The main concern for these systems is the need for a feedback link fast enough to track the time variation of the channel. The other effective approach to improve the quality of signal transmission over wireless channels is the use of channel coding techniques. Channel coding is considered as a main component of any digital communications system operating over wireless channels.

A set of power adaptation algorithms that uses the significance of information in the bits is proposed and investigated. This scheme is well suited for transmission of image and video signals over wireless channels in which different bits carry different quantity of information. The power adaptation scheme is specifically optimized for minimizing the Mean Square Error (MSE) of the image or video signal without any increase in the bandwidth requirement of the proposed system.

1.2 Motivation

A modulation technique that is commonly used for the transmission of digital signals is Pulse Code Modulation (PCM) [1]. Conventional PCM transmits all the bits obtained from the quantizer with the same energy. This scheme does not yield the minimum distortion for an uncoded case. In 1958, Bedrosian [2] proposed Weighted Pulse Code Modulation (WPCM) which demonstrated that minimization of distortion, can be achieved by weighing the PCM pulses. In WPCM, the relative amplitudes of the pulses within PCM words are adjusted so as to minimize the distortion between the transmitted and the received signal amplitude. Adjusting the amplitudes of the pulses is the same as adjusting the energy of each bit while keeping the total energy for each PCM word constant. The energies of the bits are weighed differently in order to minimize the MSE between the transmitted and received amplitudes. C.E. Sundberg [3] and D. P. Bertsekas [4] suggested near optimum methods for transmitting groups of bits at a particular energy level. For the coded case, providing different protection to streams with different reliabilities has been considered. This falls under the broad topic of Unequal Error Protection (UEP) [5]. Most of the previous works approached the problem by allocating different number of parity bits to each of these streams or in other words allocating a lower effective code rate to the stream which requires higher reliability [6]. In the present work, the problem was addressed in a different way by adapting different power levels to different bits of data to minimize MSE of the system. Various algorithms are proposed for the purpose.

The problem is how power should be adapted to the data in order to maximize performance. In order to use power efficiently and perform well, the optimization problem needs to be solved. As the amount of power available is limited, the power allocation problem becomes very critical. Many algorithms for allocating power exist [7]-[8]; however, these methods are either suboptimal and computationally efficient, or optimal, but slow to obtain convergence for the power allocation.

In this thesis, practical and efficient algorithms are presented which are guaranteed to converge to the optimal power allocation solution. This new method has significant advantages over existing schemes, and appears to be the preferred method for power adaptation.

1.3 Communication System

The fundamental concept of communication is to reproduce at one point, exactly a message selected at another point. C. Shannon [7] launched a mathematical discipline devoted to the process, transmission, storage, and use of information theory. Information theory directly addresses problems in communication, but it has also had fundamental impact on fields beyond communication engineering including probability, statistics, computation theory, physics, and economics.

Fig. 1.1 Basic Communication System

Communication systems can be broadly classified into analog communication systems and digital communication systems. Analog signals can be transmitted directly via carrier modulation and demodulated accordingly at the receiver. Modulation schemes such as Amplitude Modulation (AM) and Frequency Modulation (FM) are examples of analog communication. Digital Communication is another important way of transmitting data from the source to the destination. Analog signal can either be transmitted by carrier modulation over a channel or can be converted into a digital signal and transmitted via digital modulation. Digital communication is used in the transmission of analog and continuous time signals such as speech and images or digital signals such as text files.. A basic and sufficiently flexible abstraction of a communication system is shown in Fig.1.1.

The main advantage of digital modulation is that it provides better control of signal fidelity; the digital message can be regenerated in long distance signal transmission. In practice analog and continuous time signals are converted into digital signals for transmission. To transmit an analog signal digitally, the signal is first sampled at Nyquist rate, fs Hz, where fs is greater than or equal to twice the highest frequency component in the signal to be modulated

Source Coding and Channel Coding

The Shannon's source-channel separation theorem, states that the optimality of separating source and channel coding for point-to-point communication systems, hinges on the assumptions of unlimited complexity and delay in the system as well as an ergodic channel. While achieving optimal system performance through separate source and channel coding is deMSEable due to the modularity it provides, there is no general separation theorem for wireless communication system.

Fig.1.2. Digital Communication System

Figure 1.2 shows a more functional communication system. The signal processing steps that take place in the transmitter are, for the most, reversed in the receiver. Source encoder converts the input information to binary digits (bits); then grouped to form digital messages. It also removes all redundancy from the input bits and it outputs the message symbols. These are then passed through a channel encoder that adds redundancy in controlled level to protect against errors that might occur in the channel. For example, a channel code might take in k information bits which are output from the source encoder and output n coded bits thus forming an (n, k) channel code. The coded bits are passed through a pulse-shaping filter, represented by pulses and modulated on a carrier and transmitted on the channel. The primary purpose of the modulator is to convert a digital pulse into an analog signal which is the only practical signal that can be transmitted.

At the receiver, the demodulator extracts the received signal from the carrier waveform and obtains a value for each transmitted bit. This might correspond to an actual magnitude of the bit value transmitted or to a likelihood value of the bit being 1 or 0. The channel decoder takes in as input the received values corresponding to the n transmitted coded bits and makes the decision on the k information bits.

Coding helps in better performance over the uncoded case for the same bandwidth and same power expended, at the cost of increased complexity. Once the information bits are obtained, the source decoder can decompress them to obtain the original bits from the output of the sampler. These samples can be used to reconstruct the original signal that was transmitted. Basically, the operations at the transmitter are inverted at the receiver to obtain the signal that was transmitted. A perfect reconstruction of the signal is never possible owing to the noise in the channel, presence of quantizer which is a non-invertible operation and also the presence of a Low Pass Filter (LPF) before the sampler. Each of the above operations is important for a good reproduction of the transmitted signal at the receiver. The design of a communication system is generally constrained to one or more of the three major factors like power available for transmission of the signal, bandwidth available for transmission and the complexity of the receiver. The ultimate aim of the digital communication system is to minimize Bit Error Rate (BER) or MSE of the system. In the current work, it is looked into the aspect of minimizing MSE, which results in an optimum/near optimum bit-by-bit power allocation scheme of an uncoded and coded communication system.

Modulation and Demodulation

In digital modulation, the information signals, whether audio, video, or data are all digital. As a result, the digital information modulates an analog sinusoidal waveform carrier. The sinusoid has just three features that can be modified to carry the information: amplitude, frequency, and phase. Thus band pass modulation can be defined as the process whereby the amplitude, frequency, or phase of the carrier, or a combination of them, is varied in accordance with the digital information to be transmitted [8].

The digital modulation techniques provide more information capacity, compatibility with digital data services, higher data security, better quality communications and quicker system availability. The limitations experienced by these communication systems are:

Available bandwidth

Permissible power

Inherent noise level of the system

To face as challenge of demand for communications services, the available RF spectrum must be shared. Digital modulation schemes have greater capacity to convey large amounts of information than analog modulation schemes.

There are three major classes of digital modulation techniques used for transmission of digitally represented data:

Amplitude Shift Keying (ASK)

Frequency Shift Keying (FSK)

Phase Shift Keying (PSK)

ASK refers to a type of amplitude modulation that assigns bit values to discrete amplitude levels. The carrier signal is then modulated among the members of a set of discrete values to transmit information.

FSK refers to a type of frequency modulation that assigns bit values to discrete frequency levels. FSK is divided into non-coherent and coherent forms. In non-coherent forms of FSK, the instantaneous frequency shifts between two discrete values termed the mark and space frequencies. In coherent forms of FSK, there is no phase discontinuity in the output signal. FSK modulation formats generate modulated waveforms that are strictly real values, and thus tend not to share common features with quadrature modulation schemes.

PSK in a digital transmission refers to a type of angle modulation in which the phase of the carrier is discretely varied either in relation to a reference phase or to the phase of the immediately preceding signal element to represent data being transmitted. For example, when encoding bits, the phase shift could be 0 degree for encoding a "0," and 180 degrees for encoding a "1," or the phase shift could be –90 degrees for "0" and +90 degrees for a "1," thus making the representations for "0" and "1" a total of 180 degrees apart.

Considerations in Choice of Modulation Scheme

When choosing a modulation scheme, there are many elements to consider as listed above. This is very subjective and heavily depends on the type of application that the wireless communication is designed for. There will be some tradeoffs between some of the following elements [9].

High spectral efficiency (ability of a modulation scheme to accommodate data within a limited bandwidth)

High power efficiency (ability of the system to reliably send information at the lowest practical power level)

Robust to multipath effects (Low BER)

Low cost and ease of implementation

Low carrier-to-co channel interference ratio

Low out-of-band radiation

Constant or near constant envelope

Constant only phase is modulated

Non-constant phase and amplitude modulated

The choice of modulation method (and the demodulation scheme) depends on many different considerations, such as constraints on the transmission power and the complexity of the receiver circuitry. However, there are several common comparison criteria based on which a decision can be made between different modulation methods.

Power Efficiency: One of the many goals of a communication system is to use the least amount of energy per bit Eb to achieve reliable communication, i.e., to maintain the probability of bit error below a certain level. The amount energy needed to use depends also on the severity of the channel defects. For the simple case of the Additive White Gaussian Noise (AWGN) (or non-dispersive) channel model, to achieve a certain BER, Quadrature Phase Shift Keying (QPSK) is more power efficient than Binary Phase Shift Keying (BPSK) in this sense.

Spectral (Bandwidth) efficiency: It is preferred to choose a suitable modulation to achieve the highest bit rate possible, within a given frequency band. For example, QPSK has the same Power Spectral Density (PSD) as BPSK, but QPSK supports twice the bit rate of BPSK. Therefore, QPSK is better than BPSK in the sense that the bit rate per Hz is higher.

Complexity: Another design objective is to use the simplest transmitters and receivers. Different modulation methods could require different transmitters and receivers while the complexity of the transmitters and the receivers affects the cost of the system. Therefore, the complexity is certainly a factor of concern in determining which modulation method to use. For example, the receivers for binary communications are generally less complex than those for M-ary communications.

Robustness: Yet another consideration in choosing between modulation methods is the tolerance against variations from ideal situations, such as the AWGN model. Practical situations often contain non-ideal conditions and variations (foreseeable or not). A successful communication system must be able to tolerate (to a certain extent) unfavorable conditions. For example, FSK with non-coherent demodulation is more robust against changes in the channel phase response than BPSK which requires accurate estimation of the time-varying channel phase.

BER Performance for Digital Modulation Systems

In telecommunication, an error ratio is the ratio of the number of bits, elements, characters, or blocks incorrectly received to the total number of bits, elements, characters, or blocks sent during a specified time interval. The most commonly encountered ratio is the BER. For a given communication system, the BER will be affected by both the data transmission rate and the signal power margin. The BER can be evaluated in two different ways. One is the transmission BER defined as the ratio of the number of erroneous bits received to the total number of bits transmitted and the other is information BER that indicates the number of erroneous decoded (corrected) bits to the total number of decoded (corrected) bits.

Computation of BER

The ratio of the number of bit errors to the number of bits transmitted is the BER.

The BER is affected with the change in the parameters like receiver noise level, level of received signal, fading environment and level of interference signals

Significance of Eb/No

A better measure of signal to noise ratio is to compare the energy per bit (Eb) versus the noise power density (No) given by

- Energy per bit

- Noise density

C – Channel capacity

N – Channel Noise

B - Bandwidth

fb – Bit rate

Eb/No takes into account the bandwidth requirements and bit rates of the various formats.

Importance of Bit Error Rate in Wireless Communication

Coding and modulation provide the means of mapping information into signal waveforms such that the receiver (with an appropriate demodulator and decoder) can recover the information with reliability. The common model for a communication system is with AWGN channel. In this model, a user transmits information by sending one of M possible symbols in a given time period T, with a given amount of power. The received signal is the sum of the transmitted signal and several distinct multipath signals (noise occupying all frequencies). At low rates and low Eb/No there is virtually no loss in using QPSK modulation with the best coding compared to the best modulation and coding. It has been the goal of communication researchers and engineers to achieve performance close to the fundamental limits with small complexity and delay. BER can be used for the performance analysis of a communication system that is affected by the following parameters

Receiver noise level

Level of received signal

Fading environment

Level of interference signals

The PSK schemes are the basis of every digital modulation and transmission scheme. The different modulation techniques struggle neck to neck for getting low BER, but still with the slight change in BER the quality changes many folds. If these PSK techniques are used in designing the wireless transmitter then BER further increases due to system complexity. Therefore, there is a requirement of designing the new applications/transmission system having the basis as PSK modulation, so that BER at least remains constant.

Channel

The channel is the propagating medium or electromagnetic path connecting the transmitter and the receiver. For a wireless channel, the characteristics are typically determined by the specific geography, atmospheric effects, objects in the channel, multipath effects, etc. A reasonable assumption for a fixed, Line of Sight (LoS) wireless channel is AWGN [10] - [11] which is flat and not frequency-selective as in the case of the fading channel. Particularly fast, deep frequency-selective fading as often observed in mobile communications is not considered in the present work, since the transmitter and receiver are both fixed. This type of channel delays the signal and corrupts it with AWGN. The AWGN is assumed to have a constant PSD over the channel bandwidth, and a Gaussian amplitude probability density function.

Fig.1.3. AWGN channel model

Gaussian noise is added to the transmitted signal prior to the reception at the receiver as shown in Fig.1.3 The in-phase and quadrature components of the AWGN are assumed to be statistically independent, stationary Gaussian noise process with zero mean and two sided PSD. As zero-mean gaussian noise is completely characterized by its variance, this model is particularly simple to use in the detection of signals and in the design of optimum receivers.

1.4 Aim of the Present Work

The main aim of the present work is to

Investigate the strength and limitations of existing methods of power adaptation for image transmission over wireless channels.

Develop novel power adaptation methods that overcome some of the limitations of the existing methods

Evaluate and analyze the performance of the new methods using quantitative measures.

1.5 Problem Formulation

In the research work, a simple communication system is considered which in essence is very similar to a general communication system and the channel assumed is AWGN. Two cases are considered for implementation of the proposed algorithms. In the first case, the binary data is directly modulated and transmitted on the channel. In the second case, source coding and channel coding are applied. Source encoder uses Gray coding where as Convolution codes or Linear Density Parity Check (LDPC) codes are used for channel coding, for the transmission of image data over the wireless channel. The ultimate objective is to minimize the MSE of the image transmitted over the wireless channel.

Different power adaptation algorithms are proposed in order to achieve optimization for minimizing the MSE. Each and every algorithm has its own significance and therefore depending on the particular cause, MSE is optimized to meet the objective of the present work mentioned above.

In Image transmission, quality of the image after detection is more important. A better performance measure in such cases is the Root Mean Square Error (RMSE) rather than the BER because bits transmitted by the system do not carry the same amount of information about the message.

Quantitative measures for image quality can be classified according to two criteria: Number of images used in the measurement and Nature or type of measurement. Various objective and subjective image quality measures evaluated and are analyzed for performance. Root Mean Square Error (RMSE), Peak Signal to Noise Ratio (PSNR), Mean, Variance, Skew and Kurtosis are investigated for both conventional and proposed methods.

1.6 Scope Of The Thesis

Multimedia transmission has to handle a variety of compressed and uncompressed source signals such as data, text, image, audio, and video. On wireless channels the error rates are high and joint optimization of source and channel coding methods are advantageous. Also, the system architecture has to adapt to the bad channel conditions.

In particular, image transmission finds lot of applications. There is a large scope and potential for improving the quality of the image transmission system meeting the user requirements. Various methods are being used for optimizing the power adapted in the process of transmitting the images. This is very much required for proper reconstruction of the received image, as it gets distorted during its transmission in the channel. One way to overcome this problem is by implementing power adaptation as per the significance of the image data representation. The other way is to use channel codes.

The thesis work addresses various power adaptation methods that are suitable for still image transmission. All the algorithms developed are examined for various modulation techniques and channel codes. Wavelet approach is also studied with the proposed algorithms.

1.7 Organization Of The Thesis

In the present work carried out, computational work is carried on for minimizing the MSE of Power adaptation algorithms applied to the image transmission over wireless channels. Power adaptation algorithms are developed by using the fact that different bits carry different amount of information. These algorithms are explained in detail in the chapters following.

The thesis is organized as follows:

Chapter 1 gives a brief description of a communication system and the preliminary aspects related to power adaptation algorithms applied to the image transmission over wireless channels. These are useful for further investigation of proposed work.

Chapter 2 presents literature survey of the existing methods of power adaptation related to proposed methods. These methods can be executed either by conventional power adaptation in which equal power is allotted to all the bits, or by optimized power adaptation wherein the choice of power adapted to the bits is dynamically chosen depending on the performance metric of the channel, with appropriate algorithm. Bit by bit power adaptation is used in the current work.

The system model used for image transmission is described in Chapter 3. Four power adaptation algorithms are proposed for image transmission over wireless channel. The performances of these algorithms are analyzed in terms of convergence. Quantitative measures are used for the investigation of the proposed algorithms applied to the image transmission.

Chapter 4 deals with joint optimization of power adaptation and coding. Various channel coding techniques are discussed for applying to the image along with the power adaptation. The results obtained are compared with that of the previous chapter.

Chapter 5 introduces wavelets concept at various levels of approximation coefficients applied to the image before the power adaptation is applied. Later the concept of power adaptation is applied for Region of Interest (ROI) images providing different levels of power adaptation.

Chapter 6 summarizes the proposed work and discusses the simulation results obtained. It shows the comparison parameters, and assesses the obtained results of test images using quantitative approach.

Chapter 7 presents the conclusions and future scope of this thesis work.

Appendix presents a detailed description of the mathematical backdrop used for the proposed algorithms.