Category: digital Communication

Channel Coding Theorem The noise present in a channel creates unwanted errors between the input and the output sequences of a digital communication system. The error probability should be very low, nearly ≤ 10-6 for a reliable communication. The channel coding in a communication system, introduces redundancy with a control, so as to improve the reliability of the system. The source coding reduces redundancy to improve the efficiency of the system. Channel coding consists of two parts of action. Mapping incoming data sequence into a channel input sequence. Inverse Mapping the channel output sequence into an output data sequence. The final target is that the overall effect of the channel noise should be minimized. The mapping is done by the transmitter, with the help of an encoder, whereas the inverse mapping is done by the decoder in the receiver. Channel Coding Let us consider a discrete memoryless channel (δ) with Entropy H (δ) Ts indicates the symbols that δ gives per second Channel capacity is indicated by C Channel can be used for every Tc secs Hence, the maximum capability of the channel is C/Tc The data sent = $frac{H(delta)}{T_s}$ If $frac{H(delta)}{T_s} leq frac{C}{T_c}$ it means the transmission is good and can be reproduced with a small probability of error. In this, $frac{C}{T_c}$ is the critical rate of channel capacity. If $frac{H(delta)}{T_s} = frac{C}{T_c}$ then the system is said to be signaling at a critical rate. Conversely, if $frac{H(delta)}{T_s} > frac{C}{T_c}$, then the transmission is not possible. Hence, the maximum rate of the transmission is equal to the critical rate of the channel capacity, for reliable error-free messages, which can take place, over a discrete memoryless channel. This is called as Channel coding theorem. Learning working make money

Pulse Code Modulation Modulation is the process of varying one or more parameters of a carrier signal in accordance with the instantaneous values of the message signal. The message signal is the signal which is being transmitted for communication and the carrier signal is a high frequency signal which has no data, but is used for long distance transmission. There are many modulation techniques, which are classified according to the type of modulation employed. Of them all, the digital modulation technique used is Pulse Code Modulation (PCM). A signal is pulse code modulated to convert its analog information into a binary sequence, i.e., 1s and 0s. The output of a PCM will resemble a binary sequence. The following figure shows an example of PCM output with respect to instantaneous values of a given sine wave. Instead of a pulse train, PCM produces a series of numbers or digits, and hence this process is called as digital. Each one of these digits, though in binary code, represent the approximate amplitude of the signal sample at that instant. In Pulse Code Modulation, the message signal is represented by a sequence of coded pulses. This message signal is achieved by representing the signal in discrete form in both time and amplitude. Basic Elements of PCM The transmitter section of a Pulse Code Modulator circuit consists of Sampling, Quantizing and Encoding, which are performed in the analog-to-digital converter section. The low pass filter prior to sampling prevents aliasing of the message signal. The basic operations in the receiver section are regeneration of impaired signals, decoding, and reconstruction of the quantized pulse train. Following is the block diagram of PCM which represents the basic elements of both the transmitter and the receiver sections. Low Pass Filter This filter eliminates the high frequency components present in the input analog signal which is greater than the highest frequency of the message signal, to avoid aliasing of the message signal. Sampler This is the technique which helps to collect the sample data at instantaneous values of message signal, so as to reconstruct the original signal. The sampling rate must be greater than twice the highest frequency component W of the message signal, in accordance with the sampling theorem. Quantizer Quantizing is a process of reducing the excessive bits and confining the data. The sampled output when given to Quantizer, reduces the redundant bits and compresses the value. Encoder The digitization of analog signal is done by the encoder. It designates each quantized level by a binary code. The sampling done here is the sample-and-hold process. These three sections (LPF, Sampler, and Quantizer) will act as an analog to digital converter. Encoding minimizes the bandwidth used. Regenerative Repeater This section increases the signal strength. The output of the channel also has one regenerative repeater circuit, to compensate the signal loss and reconstruct the signal, and also to increase its strength. Decoder The decoder circuit decodes the pulse coded waveform to reproduce the original signal. This circuit acts as the demodulator. Reconstruction Filter After the digital-to-analog conversion is done by the regenerative circuit and the decoder, a low-pass filter is employed, called as the reconstruction filter to get back the original signal. Hence, the Pulse Code Modulator circuit digitizes the given analog signal, codes it and samples it, and then transmits it in an analog form. This whole process is repeated in a reverse pattern to obtain the original signal. Learning working make money

Digital Communication Tutorial Job Search Digital communication is the process of devices communicating information digitally. This tutorial helps the readers to get a good idea on how the signals are digitized and why digitization is needed. By the completion of this tutorial, the reader will be able to understand the conceptual details involved in digital communication. Audience This tutorial is prepared for beginners who are interested in the basics of digital communications and who aspire to acquire knowledge regarding digital communication systems. Prerequisites A basic idea regarding the initial concepts of communication is enough to go through this tutorial. It will definitely help if you use our tutorial Signals and Systems as a reference. A basic knowledge of the terms involved in Electronics and Communications would be an added advantage. Learning working make money

Quadrature Phase Shift Keying The Quadrature Phase Shift Keying (QPSK) is a variation of BPSK, and it is also a Double Side Band Suppressed Carrier (DSBSC) modulation scheme, which sends two bits of digital information at a time, called as bigits. Instead of the conversion of digital bits into a series of digital stream, it converts them into bit pairs. This decreases the data bit rate to half, which allows space for the other users. QPSK Modulator The QPSK Modulator uses a bit-splitter, two multipliers with local oscillator, a 2-bit serial to parallel converter, and a summer circuit. Following is the block diagram for the same. At the modulator’s input, the message signal’s even bits (i.e., 2nd bit, 4th bit, 6th bit, etc.) and odd bits (i.e., 1st bit, 3rd bit, 5th bit, etc.) are separated by the bits splitter and are multiplied with the same carrier to generate odd BPSK (called as PSKI) and even BPSK (called as PSKQ). The PSKQ signal is anyhow phase shifted by 90° before being modulated. The QPSK waveform for two-bits input is as follows, which shows the modulated result for different instances of binary inputs. QPSK Demodulator The QPSK Demodulator uses two product demodulator circuits with local oscillator, two band pass filters, two integrator circuits, and a 2-bit parallel to serial converter. Following is the diagram for the same. The two product detectors at the input of demodulator simultaneously demodulate the two BPSK signals. The pair of bits are recovered here from the original data. These signals after processing, are passed to the parallel to serial converter. Learning working make money

Digital Communication – Sampling Sampling is defined as, “The process of measuring the instantaneous values of continuous-time signal in a discrete form.” Sample is a piece of data taken from the whole data which is continuous in the time domain. When a source generates an analog signal and if that has to be digitized, having 1s and 0s i.e., High or Low, the signal has to be discretized in time. This discretization of analog signal is called as Sampling. The following figure indicates a continuous-time signal x (t) and a sampled signal xs (t). When x (t) is multiplied by a periodic impulse train, the sampled signal xs (t) is obtained. Sampling Rate To discretize the signals, the gap between the samples should be fixed. That gap can be termed as a sampling period Ts. $$Sampling : Frequency = frac{1}{T_{s}} = f_s$$ Where, $T_{s}$ is the sampling time $f_{s}$ is the sampling frequency or the sampling rate Sampling frequency is the reciprocal of the sampling period. This sampling frequency, can be simply called as Sampling rate. The sampling rate denotes the number of samples taken per second, or for a finite set of values. For an analog signal to be reconstructed from the digitized signal, the sampling rate should be highly considered. The rate of sampling should be such that the data in the message signal should neither be lost nor it should get over-lapped. Hence, a rate was fixed for this, called as Nyquist rate. Nyquist Rate Suppose that a signal is band-limited with no frequency components higher than W Hertz. That means, W is the highest frequency. For such a signal, for effective reproduction of the original signal, the sampling rate should be twice the highest frequency. Which means, $$f_{S} = 2W$$ Where, $f_{S}$ is the sampling rate W is the highest frequency This rate of sampling is called as Nyquist rate. A theorem called, Sampling Theorem, was stated on the theory of this Nyquist rate. Sampling Theorem The sampling theorem, which is also called as Nyquist theorem, delivers the theory of sufficient sample rate in terms of bandwidth for the class of functions that are bandlimited. The sampling theorem states that, “a signal can be exactly reproduced if it is sampled at the rate fs which is greater than twice the maximum frequency W.” To understand this sampling theorem, let us consider a band-limited signal, i.e., a signal whose value is non-zero between some –W and W Hertz. Such a signal is represented as $x(f) = 0 for |flvert > W$ For the continuous-time signal x (t), the band-limited signal in frequency domain, can be represented as shown in the following figure. We need a sampling frequency, a frequency at which there should be no loss of information, even after sampling. For this, we have the Nyquist rate that the sampling frequency should be two times the maximum frequency. It is the critical rate of sampling. If the signal x(t) is sampled above the Nyquist rate, the original signal can be recovered, and if it is sampled below the Nyquist rate, the signal cannot be recovered. The following figure explains a signal, if sampled at a higher rate than 2w in the frequency domain. The above figure shows the Fourier transform of a signal $x_{s}(t)$. Here, the information is reproduced without any loss. There is no mixing up and hence recovery is possible. The Fourier Transform of the signal $x_{s}(t)$ is $$X_{s}(w) = frac{1}{T_{s}}sum_{n = – infty}^infty X(w-nw_0)$$ Where $T_{s}$ = Sampling Period and $w_{0} = frac{2 pi}{T_s}$ Let us see what happens if the sampling rate is equal to twice the highest frequency (2W) That means, $$f_{s} = 2W$$ Where, $f_{s}$ is the sampling frequency W is the highest frequency The result will be as shown in the above figure. The information is replaced without any loss. Hence, this is also a good sampling rate. Now, let us look at the condition, $$f_{s} The resultant pattern will look like the following figure. We can observe from the above pattern that the over-lapping of information is done, which leads to mixing up and loss of information. This unwanted phenomenon of over-lapping is called as Aliasing. Aliasing Aliasing can be referred to as “the phenomenon of a high-frequency component in the spectrum of a signal, taking on the identity of a low-frequency component in the spectrum of its sampled version.” The corrective measures taken to reduce the effect of Aliasing are − In the transmitter section of PCM, a low pass anti-aliasing filter is employed, before the sampler, to eliminate the high frequency components, which are unwanted. The signal which is sampled after filtering, is sampled at a rate slightly higher than the Nyquist rate. This choice of having the sampling rate higher than Nyquist rate, also helps in the easier design of the reconstruction filter at the receiver. Scope of Fourier Transform It is generally observed that, we seek the help of Fourier series and Fourier transforms in analyzing the signals and also in proving theorems. It is because − The Fourier Transform is the extension of Fourier series for non-periodic signals. Fourier transform is a powerful mathematical tool which helps to view the signals in different domains and helps to analyze the signals easily. Any signal can be decomposed in terms of sum of sines and cosines using this Fourier transform. In the next chapter, let us discuss about the concept of Quantization. Learning working make money

Digital Communication – Differential PCM For the samples that are highly correlated, when encoded by PCM technique, leave redundant information behind. To process this redundant information and to have a better output, it is a wise decision to take a predicted sampled value, assumed from its previous output and summarize them with the quantized values. Such a process is called as Differential PCM (DPCM) technique. DPCM Transmitter The DPCM Transmitter consists of Quantizer and Predictor with two summer circuits. Following is the block diagram of DPCM transmitter. The signals at each point are named as − $x(nT_{s})$ is the sampled input $widehat{x}(nT_{s})$ is the predicted sample $e(nT_{s})$ is the difference of sampled input and predicted output, often called as prediction error $v(nT_{s})$ is the quantized output $u(nT_{s})$ is the predictor input which is actually the summer output of the predictor output and the quantizer output The predictor produces the assumed samples from the previous outputs of the transmitter circuit. The input to this predictor is the quantized versions of the input signal $x(nT_{s})$. Quantizer Output is represented as − $$v(nT_{s}) = Q[e(nT_{s})]$$ $$= e(nT_{s}) + q(nT_{s})$$ Where q (nTs) is the quantization error Predictor input is the sum of quantizer output and predictor output, $$u(nT_{s}) = widehat{x}(nT_{s}) + v(nT_{s})$$ $$u(nT_{s}) = widehat{x}(nT_{s}) + e(nT_{s}) + q(nT_{s})$$ $$u(nT_{s}) = x(nT_{s}) + q(nT_{s})$$ The same predictor circuit is used in the decoder to reconstruct the original input. DPCM Receiver The block diagram of DPCM Receiver consists of a decoder, a predictor, and a summer circuit. Following is the diagram of DPCM Receiver. The notation of the signals is the same as the previous ones. In the absence of noise, the encoded receiver input will be the same as the encoded transmitter output. As mentioned before, the predictor assumes a value, based on the previous outputs. The input given to the decoder is processed and that output is summed up with the output of the predictor, to obtain a better output. Learning working make money