Data Signalling Rate | HIGH DENSITY BIPOLAR (HDB) SIGNALLING | B8ZS LINE CODE

HIGH DENSITY BIPOLAR (HDB) SIGNALLING , what is definition of Data Signalling Rate ,  B8ZS LINE CODE ?

1. Definition

In case of bipolar NRZ or AMI signal, the transmitted signal is equal to zero when a binary “0” is to be transmitted. This is true even for the unipolar RZ and unipolar NRZ signals. The absence of transmitted signal can cause problems in synchronization at the receiver, if long sequence of binary “0”s are being transmitted. This problem can be solved by adding (transmitting) pulses when long strings of 0’s exceeding a number n are being transmitted. This type of coding is called as High Density Bipolar coding. It is denoted by HDBN. Here, N = 1, 2, 3, ……..The most widely used HDB format is with N = 3 i.e., HDB3.

2. Waveforms

In the string of message bits, when (N + 1) or mm number of zeros occur, they are replaced by special binary sequences of (N + 1) length. As shown in figure 6.11, these sequences contain some binary l’s which are necessary for synchronization at the receiver end. The (N + 1) long special sequences for the HDB3 coding are 000V and BOOV where B and V both are considered to be binary l’s. When the number of consecutive zeros exceed (N + 1) i.e., 4 in case of HDB3, the abovementioned special sequences are inserted as shown in figure 6.11.
DIAGRAM
FIGURE 6.11.
6.12 B8ZS LINE CODE

1. Definition and Working Principle

            We have discussed about the codes in this chapter. We know that in order to have synchronization between the transmitter and receiver, the line code needs to cross the zero line frequently. As per U.S. T₁ standard, not more than 15 0’s can be sent in succession to ensure proper synchronization. In order to solve the problems related to synchronization a new line code called B8Zs (Binary 8-zeros suppression) was developed. Whenever eight successive 0’s are detected, the implementation of this line code will automatically insert a special 8 bit sequence containing a bipolar violation. This can bed easily detected and corrected by the CSU/DSU (channel service unit/digital service unit).

2. Waveforms

            Figure 6.12 gives a clear idea about the B8ZS line code. The violations (BPV in figure 6.12), will distinguish a byte substituted for all 0’s from a normal byte which contains l’s. The B8ZS does not allow more than 8, consecutive 0’s and the bipolar violation pattern uniquely identifies the eight 0’s. It may that the voltage levels in the “violating byte”, has a zero average (dc) value.
DIAGRAM
FIGURE 6.12.
6.13 POWER SPECTRA OF DISCRETE PAM SIGNALS (VARIOUS LINE CODES)
As discussed earlier, we can represent all the discrete PAM signals with the help of a single expression as under:
EQUATION                                      …(6.17)
where                                      a_k= coefficient
p(t) = the basic pulse shape
T = symbol duration
Now, let us assume that the basic pulse p(t) is centered at the origin (t = 0) and normalized such that p(0) = 1.
Table 6.2 lists the value of coefficients a_k for different PAM formats.
Table 6.2. Values of a„ for various data formats.

 
Now, let us discuss few important terms as under:
(i)         Data Signalling Rate
            It is defined as the number of bits of data transmitted per second. It is measured in bits/ second.
The data signalling rate is also called as data rate and it is defined as follows:
Rb = 1/Tb                                                        …(6.18)
where T_b represents the bit duration.
(ii)        Modulation Rate

It is defined as the rate at which the signal level is changed. The modulation rate is measured in bauds or symbols per second.
(iii)       Power Spectra
We can represent any PAM format as follows:
equation
Each format x(t) may be considered as a random process and each coefficient a_k as a random variable. Let these coefficients be generated by a discrete stationary random source which is characterized by the following relation between autocorrelation and ensemble average i.e.,
R(n) = E[a_k a_k-n]                                                        …(6.19)
where              R(n) = Autocorrelation function
and                              E = Expectation operator
Also, power spectral density (psd) of PAM signal x(t) is given by
EQUATION                                      …(6.20)
where PO = Fourier transform of the basic pulse p(t).
It may be noted that the values of P(f) and Rt(n) depends upon the type of PAM format.
POWER SPECTRAL DENSITY (PSD) OF NRZ UNIPOLAR FORMAT
For simplicity, let us assume that the 0s and is are equally likely to happen or have equal probability.
P(a_k = 0) = P(a_k = A) = 1/2
We know that a discrete stationary random source is characterized by the following autocorrelation:
R(n) = [a_k a_k-n]
Hence, for n = 0, above expression becomes
R(n) = E[a_k a_k] = E[a_k²]                                             …(6.21)
E[a_k]² = 0²P(a_k = 0) + (A)² P(a_k = A)
or                                             E[a_k]² = A² =                                            …(6.22)
Now, let us obtain the product a_k a_k-n for n  0. The four possible values of this product are 0, 0, 0 and A². With the assumption that the successive symbols in a binary sequence are equiprobable (with a probability equal to 1/2), the probability of the four values 0, 0, 0 and a² will be equal to 1/ 4 each.
Therefore, for n  0, we have
E[a_k a_k-n] = (3 x 0 x 1/4) + (A² x 1/4)
Or                                E[a_k a_k-n] =   for n  0                                                            …(6.23)
Thus, the autocorrelation function R(n) can be expressed as under:
EQUATION                                      …(6.24)
EQUATION                                      …(6.25)
The basic pulse p(t) is a rectangular pulse of unity amplitude and duration T_b. Hence, its Fourier transform is given by
P(f) = T_b sinc (fT_b)                              …(6.26)
where the sinc function is expressed as,
sinc
Now, substituting the expression for P(f) and R(n) in equation (6.20) and substituting T = T_b to get power spectral density (psd) as under:
EQUATION                                      …(6.27)
or                                                            EQUATION
or                                                            EQUATION                                                  …(6.28)
According to Poisson’s expression, we can write,
EQUATION                                      …(6.29)
where (f) is the unit impulse at f = 0 in the frequency domain. Substituting equation (6.29) into equation (6.28) and noting that the sinc function passes through zero at f = ±1/Tb, ±2/Tb…., we can write equation (6.28) in the simplified form as under:
S(f) =  sin c² (fT_b) +                               …(6.30)
This expression can be plotted as shown in figure 6.13 (curve a).