# Criteria for assessing QC quality in the transmission of discrete...

## Criteria for assessing QC quality when transmitting discrete information

When transmitting a discrete signal (Fig. 4.9) in the form of rectangular pulses ("1" and "0") for an exact reproduction on the receiving side, it is required to have a channel with an infinite frequency range. Therefore, for limited frequency ranges, modulation of a discrete signal is carried out by two different frequencies.

Fig. 4.9. Frequency modulation of a discrete signal

Then, for the transmission of a discrete signal via an analogue communication channel, it is necessary to have matching devices between the transmission channel and the digital device (computer) that perform the modulation and demodulation (MODEM) of the signal (Figure 4.10).

Fig. 4.10. Communication channel devices used for transmitting a discrete signal

Let's see how the type of criteria that evaluate the quality of channels when transmitting a discrete signal is changed by the example of a telegraph device.

Option 1. In the first telegraphs, one alphabet character was encoded using 5 bits. The five-bit code allows to encode the maximum number of characters: 25 = 32 characters (26 letters + 6 symbols for controlling the operation of the device). The maximum speed of work on the telegraph of an employee with the qualification "Master" is 6-7 characters/s or 30-35 bps. Thus, the criterion Frequency range is transformed into the Transfer rate criterion.

Since signals of a fixed type are transmitted to the channel, the dynamic range does not change (const).

Criterion Signal to Noise Ratio is transformed into Probability of error occurrence & quot ;. The channel must contain only two kinds of signals "0" or 1 (signal is or no ) (Figure 4.11, a ), but in fact an analog (eg, amplitude-modulated) signal (see Figure 4.9), therefore its recognition occurs by comparison with some reference value trigger threshold & quot ;. If the value of the signal exceeds this threshold, it means that in the channel 1 & quot ;, and if less, then 0 & quot ;.

In nature, there are no ideal channels for signal transmission, in each of them there is necessarily interference, which distorts the input signal (Figure 4.11, a ). As a result, at the output of the channel, when comparing the signal value with the trigger threshold false positives may occur (error): instead of 0 is recognized 1 (Figure 4.11, b ) or, conversely, instead of 1 is recognized 0 (Figure 4.11, in ). The frequency (probability) of the occurrence of an error depends on the level of interference in the channel. Thus, the transformation of the criterion Signal-to-noise ratio in the Probability of error error.

Therefore, when transmitting a discrete signal in an analog channel, the selected criteria take the following values: the information transfer rate is 6-7 characters/s or 30-35 bits/s (baud); the dynamic range is constant (const); The error probability is 104.

Option 2: In later telegraphs, one alphabet character is encoded using 8 bits. The eight-bit code allows you to encode the maximum number of characters: 2 8 = 256 characters. For such telegraph units when transmitting a discrete signal in an analog channel, the selected criteria take the following values: the rate is 6-7 characters/s or 48-56 bits/s (baud); the dynamic range is constant (const); the probability of an error is 106.

Fig. 4.11. The effect of interference in a channel on a discrete signal form

Any analog signal (audio, video) can be represented in discrete form using an analog-to-digital conversion. It is convenient to illustrate this in the following way (Figure 4.12).

A grid with a constant pitch is superimposed on a one-dimensional signal (for example, a musical signal). Horizontally, this will be a fixed time discrepancy (Δ t = const), and vertically the value (in digital form) of the signal amplitude. Thus, the sequence of digits will determine a successive change in the amplitude of the signal in time, and the smaller the step at the grid, the more accurately the initial signal will be digitized, but the amount of information digitized per unit of time will also increase. The reverse digital-to-analog conversion allows you to restore the original analog signal from the digit. An example is the recording and playback of music on a music CD.

Below is the transformation of the criteria for estimating the information transfer channel.

Fig. 4.12. Example of analog-to-digital conversion of a continuous signal

In order to carry out a comparative analysis of the first-type criteria describing the different types of signals (continuous and discrete), it is necessary to bring them to the same units of measurement, for this it is convenient to use an approximate ratio: 1 Hz - 1 bit/s (baud).

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