Kulyk A.Y., Oleksyk A.Y.

Vinnitsia national technical university

Information transmitting with repeating

In the information transmitting technology it is widely known a family of algorithms for information transmitting with repeating [1 – 3]. These include.

Ä code with doubling elements or correlative, when 1 is transmitted by a combination 10, and 0 is transmitted by a combination 01;

Ä inverse code for which an even number of units in combination means repetition and odd means repetition with inversion;

Ä code with repetition when the code pattern is simply repeted.

In the case of code building according to a classical algorithm they can be refered to the codes with error while they are able to identify individual signal distortion. Using the m-fold repetition with arbitration allows error correction [1, 3]. The algorithm simplicity determines the efficiency of its use.

But, in practice, the construction of such algorithm is connected with certain difficulties. In the terms of arbitration it can be determined that the number of repetitions should be odd, through how many times exactly should the code combination (three, five, seven, etc.) be passed it is unknown. Absolutely workable this algorithm is when the pass code combination now is transmit from the transmitter to the receiving side, then backwards, compared. And now only in the case of matching it can be transmit to the receiving side to verify the accuracy of acceptance. But, despite the reliability of the algorithm, it requires excessive bandwidth communications half-duplex mode symmetric, or rather duplexes etc. Thus, to implement the algorithm with repetition and transmission arbitration necessary to determine the multiplicity of repeating code combinations of the conditions of transfer.

If, over time, information transfer, signal level constant and equal to U_c, and the additional noise affects the signal U_ξ, then the sequence counting can be represented as

, (1)

where U_ξi – voltage value noise at the moment of і-count.

In the communication channel signal will be

, (2)

The ratio of signal and noise will be determined by the alignment

, (3)

where – variance of noise in communication channel.

Taking into account that noise level values are always uncorrelated, dispersion sum of deductions U_ξi equals the sum of variances deductions

. (4)

Limited time information transfer process makes quite probable assumption that during the transfer of additional noise can be considered as a stationary random process. Then

. (5)

Correlation of signal and noise in channel with m time repeating may be represented the next way

. (6)

Correlation of signal and noise is related with mistake probability while transmitting by probability integral

, (7)

Value of this integral is counted by numeric methods and shown in tables [1, 4]. Taking into account, that for asymmetrical channels (probabilities of zero р₀₁ and unity р₁₀ distortion are not equal) transmitting conditions are stricter, it is necessary to determine coefficients for the worst cases

, (8)

, (9)

where U_пор is a liminal value of unity identification on receiving side.

Specifying mistake probability in advance, one can determine necessary energy parameters of transmitting and signal volume for correct transmitting

, (10)

where F is a frequency band, which is employed by a signal;

T is an information transmitting time.

. (11)

Expression (11) may be interpreted the next way: if noise level is increased m times in channel, then for signal volume preservation transmitting time must be increased ( l + log m) times. As signal volume was determined for providing of necessary transmitting conditions, so they will be saved. Hence, if noise level exceed base one m times, transmitting of code combination must be additionally transmitted log m times. Logarithm base is determined by unities of signal/ noise correlation determining. If it is measured in decibels the base is 10, and if in binary unities – the base is 2.

Signal volume may be determined this way in the case of information transmitting with limiting of frequency band in computer format.

, (12)

but in this case it is necessary to increase not the transmitting time but the volume of information N which is transmitted to the connection channel. The same correlations may be gained for signal amplitudes.

This algorithm may be realized basing on computer or microprocessor for any kind of registration (programmatic poll, aborting or direct memory access).

Texas Instruments microprocessors can be used for this purpose. Using the MSP-EXP430FG4618 Development Tool establish a data exchange between the MSP430FG4618 and MSP430F2013 devices. The MSP430FG4618 uses the USCI module while the MSP430F2013 uses the USI module.

Testing process consist in determination of mean-square noise voltage level, that is measured in idle mode (without data transmitting). Voltage value registration must be carried out in conditions which are close to real transmitting mode (taking speed into account) for dynamic mistake avoiding. The period of noise voltage measuring must be determined from the next expression

, (13)

where k is a scale coefficient, which determine correlation of data transmitting speed and synchronization speed, it differs from 1 bit per symbol only for differential modulation;

v is a data transmitting speed, bit per sec;

τ_інф is an impulse transmitting time.

Time notes of noise signal measuring is set by timer.

communication channel 1

л

#

2

System Channel 4

Media Information 9

RAM 10

ROM 11

3 Personal computer system

Fig. 1 – Structure of testing channel and data transmission

As it is not necessary to implement half-duplex symmetric mode in this case, one may only to transmit data in one direction, so the time benefit will be doubled. Thus efficiency of channel using is increased, but time for testing the channel is wasted beforehand.

Features of this method realizing for fibre-optic lines consist in energy distribution by modes on receiving side, quantity of which for homogeneous two-layer fibre-optic line is determined by the next expression

, (14)

where a is a core radius,

V is a normalized work frequency;

λ is a work wave length;

n₁ and n₂ are core and cover refraction coefficients appropriately.

So impulse power on receiving side must be determined as a sum of all modes

, (15)

where m(l) is a largest radial mode index with specified azimuthal;

l_m is a largest azimuthal mode index which is distributed on V frequency;

δ(t) is a delta-function.

But in all cases using of offered algorithm seems to be perspective.

References:

1. Квєтний Р.Н., Компанець М.М., Кривогубченко С.Г., Кулик А.Я. Основи техніки передавання інформації. – Вінниця: УНІВЕРСУМ-Вінниця, 2002 – 358 с.

2. Кузьмин И.В., Кедрус В.А. Основы теории информации и кодирования. – К.: Вища школа, 1986, с. 90 – 91.

3. Кузьмин И.В., Литвин

4. Тутевич В.Н. Телемеханика. – М.: Высшая школа, 1985 – 423 с.

5. Кулик А.Я., Кривогубченко С.Г., Компанець М.М., Дідик О.М. Особливості побудови засобів передавання дискретної інформації лініями зв’язку колективного користування // Оптико-електронні інформаційно-енергетичні технології, 2001, № 2, с. 192 – 199.

6. Волоконно-оптические линии связи / Под ред. Свечникова А.В., Андрушко Л.М. – К.: Техніка, 1988 – 239 с.