# Method of monitoring the status of the data channel based on the probability of undetected errors

(57) Abstract:

The invention relates to telecommunication. On the transfer of blocks of information to encode M-cascade code, and at the reception decode stages, completing the decoding or when errors are detected, or after the M-th stage. The inspection interval for each stage of the decoding count the number of blocks with detected errors, which determine the probability of undetected errors for each of the stages from the first to the (M-K)-th and predict using mathematical expression of the probability of undetected errors for each stage (M-K+1) th to M-th as a function of two parameters - the number of control characters and multiplicity are guaranteed to find errors of the respective cascades of code, thereby improving the accuracy of monitoring data transmission channel based on the probability of undetected errors. 2 Il., table 1. The invention relates to telecommunication and can be used in data transmission systems to assess the quality of the communication channel based on the probability of undetected errors and select the required parameters of error-correcting coding.There is a method of estimating the probability of undetected errors based on the second combination; k is the number of information symbols of the code; (n-k) - number of control code symbols; P_{BO}- probability of error-free reception of code information (the cookie monster Century. I., Fink L. M., error-correction coding of discrete messages in channels with random structure. Statistical theory of communication. Vol. 4. - M.: Communication, 1975).In data transmission systems with a high degree of protection against errors P

_{GS}>> P

_{BUT}, (1-P

_{BO}) = P

_{GS}+P

_{BUT}P

_{GS}where the probability of detected errors is defined as

However, this estimate is very rough and does not take into account neither the weight structure of the error correcting code or specs for the error stream in discrete communication channel.Closest to the proposed method is a method of monitoring the status of the data channel based on the procedure of gradual decoding cascade code with the error detection and the use of statistics of detected errors for each stage of the decoding to assess the probability of undetected errors:

< / BR>

where N

_{}- the total number of received blocks; N

_{ooi}- the number of code blocks received with detected errors; i = 1...M is the number of the stage decoding (ed. St. USSR N 1594708 is Eugenia errors at each subsequent stage of decoding is the value which decreases the probability of undetected errors in relation to the previous stage of decoding:

< / BR>

Estimation of the probability of undetected error - P

_{BUT}as a function of the number of control characters code - r at the point may be effected either by a linear approximation of P

_{BUT}in logarithmic scale

< / BR>

where i is the number of stages of decoding, for which the evaluation; k is the number of decoding steps? you additionally need to ensure the required accuracy of control, or is determined by the expression:

< / BR>

where is the coefficient of proportionality, taking into account the reduction of the probability of undetected errors on one check digit code for (i-1)-th stage decoding.For the minimum required two-stage decoding procedure

< / BR>

This method of control channel status data to assess the probability of undetected errors of all parameters of error-correcting code only deals with a number of control characters and gives good results in accuracy control using discrete communication channels with packet errors. For the more sophisticated nature of the error stream in discrete communication channel precision counter is standing error correcting code d. A similar effect when introduced to control the reliability information of the error correction mode, for example, majority decoding. The majority decoder thins and decorrelated error stream.The objective of the invention is to improve the accuracy of monitoring data transmission channel based on the probability of undetected errors when using discrete channels due to the complex nature of the error stream.Improving the accuracy of control is achieved in that in the method of monitoring the status of the data transmission channel, comprising forming on the transfer of blocks of information, coding their M-cascade code that detects errors, transmission over a discrete channel sequence code blocks, reception, decoding of each code block is carried out in stages and complete or error detection at the next stage, or after the M-th stage decoding, during a cycle control for each stage of the decoding count the number of code blocks with detected errors, which determine the probability of undetected errors for each of the stages from the first to the (M-K)-th and predict the probability of undetected errors for each of Fouls code for the relevant stages of the decoding, additionally, we introduce a parameter characterizing the code distance of the code at the relevant stages of decoding.The essence of the proposed method of monitoring the status of the data channel based on the probability of undetected errors is as follows.To obtain an estimate of the probability of undetected errors as functions of two parameters-the number of control code symbols r and a minimum code distance of the code d is used the statistics of detected errors in the decoding steps M-cascade code:

< / BR>

Each stage of the decoding corresponds to a code that has a number of control symbols r

_{i}and guaranteed detects

_{i}= d

_{i}-1 error, where d

_{i}- minimum code distance of the code, i is the number of stages of decoding, and the sign indicates that the specified parameters are the corresponding increments of these parameters for M-cascade code:

< / BR>

Estimation of the probability of undetected errors for cascades of code from the first to the (M-K)-th is defined as:

< / BR>

where K is the minimal number of summands (subsequent decoding steps) to meet the required accuracy assessment.Evaluation of ve is"ptx2">Additionally, for (M-K)-th stage is determined by the second estimation of the probability of undetected errors through the P

_{NOM-K-1}(based on the statistics of detected errors) and the dependence of P

_{BUT}from the increment of the number of control characters code for (M-K)-th stage:

< / BR>

Naturally P

_{NOM-}and will differ from each other, the second does not take into account the real nature of the error stream and detecting properties of the code (M-K)-th stage (code length).To assess the relative influence of these factors on the actual values obtained based on the statistics of detected errors on subsequent decoding steps, entered the proportionality coefficient

< / BR>

taking into account the reduction of the probability of undetected error per unit increment amount is guaranteed to find the error code (M-K)-th stage (

_{m-K}= d

_{m-K}-1).Further, assuming a monotonic character of the dependence of P

_{BUT}believe that

_{m-K+1}

_{m-K}< / BR>

then the probability of undetected errors for the (M-K+1)-th stage can be defined as:

< / BR>

For other possible values, the probability of undetected errors relative to the (M-K)-th stage will be determined by four the parameters specific possible code and can be specified only in a pair.Joint consideration of the two main parameters of error-correcting code is a minimum code distance and number of control characters in comparison with the prototype, taking into account only the number of control code symbols, which can significantly improve the accuracy of estimating the probability of undetected errors.Proposed method of control implemented by the control unit channel status data (Fig. 2.).The device comprises an M-stage decoder 1, counter 2 number of received blocks, the counter group 3 number of blocks with detected errors for each of the cascade of decoder 1, block 4 of the comparison, the control unit 5, the group of registers 6 for temporary storage of the number of blocks with detected errors for each stage of the decoding, the transmitter (microcomputers) 7 to calculate the probability of undetected errors and block 8 registration and display of channel status data.The invention is illustrated in Fig. 1 - 2.The device operates as follows. On a start signal, the control unit 5 generates a signal that is set in the initial state, the counter 2 number of received blocks and all 3 counters number of blocks which joins the initial sample size for the number of received blocks and the code number is given to block 4 comparison.Then begins the cycle control in which on input M-cascaded decoder 1 receives the code blocks, followed by a synchronization signal (SS). Simultaneously, the signals of the reception code blocks are served at the summing input of counter 2 number of received blocks. Each code combination of the first decoded by the decoder 1 cascade and, if decoding any errors are found, no further decoding is terminated and the signal detection error is summed up by the first counter 3 number of blocks with detected errors. If the first stage of the decoder 1 error not found, the code combination is transmitted to the second cascade of decoder 1, and so on to detect errors at a subsequent decoding steps, or until full decoding M-cascaded decoder 1 without detecting errors.During the cycle control counter 3 accumulate data on the number of code blocks received with errors and detected at respective stages of decoding. Unit 4 compare compares the contents of the counter 2 number of received blocks ID of the initial volume of the sample coming from the control unit 5 and the coincidence generates a signal by which the contents of the counter 3 is moved into an appropriate is it the program checks the adequacy of the sampling codes number of blocks with detected errors for the corresponding decoding steps in registers 6 are compared with the minimum allowable values. If the sample size is insufficient, the computer 7 increases the sample size by the number of received blocks and writes the new value of the sample in the control unit 5. The control loop continues until the next signal matches the output of block 4 comparison. The accumulation of a sufficient sample of the computer 7 reads the parameters of the codes M-cascaded decoder 1 and the programme of work consistently for each stage of the decoding calculates an estimate (i = 1...M-K) and the forecast for subsequent decoding steps (i = M-K+1...M).The results of calculations are given in box 8 registration and display of channel status data.After computing the transmitter 7 records in block 5 of the control code of the initial volume of the sample by the number of received blocks, the control unit 5 generates a signal initial setup of counters 2 and 3 and starts a new cycle control.The positive effect of the proposed method of monitoring the status of the data channel based on the probability of undetected errors is confirmed by the results imagry decode (M=2, K=l).If the condition r

_{2}3 required to obtain acceptable accuracy, the probability of undetected errors at the point r

_{2}= r

_{1}+r

_{2}and =

_{1}+

_{2}= (d

_{1}-1)+(d

_{2}-1) was determined by the formula:

< / BR>

As the original model of discrete communication channel used as a model Hilbert two conditions are good, when there are no errors, and bad, when there are independent errors with probability 1-h, and the probability of a change of state during the transmission of each character are characterized by count

< / BR>

For the simulation was set the parameters of the model, the corresponding low as a discrete communication channel.As the cascade code used in the system of nested cyclic codes (Hamming codes, supplemented by parity (odd)). Internal codec (at the first stage decoding) used code with parity (odd) g

_{1}(x) = x + 1; minimum code distance d

_{1}= 2; the number of control symbols r

_{1}= 1 . In the external codec (at the second stage decoding) - code forming polynomial g

_{2}(x) depending on the length of the information part code k, with the minimum code distance d

_{2}=the

_{1}=2-1=1, for the second phase of the minimum rate guaranteed to find errors equal

_{2}=3-1=2, in General, such a system of nested codes guaranteed to detect three errors =

_{1}+

_{2}= 1+2=3

This option cascade code provides minimum time control to set the required statistics .Simulation statistical simulation was conducted on the original discrete channel, and using the preliminary error correction majority decoder of sample 2 of 3 and 3 out of 5. Information about the simulation results are presented in the table.In the table, the following notation: PHOR - score P

_{BUT}produced using only the number of control characters code, PHOD - score P

_{BUT}obtained using two code parameters r and = d-1, PHOF actual chastoty undetected errors, obtained from simulation,

< / BR>

respectively represent the relative error of the estimates obtained in a known manner (3) and the proposed method (6).Average relative errors when using discrete communication channels are of low quality, for different codes and different proced agenoy errors 1.5 - 2 times reduces the relative error control.Thus the proposed method of control can significantly improve the accuracy of the control channel status data on the probability of undetected errors.Comparative analysis of the prototype shows that the proposed control method to assess the probability of undetected errors additionally takes into account the effect of the increments of the minimum code distance on the relevant stages of the code.Thus, the proposed method of monitoring the channel status data meets the criterion of "novelty."Comparison of the proposed solution not only prototype, but also with other technical solutions and methods can not detect in them the features that distinguish the proposed solution to the prototype that allows to conclude that the criterion of "substantial differences". Method of monitoring the status of the data transmission channel, comprising forming on the transfer of blocks of information, encoding them with education code blocks M-cascade code that detects errors, transmission over a discrete channel sequence code blocks, reception, decoding kasle M-th stage, during the cycle control for the same stages from the first to the (M, K)-th (where K is the number of decoding steps, necessary for the required accuracy of control), count the number of code blocks with detected errors, which determine the probability of undetected errors for each of the stages from the first to the (M) th, determine the probability of undetected errors for each stage (M + 1) th to M-th, characterized in that when determining the probability of undetected error of each stage (M + 1)th to M-th consider the parameter characterizing the minimum code distance of the code at the relevant stages of the decoding, the probability of undetected errors for each stage (M + 1) th to M-th for r the total value of the number of control code symbols and multiplicity are guaranteed to find errors is determined by the formula

< / BR>

where r

_{M-K}the increment of the number of control code symbols;

_{M-K}= d

_{M-K}-1 - increment ratio is guaranteed to detected errors;

d

_{M}

_{-}

_{TO}minimum code distance of the code (M - K)-th cascade;

r, - increment the corresponding parameters of the code.

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