Method of decoding convolutional codes

FIELD: radio engineering, communication.

SUBSTANCE: method of decoding convolutional codes involves receiving radio signals, automatic gain control, demodulation, first deinterleaving, Viterbi algorithm decoding, amplitude detection, averaging, second deinterleaving, nonlinear conversion and multichannel multiplication-summation.

EFFECT: low error probability when decoding and high noise-immunity of transmitted information.

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The method of decoding convolutional codes relates to the field of communication technology and can be used for the transmission of digital signals by interleaving symbols in terms of the impact of the fading amplitude of the signal.

There are different ways of decoding convolutional codes, are described for example in the book: Ipatov VP, V.K. Orlov, Samoilov IM System for mobile communications): Hot line - Telecom, 2003; Morelos-Zaragoza, R. the Art of error correcting coding. Methods, algorithms, applications. - M.: Technosphere, 2006. They are based on deteremine after reception of digital symbols, i.e. the restoration of the original order, which was rotated when passing to fight grouping errors caused by fading. Next is the decoding in accordance with the Viterbi algorithm. This identifies the total metric different paths on the lattice decoding, and selects the path with the minimum metric. This path corresponds to a particular sequence of characters, it is taken as the decoded version of the transmitted sequence.

This method does not provide the required level of noise immunity, since the remaining number of erroneously decoded characters in many situations (for example, a low average level of the received useful signal is Ala) is unacceptably high.

Closest to the claimed method is described in the book: Sklar, B. Digital communications. Theoretical foundations and practical applications - M.: Izd. house "Williams", 2003. After automatic gain control, demodulation and deteremine received binary symbols are decoded according to the Viterbi algorithm, with the adoption of the group code corresponding to one transmitted information symbol, is the next calculation of a new set of metrics for all possible States of the encoder. (The number of characters in a group is inversely proportional to the speed of the code).

A new set of metrics of all States is calculated for each metric by comparing the values of the metrics of the two paths that are suited to it and connect it with a particular two previous States. Selects the path that has the minimum metric. (If the metrics are equal, then select any of the paths).

The metric of each path is the sum of the metric of the previous state from which he comes, and metrics of the transition to the given state. In the prototype is "soft" decoding. When demodulating the received digital signal value of the received demodulated signal is quantized by a certain constant number of levels. (The number of levels between the two possible maximum values of the binary signal from the automatic gain control constantly, and is usually chosen equal to eight).

The metric of each transition is determined by the difference between the expected values of each character in the group of demodulated symbols and symbols of each particular transition, which are determined by the initial state of the encoder and its final state, which he acquires as a result of this transition. Differences are calculated using the Euclidean distance between the symbols. The operation is as follows. Let the two possible binary values of each character in the group each transition correspond to the relative levels "+1" and "-1". The actual values of the symbols yiafter decoding can take any intermediate levels between the "+1" and "-1". Then, if the value of a particular i-th symbol in the code of any transition is equal to "+1", then the Euclidean distance between the symbol and its corresponding time received, demodulated symbols is equal to the difference between (yi-1). If the value of a particular i-th symbol in a group of any transition is equal to "-1", then the Euclidean distance between the symbol and its corresponding time received, demodulated symbols to be equal to the module size (yi+1). When using this method as the number of remaining paths constantly decreases until there is only the path, the corresponding decoded the transmitted sequence of information symbols.

The disadvantage of this method consists in the following. As is known, successful decoding of convolutional codes is possible if consecutive time should not be a large number of erroneously demodulated symbols. And in the case of impact on the transmitted signal fast deep fading level, which is quite typical for many types of transmission channel signals, just a large number of in a row the following characters can be correctly demodulated, due to the fact that the quality of the demodulation depends on the level of the received useful signal. To avoid this, the signal on the transmission side is subjected to interleaving, i.e. by a specific rule symbols carry on time. At the receiving side adopted a sequence of characters subjected to reverse the operation, restoring the original order of their sequence in time. As a result of erroneous symbols previously followed in succession, are posted that allows you to successfully apply decoding.

However, a possible incorrect selection of the best path in the lattice, and, as a consequence, incorrect decoding of some of the plot of the transmitted information sequence. This occurs for the following reason. When you select one of the Vuh ways, appropriate to each state, equal in size metrics in these ways. And they are the sum of the metrics of all transitions along the length of each path. But each of these metrics is calculated according to the same rule. Essentially this corresponds to the assumption that the average noise level (average ratio "signal/noise") throughout the length of the path that when comparing different paths may reach several tens of symbols remains constant.

In the absence of alternation of characters, this assumption is fairly accurate. However, the alternation in comparing the length of a path are the characters that are articulated at the time of transfer. The ratio "signal/noise" in the moments of their reception can vary greatly. In other words, the "weight" of the contribution of each symbol in the formation of an aggregate metric of each path must also vary because the "quality" of each character different. As in the known method such accounting is not performed. The result is not ensured achievable lower probability of error and the greater immunity of transferring information.

The objective of the proposed method of decoding convolutional codes is to reduce the error probability of decoding and improve noise immunity of the transmitted information.

The problem is solved in that in the method of decoding swerte the different codes, includes sequentially carried out by the reception of radio signals, automatic gain control, demodulation, the first deteremine and decoding by the Viterbi algorithm, which is a turn-defining metrics transitions in lattice diagram, then obtaining metrics of paths by summing the metrics transitions and metrics of the States of the previous step, then the comparison of the value metrics ways appropriate to the conditions of the subsequent step and selecting the path with the minimum metric, the transition to the next step with the drop paths with large metrics and memorizing the left path and then recovering the transmitted information sequence on the remaining path, enter the amplitude detection, averaging, second deteremine, nonlinear conversion and multi-multiplication-summation, and amplitude detection, averaging, second deteremine and nonlinear conversion is carried out successively after the reception of radio signals simultaneously with automatic gain control, demodulation and the first deteremine, multi-multiplication-summation is introduced into the decoding algorithm Viterbi between the definition of metrics transitions and multi-summation and produce before summation by multiplying the metric in the output signal, obtained after nonlinear transformation.

The drawings show: figure 1 - schematic of the sequence of operations of the proposed method; figure 2 is a drawing explaining the reasons for disparities information on the different steps used to determine metrics transitions; figure 3 is a generalized block diagram of receipt on the transmission side of the convolutional code with rate coding1/2; figure 4 is an example of the enlarged structural diagram of the proposed method; figure 5 is an example of a detailed implementation of the proposed method; figure 6 is an example of numbering of States and transitions in a single cell of a lattice diagram for decoding; figure 7 - example of calculation of state metrics for the next step based on the state of the previous step and metrics jump this step.

Figure 1 is indicated operations: reception of radio signals 1; automatic gain control 2; the demodulator 3, the first deteremine 4; define metrics 5 transitions; multi-summation 6; comparing the metrics of paths and selecting the path with the minimum metric 7; move to the next step with the drop paths with large metrics and memorizing left paths 8; recovering the transmitted information sequence on the remaining path 9; amplitude detection 10; averaging 11; the second deteremine 12; not inane conversion 13; multi-multiplication-summation 14 and the Viterbi algorithm 15.

Figure 3 illustrates: shift register 44, the first 45 and second 46 adders modulo 2; switch 47.

Figure 4 marked: receiver 16; a Viterbi decoder 17; multichannel myCitadel 18; multi-multiplier-adder 19; amplitude detector 20; averager 21; block automatic gain control 22; a demodulator 23, the first 24 and second 25 units deteremine; nonlinear block 26.

Figure 5 illustrates: the receiver 27; block automatic gain control 28; a demodulator 29; amplitude detector 30; averager 31; the first 32 and second 33 blocks deteremine; nonlinear block 34; multi-multiplier-adder 35; the Viterbi detector 36; the first 37 and second 38, 39 third and fourth 40 memory blocks; multi-line myCitadel 41; multi-channel adder 42; block comparison and selection of 43.

Operation of the proposed method are as follows. Receive radio signals from the transmission channel (operation 1), i.e. the gain and the transfer signal in the low-frequency part of the spectrum required for further processing. This is followed by an automatic gain control (operation 2), then the average level of the received signal becomes constant, which is necessary for soft demodulation and Viterbi algorithm. Further implementation of tsetse demodulation (step 3) in accordance with the modulation method of the binary signal, used on the transmission side. When using the BPSK (binary phase shift keying) demodulation is commonly used correlation reception when the received signal equalized in level, multiplied by the reference sinusoidal oscillation and the result is integrated over the interval of time equal to the duration of one symbol. And is soft demodulation, i.e. the result is some level of stress lying between previously known constant maximum positive and maximum negative levels depending on the instantaneous realization of the noise at a specific time interval the duration of the symbol.

In subsequent operation of the first deteremine 4 the sequence of received symbols is changed back to the interleaving performed at the transmitter side, and produces a sequence of symbols yidifferent level. (This level depends on the implementation of the total signal noise process on the time interval of this symbol.) As a result of this newly restored the original order of encoded symbols with which they followed after encoding in the transmitter.

Simultaneously with the demodulation and the first deteremined after receiving the operation 10 of the amplitude detecting taken is of molov. It results in a sequence of signals proportional to the level of the received symbols. After that adopted the sequence is averaged on a time interval TSdefined as TS=1/F, where F is the maximum frequency of fading (operation 11). In fact, when this is averaged over the interval duration of several characters to avoid the influence of noise components, different time interval of each symbol.

After this is the second deteremine (operation 12), i.e. the order of the signals received after the detection level is changed, and then performed a non-linear transformation (operation 13) levels of the received signals. This results in the sequence of values of αivoltage, which will be used as weights in the Viterbi algorithm. A non-linear transformation is performed using non-linear amplitude transfer characteristic of the form UI=f(UO), where UIthe voltage after the first deteremine, UO- stress after a nonlinear transformation, F is a nonlinear function, defined as the method used modulation-demodulation. (In the case of sufficiently large values of the received signal as a function F which can be used squaring)

The second deferiprone 12 is identical to the first deteremine 4 and is made so that generated by the sequence αicorresponded to the time sequence yii.e. in the i-th point in time after the first interleave 4 was obtained signal, and after the second interleave 12 and the nonlinear transformation 13 (instantaneous) was obtained signal αidetermined by the level of yiafter reception of the transmission channel.

The detection algorithm Viterbi 15 includes several operations. Operation 4-9, the standard Viterbi algorithm. In particular, on the basis of codes of transitions δjthat are determined by the structure of the underlying convolutional code is known in advance and remain constant in the process, define metrics transitions to make the correction on the basis of the levels of the received symbols (operation 5). To do this, for each of the adopted symbol are the squared differences of the values of yiand codes for each transition of the encoder at this step from the previous state to the next. Next, the operation of the multi-multiplication-summation 14, which is introduced in the present method in the standard Viterbi algorithm. In this operation, all of the obtained metrics for each symbol are multiplied by the coefficients equal to αithis SIM is Ola, and the resulting works are summed over all characters of this code group. The result is a metric for each transition µ for this step.

In the operation of the multichannel summing get 6 metric paths. For this to metric Gjall the previous States of the encoder are added obtained in the previous operation metric µ those transitions that depart from each state. In operation, subsequent operations 7 are analyzed for each condition of the two transitions that come to it, in particular obtained in the previous operation of the magnitude of their sum Gjand µ. For each state is chosen, the transition from whom such amount is smaller. It becomes a metric of the given state for further processing. The second transition with a large sum value is discarded. Left transition is added to the set of transitions that led to the state from which this passage comes, forming one of the ways.

In operation 8, all remaining paths are remembered, and the path ended discarded at this step, the transition from the memory are deleted. When moving to the next step after receiving the group code corresponding to the new information transmitted symbol, the received new metrics transitions are used in the operation of the multichannel summing 8 now to the operation of the source for computing the next step. In addition, on those previous steps, which left only one way, it transitions into operations 9 are correlated with their corresponding symbols and the received decoded sequence of information symbols is supplied to the output for later use.

The blocks in figure 3 are as follows. The serial input shift register 44 receives a sequence Silogical information symbols "0" or "1". Upon receipt of each new character all memorized the sequence is shifted to the right by one digit. In this example case, consisting of three digits. In the first adder 45 modulo two received signals from all bits of the register. The second adder 46 modulo two signals from the first and third bits of the register. In both adders is a logical summation modulo two, i.e. at the output of each adder appears logical unit, if the number of logical units on its inputs is odd, if the number of logical units on its inputs is even, then its output is a logical zero. The output signals of both adders modulo two are fed to the inputs of the switch 47.

The switch 47 in turn connects to the output signals from their inputs. The switching frequency in this is the example twice the frequency of receipt of information symbols at the input of the register, each information symbol Siproduced by two coded symbol, xi1and xi2.

Blocks are enlarged schematic (figure 4) implementation of the proposed method are as follows. In the receiver 16 is the reception of radio signals passing through the transmission channel, the required gain and the transfer signal spectrum in the low frequency region for further processing. In block automatic gain control 22 is automatic gain control, then the average level of the received signal becomes constant,

In the demodulator 23 is demodulated (phase detection) using correlation processing, i.e. after alignment on an average level signal is multiplied by a sinusoidal voltage reference generator constant amplitude whose frequency coincides with the frequency of the signal, and their results averaged for the time interval equal to the duration of the symbol.

In the first block of deteremine 24 restores the sequence of encoded symbols, which was to interleave the transmitter. In the amplitude detector 20 is allocated a voltage proportional to the received signal strength. In the averager 21 is averaging the levels of the received symbols in the time interval equal to quasiperiod C is mirani. In the second block of deteremine 25 is the same deteremine by adjusting a Cup spring order of the characters, what was done in the first block of deteremine 24. In the nonlinear block is non-linear conversion of the input voltage, determined by the kind of the used modulation-demodulation in the transmission system.

The Viterbi decoder 17 performs convolutional decoding on the soft algorithm. To break his chains connecting the multichannel myCitadel 18 with subsequent circuits placed multichannel multiplier-adder 19, which is the multiplication of the signal of each of the outputs of multichannel vicites on the output voltage of the second unit deteremine 25.

Figure 5 presents a more detailed example block diagram of a device that implements the proposed method. Blocks: receiver 27, block automatic gain control 28, the demodulator 29, amplitude detector 30, the averager 31, the first 32 and second 33 blocks deteremine, nonlinear block 34, and clock multiplier-adder 35 correspond to the blocks: receiver 16, the amplitude detector 20, the averager 21, block automatic gain control 22, the demodulator 23, the first 24 and second 25 units deteremine, nonlinear block 26 and clock multiplier-adder 19 figure 4.

In the Viterbi detector 36 of the first memory block 37 which holds the codes of transitions δ i. In multichannel myCitadel 41 calculates the squared differences of the values of yiand code for each transition. Further, in multi-channel multiplier-adder 35 they each symbol is multiplied by a factor αifrom the output of the nonlinear block 34, forming a metric transitions µj. From the second memory unit 38 receives the values of the metrics of the States of Gjobtained in the previous step. In multi-channel adder 42 they develop metrics for those transitions that go from each state. After that, the block comparison and selection 43 the analysis of these amounts for each new state. In each condition included two transitions. Compares the corresponding amount, and selects the transition, the amount of which is smaller in size, another transition is discarded. Thus, we obtain a new metric of States Gi+1that will be used in the next step. These metrics are stored in the third memory block 39 and at the beginning of the next step is transferred to the second memory block 38.

Also in the third memory block 39 remember the number of the remaining transitions for each state and join those rooms transitions that was the path to a given state. The way that approach discarded at this step, the transitions from the memory are deleted. In memory at each step are stored the way, if the x is still more than one. When remains for each step, only one transition, the information symbol encoded in this step is decoded, and the number of transitions that comprise the path from the third memory block 39 are removed and transferred to the fourth memory block 40. It codes for these transitions are compared with the corresponding values of information symbols and decoded information sequence from the output of the fourth memory block 40 is supplied to the output device.

The principle of signal processing in accordance with the proposed method consists in the following.

As you know, the basic principle known way to "soft" decoding by the Viterbi algorithm is to select the path on the trellis diagram, which generally has the lowest metric, i.e. the minimal sum of the Euclidean distances to all the accepted characters from the version code corresponding to each character, to the value of the voltage obtained from the output of the demodulator during the advent of this character. Each variant of the path corresponds to a particular variant of the sequence of transmitted symbols, the path with the lowest metric corresponds to the most likely transmitted sequence of symbols.

This rule due to such correlations. According to the method of maximum likelihood, we are from all possible the s variants of the sequences of received symbols must choose the most likely. Let the probability of the q-th variant sequence is equal to Pqso you need to find the number q, which is provided max{Pq}.

Let the length of the sequence of symbols equal to N. Each option q consists of its logical zeros in units. Denote byaiqthe value of the i-th symbol in the sequence numbers q. Since it is usually assumed that the values of the transmitted symbols and noise realization at time intervals different symbols are mutually independent, then the probability Pqequal to:

Pq=iNpi(q){yi/aiq},(1)

wherepi(q){yi/ai(q)} - the conditional probability that if the value is transferred to the i-th symbol isai(q)at the output of the demodulator will receive a voltage equal to yi.

Initially consider the situation when the fading of the received signal is absent, i.e. when the transmission alternation and when taking deteremine not performed. Then when exposed to noise with Gaussian distribution, each conditional probability in the formula (1) is equal to

pi(q){yi/ai(q)}=1q2exp{-[yi-ai(q)]22σ2},(2)

where σ2- the noise power, the same DL is all accepted characters.

When the sequence with the maximum value of Pqwe will not compare the values of Pqand the value of ln(Pq)that will give the same result, since the logarithm is a monotonic function. Then

ln(Pq)=-Nlnσ-0,5Nln2-12σ2iN[yi-ai(q)]2.(3)

Because all variants of the q value is Nlnσ-0,5ln2 remains the same, when determining the maximum Pqit can be ignored and also you can ignore the factor 1/2σ2in front of the amount. Since the sign of the sum is negative, then the maximum value of Pq is at the minimum value of this sum without the minus sign, i.e. ifmin{iN[yi-ai (q)]2}. Thus, we get the rule of the Viterbi algorithm, which consists in selecting the path with the minimum sum of the distances between the adopted values of yiand their variantsai(qfor each alternative path.

Another picture is observed in the presence of fading, when the transmitting side is the alternation of characters, and at the receiving side - back deteremine. In this case, the neighboring decoded symbols in the transmission channel will defend each other at a considerable interval of time. The received signal thus can vary greatly. Thus, at a constant noise level of the input circuits, which mainly determines the overall level of noise, the signal-to-noise ratio of signals received at different points in time can vary greatly.

Since the phase demodulation of the signal pre-cleaned amplitude, decreasing the signal-to-noise ratio at the demodulator input, it decreases and output, but the output level remains constant, and the noise level increases. Therefore, with the front decoded symbols, the noise levels may be different and the formula (2) and (3) do not describe the best method of decoding. In particular, now the conditional probability of each symbol is equal to:

pi(q){yi/ai(q)}=1σi2exp{-[yi-ai(q)]22σi2},(4)

where σi- RMS noise in the time interval of the i-th symbol. Formula (3) is also transformed into:

ln(Pq)=-iNlnσi-0,5Nln2-iN12σi2[yi-aimrow> (q)]2=-iNlnσi-0,5Nln2-iNαi[yi-ai(q)]2,(5)

whereαi=1/2σi2- some correction factors. Since the length of all paths are equal, the component ofiNlnσifor all Pqis also the same and when the identification greatest it can be ignored.

Thus, in the proposed method, the decoding rule is to select the sequence of symbols, which corresponds to the minimum amount ofi Nαi[yi-ai(q)]2

Indeed, when summed for each alternative path for all metrics it transitions cannot be equated their "quality". This is displayed by the drawing in figure 2. Consider the upper graph in this figure. It corresponds to the situation when the demodulation signal-to-noise ratio has a greater value, that is, after demodulation, the noise level is relatively small. The level of ykcharacters after demodulation in the absence of noise can take the values +1 or -1 in accordance with the logical values "1" and "0" is transmitted symbols xk.

When noise is present, the level of symbols ykcan take any value from a continuous interval. The conditional probability P{yk/xk=1}, that the transmission of xk=1 symbol value after demodulation will be equal to ykhas a density distribution shown in the figure, the solid curve (right graph). The conditional probability P{yk/xk=0}, that the transmission of xk=0 symbol value after demodulation will be equal to ykhas a density distribution, showing the percent figure dashed curve (left).

Wide vertical line shows the situation obtaining in the demodulation values of yqsome of the specific symbol. The conditional probability P{yq/xq=1}, which is thus transmitted xq=1, indicated by the dot under the number 1. The conditional probability P{yq/xq=0}, which is herewith transmitted xq=0, indicated by point 2. The conditional probability of the former is substantially higher than the second, and when a decision will be made that the value of xq=1, this solution is quite plausible.

Now consider the bottom drawing in figure 2. It corresponds to the situation when the demodulation signal-to-noise ratio is low, the level of noise after demodulation is significantly higher than in the first situation. Accordingly, both curves conditional density function significantly more stretched on the horizontal axis.

In this case, when receiving the demodulated with the same values of the symbol yqpoint 1 corresponding to the transmission of xq=1, is also located above the point 2 corresponding to the transmission of xq=0. However, both points are located substantially closer to each other, i.e. the values of the conditional probabilities for both values of xqvary little. And, although in this case will also be decided that the transmitted symbol xq=1, but the value of "quality" that the CSOs solutions will be much lower than in the first situation.

Returning to the comparison of different paths on the lattice diagram to select the path with the minimum total metric transitions, it can be noted that a simple summation metrics transitions will give the correct solution only in the case of equality and sameness of conditions calculation of each metric. If conditions are not uniform, then a simple summation, as is done in the case of the prototype, may give incorrect selection of the best path, and, therefore, incorrect decoding of the received sequence.

In this case it is necessary to take into account at the calculation of each metric transition, and perform a weighted summation to calculate metrics of different ways, as suggested in the present method. As was shown above that the decision was maximum likelihood, the weights should be determined in accordance with the above formulas.

In accordance with the necessity to implement such signal processing operations of the proposed method. In operation 1 is the usual procedure, i.e. the radio signals from the transmission channel are received, amplified in a linear channel receiver and transferred to an intermediate frequency for further processing. In operation 2 assests what is automatic gain control, thus, the average signal level is kept constant for further demodulation. When demodulation (step 3) this signal is subjected to correlation processing. While it is multiplied by the signal of the reference oscillator, whose frequency is equal to the average frequency and phase adjusts the phase of the received signal so that when transmitting a logical unit is the result of multiplying took a positive value, and when transmitting a logical zero to a negative value. The result of the multiplication is averaged over the interval T equal to the duration of one symbol.

The amplitude of the reference signal is constant and is of such a magnitude that without considering thermal noise is the result of averaging was equal to some value USwhen transmitting a logical unit, and was equal to-USwhen transmitting a logical zero. The value of USthe principle does not matter, for ease of presentation, we assume US=1.

However, the presence of thermal noise in the measure of real receivers leads to the fact that the result of averaging after demodulation takes two possible values (+1 and -1), and may lie in a continuous range of values between +1 and-1. We assume that if the result of the multiplication is obtained more than +1 or less than -1, then the demodulation it is equal to +1 or -1, respectively. (DL the convenience of the further processing of the result of the multiplication can azithromyacin, although the ultimate goal of the proposed method is the increased robustness of the transmission is achieved, and when the result of multiplication in analog form).

This is followed by deteremine characters, that is, the restoration of that order, which was original to the alternation in the transmitter. (Exactly in this order they were received from the information source for transmission). The result is a sequence of symbols yiwhose values lie in the range from +1 to-1. This sequence is fed for further processing by the Viterbi algorithm. The set of operations 2-4 is a well known and standard in the implementation of "soft" decoding.

In the proposed method, in parallel and simultaneously with this operation sequence is another sequence of operations (operations 10-14). When the amplitude detection 10 is determined by the current level of the received signal. Next is the averaging of the detection (operation 11) to reduce the effect of interference and noise. The averaging time interval TSis determined by the rate of change of received signal level as a result of fading and equal, TS=1//F, where F is the maximum frequency of fading, i.e., the averaging is performed over the time interval during which relates the global changes of the signal level is small.

After this is the second deteremine 12, which is completely identical to the first deteremine 4 and is at the same time. Thus, the magnitude of the signals after the second depramine in each i-th point in time corresponds to the time level of the symbol yiimmediately after admission to adjust its level and demodulation.

This is followed by a nonlinear transformation (operation 13) levels of the signals received after the second deteremine. As is well known (see, for example, kN. Gonorovski I.S. Radio circuits and signals - M.: Radio and communication, 1986), after demodulation, for example, phase detection, the ratio "signal / noise" UOOconnected with this relation to detection UII;

as:

UOO=f(UII),

where UIand UO- the average level of useful signal before and after demodulation; σIand σO- RMS noise level before and after demodulation; f is some monotonically increasing nonlinear function, the type of which depends on the modulation type. For large relations "signal/noise" to demodulation this function is linear, i.e.

UOO=k1(UII),

where k1is some proportionality constant.

The input level is mind σ I- the value is known and generally constant during the transmission, i.e. σI=const. The level of the useful signal after demodulation is determined by the modulation parameters and phase manipulation of the amplitude of the input signal is not affected. Therefore, when the decrease of the ratio "signal/noise" due to the reduction in the average level of the useful UIsignal to demodulation in the signal after demodulation the signal-to-noise ratio also decreases, but at the expense of increasing the noise level σO.

To obtain the coefficients αirequired for signal processing in accordance with formula (5), it is necessary to find the value of 1/σ2O.

αi=1σInSX2=1UInSX2f2(UInXσInX)=F(UInX).(6)

This value varies tol is to changes in the average level of the input signal, because the other values can be considered constant. For large input relations "signal/noise" formula (6) takes the form:

αi=1σInSX2=k12UInSX2σInX2UInX2=k2UInX2

where k2- certain factor.

Thus, after the nonlinear transformation (13) produces the values of the coefficients αithat match the symbols yi. These coefficients when the multiplication-summation are multiplied by the Euclidean distance between the received symbol and all variants in different transitions, and each transition of the received works consist of all characters received code group, forming a metric for the transition.

Also entered in the inventive method, multi-multiplication-summation (14), the remaining operations of the Viterbi algorithm 15 are produced in a known manner.

The proposed method of decoding can be Provillus is recorded on a concrete example. Consider the implementation of convolutional coding in the transmitter on the basis of figure 3.

As you know, when convolutional coding is obtained after each encoding symbol is defined multiple-valued information symbols (in this example, three characters). In addition, when receiving from an information source of each new information symbol based on it and several previous information symbols is produced not one, but a group of consecutive code symbols (in this example - a group of two characters), they all received various logical operations.

Thus, in this example, the encoder (figure 3) contains a shift register 44, consisting of three digits. In his serial input information symbols Si(enter from left to right, the numbering of the bits from left to right). As you enter each new character all their combination is shifted one digit to the right. Characters are entered through the time interval 2T.

At first adder 45 modulo two received signals from all three bits of the shift register. The second adder 46 modulo two signals from the first and third bits of the shift register. The results of the summation modulo two form signals, respectively, xi1and xi2that are fed to the inputs of commutat the RA 47. Switch intervals equal to T, turn connects at its output one or the other of these signals. Thus, with the arrival of each new data symbol Siat the output of the encoder consistently served the corresponding group of symbols xi1and xi2.

At the receiving side (figure 4) signals from the transmission channel are accepted by the receiver 16 where it is pre-processing (amplification and transfer spectrum signals with a carrier frequency corresponding to the intermediate frequency.) Using the automatic gain control 22 the average signal level is then maintained constant, which is necessary for the operation of the demodulator. In the demodulator is soft demodulation and output each character has any value between the previously known maximum positive and maximum negative values. After that, in the first block of deteremine 24 the order of symbols on the time change, they are rearranged in the order in which the transmitter followed with the output of the encoder to alternations. Thus, the result is a sequence of symbols yinecessary to implement decoding.

In parallel with these procedures is obtaining weighting coefficients αicorresponding to each IC is at y iand necessary for decoding according to the claimed method. For this, the signals from the receiver are detected by amplitude amplitude detector 20, and their level is averaged in the averager 21 with a time constant determined by the rate of change of the amplitude of the input signal of the receiver. Then samples the voltage output of the averager rearranged by the time the second unit deteremine 25 in the same manner as in the first unit deteremine 24. Further, the voltage level of the output signals of the second block depramine in nonlinear block 26 is changed in accordance with a non-linear transfer function amplitude defined by the used modulation. Thus, the level of each received from the output of the nonlinear block of the reference voltage αiis determined by the level of the symbol yithe receiver output and supplied to the Viterbi decoder 17 at the same time.

Block Viterbi decoder augmented multi-channel multiplier-adder 19, which is placed after multichannel vicites 18. A more detailed diagram of the Viterbi decoder is presented in figure 5, figures, explaining his work, is shown in Fig.6 and Fig.7.

Consider the decoding procedure on the well-known Viterbi algorithm. In the first memory unit 37 stores the options codes output signals of the encoder δjthat he verbatime is when receiving at its input the next information symbol and taking into account those characters, which came before. In this example, the incoming character will be written into the first bit shift register 44 (Fig 3), the two previous characters are placed in the second and third bits of the shift register.

These previous two characters specify the status register until another character. Depending on the logical values of the possible four combinations 00, 10, 01 and 11 (where the first digit corresponds to the second digit, the second digit character in the third position of the register). Figure 6 these States are numbered rooms, respectively, 1, 2, 3 and 4. With the arrival of the next information symbol of the entire sequence recorded in the register of symbols is shifted to the right. The incoming character is placed in the first level, a character from the first category is moved to the second, from second to third and from the third category, the symbol is removed. Thus, the combination of symbols in the second and third digits are either changed or not.

Figure 6 left column bold dots and numbers 1-4 correspond to the previous state of the encoder, the right-hand column of pixels corresponds to its next state. Arrows indicate possible transitions from the previous state to follow in the parish of the next character. Solid arrows indicate transitions if the first p which would be loaded on the shift register is written to logic zero, dashed arrows mean that the first digit is written to the logical unit. Thus, the possible transitions - eight, they correspond to the eight different combinations of the contents of the register.

The codes generated by the encoder are determined by the combination, which is recorded in the register. In this example, the codes consist of groups containing two symbols, xi1and xi2. These characters are the result of logical operations:

xi1=S1⊕S2⊕S3,

xi2=S1⊕S3,

where S1, S2, S3- the characters in the first, second and third cells of the shift register, respectively; the sign ⊕ indicated the operation of addition modulo two. We denote the group of the values of these two characters through δj, j=1÷8, i.e. eight possible variants of code groups corresponding to the eight variants of transitions. (Figure 6 about transitions written options corresponding code groups).

At the receiving side, all variants are known and stored in the first memory block 37, where multi-channel bus comes to multichannel myCitadel 41. In multichannel myCitadel for each i-th symbol is calculated, the set voltages of the form [δj(1)-yi1]2and [δj(2)-yi2}2, j=1÷8 where δj(1) the value of the first character in j-is a variant of the code group, δj(2) the value of the second character in this version; yi1yi2- the received symbols corresponding to the transmitted symbols xi1and xi2.

These voltage multi-channel bus is coming to the multichannel inputs of the multiplier-adder 35, where metrics are calculated transitions for each j-th variant of the transition by the formula:

µi12i1j(1)-yi1]2i2j(2)-yi2]2,

where α1and α2weighting coefficients corresponding to the symbols yi1and yi2.

In multi-channel adder 42, these metrics transitions develop metrics of States G1,i, G2,i, G3,i, G4,icorresponding to the previous step (before the adoption of the current code group). The metric of each transition is formed with a metric that state, whence comes this transition (in accordance with figure 7).

In the block matching, and 43 are formed of a metric for the next state i+1. To do this, for each state (each state consists of two transition) compares the two sums of these two transitions. Select the transition, the amount of which is smaller in magnitude. Another transition is discarded. This amount becomes the metric of the given state for the next step and stored in the third memory block 39.

In this example, the new met the space of States of G 1,i+1, G2,i+1G3,i+1G4,i+1are determined by the formulas (metric transitions obtained in this step, numbered according to the numbers of transitions index j from 1 to 8.7=1÷8):

G1,i+1=min{G1,i+μ1;G3,i+μ5},G2,i+1=min{G1,i+μ2;G3,i+μ6},(7)G3,i+1=min{G2,i+μ3;G4,i+μ7},G4,i+1=min{G2,i+μ4;G4,i +μ8}.

In the calculations in this step, the metrics are taken from the second memory block 38. After receipt by the formulas (7) metric G1,i, G2,i, G3,i, G4,ifor calculations in the next step, these metrics do in the second memory block 38, where the previous metrics are removed, and instead are now saved metric G1,i+1, G2,i+1, G3,i+1, G4,i+1before carrying out similar procedures with the arrival of the next code group. Before the beginning of the session metrics of all States is equal to zero.

In the third memory block stores the numbers of the transitions that remained after the comparison rule (7), and the number of the previous remaining transitions that came to each condition and were left as the corresponding amounts were minimal. If any previous state was coming transition left on (i-1)-th step (i.e. step to consider now), and now the transition to this state has been discarded, it is discarded and removed from the third memory block number and the previous transition, left (i-1)-th step.

Thus, in the third memory unit 39 stores number of transitions, while for each step remain memorized numbers of more than one transition. When moreprecise new code group to the previous steps will remain memorized the room only a single transition, these rooms are transmitted in the fourth memory block 40. It contains information about the compliance of each non transition the transfer of either a logical one or a logical zero. Then the logical symbol transmitted in this step is decoded and fed to the output device.

If you do not enter amendments by multiplying by the weighting coefficients αithen the algorithm is a standard procedure soft Viterbi decoding. But without the introduction of such amendments in the case of alternation-deteremined characters when determining the best path by selecting the path with the minimum metric, there will be errors of choice, because in these conditions, the rule of calculation of the minimum metrics should be different and implemented by the formulas (4) and (5). As a rule of calculation used in the known method does not correspond to the maximum likelihood principle for the considered operating conditions, means will generate a wrong choice and a large number of decoding errors.

Thus, the use of the proposed method when working in conditions of alternation-deteremine transmitted encoded convolutional code symbols can reduce the likelihood of errors when decoding and to improve the noise immunity of the transmitted information.

The method of decoding from the internal codes includes sequentially carried out by the reception of radio signals, automatic gain control, demodulation, the first deteremine and decoding by the Viterbi algorithm, which is a turn-defining metrics transitions in lattice diagram, then obtaining metrics of paths by summing the metrics transitions and metrics of the States of the previous step, then the comparison of the value metrics ways appropriate to the conditions of the subsequent step and selecting the path with the minimum metric, the transition to the next step with the drop paths with large metrics and memorizing the left path and then recovering the transmitted information sequence on the remaining path, characterized in that it is injected amplitude detection, averaging the second deteremine, a non-linear transformation and multi-multiplication-summation, and amplitude detection, averaging, second deteremine and nonlinear conversion is carried out successively after the reception of radio signals simultaneously with automatic gain control, demodulation and the first deteremine, multi-multiplication-summation is introduced into the decoding algorithm Viterbi between the definition of metrics transitions and multi-summation and produce before summation with p the power of multiplying the metric on the output signal, obtained after nonlinear transformation.



 

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