# Device for coding convolutional code

(57) Abstract:

The invention relates to telecommunication and can be used in high-voltage modems for forming surtace-coded signals. The purpose of the invention is improving the noise immunity of the device. The device comprises adders 3, 5, 6, 7, 8, and 12,an inverter 13, items 1, 2, 4 and 9 and the block 11 permanent memory. 4 Il. The invention relates to telecommunication and can be used in high-speed modems for forming surtace-coded signals.A device for convolutional coding, containing the shift register, the first adder, the second adder and the switch [1]It is also known a device for forming surtace-coded signals containing the first delay line, a second line delay, the third delay line, the first adder, the second adder and the block selection signal point [2]

The disadvantages of these devices are low immunity generated surtace-coded sequences at low signal to noise ratio (< 20 dB), and their sensitivity to surges phase of the carrier wave, is equal to n /2, where n 1, 2, 3, under which the communication channel is not the of the technical essence is a device for forming surtace-coded signals, insensitive to phase jumps carrier oscillation in the communication channel, a multiple of the 90

^{about}containing the unit's permanent memory, the first and second outlet through which the first and second delay lines connected respectively to third and fourth inputs of the unit's permanent memory, connected in series to the third delay line, a first adder, a second adder, a fourth delay line, the third adder, the fourth adder, the fifth delay line, the block selection signal point, and the fifth adder, the first multiplier and the second multiplier, the output of the fifth adder connected to the second input of the first adder, the inputs of the fifth adder are the first and second outputs of the unit's permanent memory, and the output of the fifth delay line is combined first input of the third delay line, the first multiplier and the second multiplier, the second inputs of the first multiplier and the second multiplier are respectively the output of the third adder and the second output unit's permanent memory, the outputs of the first multiplier and the second multiplier connected respectively to the second inputs of the second adder and the fourth adder, the first output of the unit's permanent memory is the second input of the third adder and the third the second memory, moreover, the first and second inputs of the unit's permanent memory and the block selection signal points are informational inputs, and outputs a block selection signal points are outputs of the device [3]

The device generates surtace-coded signals, which allow you to send 4 information bits (m 4) in one interval modulation. Used for convolutional coding code speed R /+1 2/3 provides asymptotic coding gain from coding (AMC) 4 dB compared to the unencrypted transmission method quadrature-amplitude modulation QAM-16.AMC due to the amount of free distance (minimum Euclidean distance) between any two transmitted surtace-coded sequences of signals are equal .Surtace-coded signals are insensitive to the jumps of the phase of the carrier wave in the communication channel, a multiple of the 90

^{about}. This is achieved at the expense made in a certain way device prototype assignment of subsets of signal points obtained by partitioning [1, 4] of the original ensemble signal transition graph state corresponding destination bit signal points of the ensemble of signals and the sequences of signals on the technique uses the maximum likelihood decoder with soft decision [5, 6] decision rule such a decoder can be formulated as follows. As decisions are made, such information sequence} which would give the output of the block selection signal point sequence} is closest to the received} by Euclidean distance

min

this}c where C is the set of all possible sequences at the output of the block selection signal point.Characteristics of "soft" decoding depend on the free distance

d

_{free}= min

when S

_{n}} {P

_{n}} S

_{n}}P

_{n}} c.Assume that the signal S

_{n}} IR

_{n}} with the minimum Euclidean distance between them d

_{free}originate, respectively, the binary posledovatelnostyu

_{n}} ia

_{n}'} Then the probability that instead transferred to posledovatelnostyu

_{n}} is decoded posledovatelnostyu

_{n}'} is defined as

P{ }P

_{n}}{S

_{n}} P{}a}{a

_{n}} Q(d2), where Q interval probabilities;

- the standard deviation of the noise.When the signal-to-noise tending to infinity, the probability that a solution will be adopted consistently the S

_{n}} can be neglected compared to the likelihood that the solution will be adopted posledovatelnosti

_{n}} at a distance of d

_{free}S

_{n}} So

P N(d

_{free})Q(d

_{free}/2), (1) where N(d

_{free}) the number of error sequences, located at a distance of d

_{free}from indeed passed S

_{n}} and depends on the structure of the transition graph [4]

As can be seen from (1), a determining influence on the immunity surtace-coded sequence of signals has a free distance of d

_{free}. AMC, due to the amount of free distance is 4 dB. However, in channels with additive white Gaussian noise (abgs) and on changes in phase of the carrier wave that are multiples of 90

^{about}the benefit of coding is greatly reduced at low and medium signal-to-noise (s/n) (15-20 dB). For example, if the error probability P

_{Osh}10

^{-4}the benefit of coding is about 2.5 dB.Thus, surtace-encoded sequence of signals generated by the device has low noise immunity, due to the amount of free distance.In addition, the use operativ the receiver of the modem in case of wrong decisions of the maximum likelihood decoder (Viterbi decoder).The aim of the invention is to increase the noise immunity of the device and eliminating the operation of differential encoding, leading to the propagation of errors in differential decoding in the receiver of the modem in case of wrong decisions of the Viterbi decoder and the increase due to this energy gain from coding in channels with irregular phase of the carrier wave that are multiples of 90

^{about}when small and medium-relations/W.In Fig. 1 shows a structural electrical diagram of a device for coding convolutional code of Fig.2 and 3 tridcatyh and shestnadcatiletnie ensembles of signals of Fig.4 transition graph of the convolutional encoder.The device comprises a first element 1 delay, the second delay element 2, the first adder 3, the third delay element 4, the second adder 5, the third adder 6, a fourth adder 7, the fifth adder 8, the fourth delay element 9, a multiplier 10, block 11 permanent memory, the sixth adder 12 and the inverter 13.The device operates as follows.The information input device at time n received data bits Q1

_{n}', Q2

_{n}', Y3

_{n}, Y4

_{n}(m 4). Bits Y3

_{n}, Y4

_{n}served directly on pinene first delay element 1, a second delay element 2, the first adder 3, the third delay element 4, the second adder 5, the third adder 6, a fourth adder 7, and connected in series with the fifth adder 8, the fourth delay element 9 and the inverter 13 and the multiplier 10 and the sixth adder 12. The work of the coder describe the following logical functional dependency

W1

_{n+1}W2

_{n};

W2

_{n+1}W3

_{n};

W3

_{n+1}= W3

_{n}Q1;

W4

_{n+1}= W1

_{n}W3

_{n}W4

_{n}Q1 Q2;

Y1

_{n}= W4

_{n}Q1;

Y1

_{n}=.They bind subsequent state W1

_{n+1}W2

_{n+1}W3

_{n+1}W4

_{n+1}and output bits Y1

_{n}and Y0

_{n}encoder with the current state of W1

_{n}W2

_{n}W3

_{n}W4

_{n}and output bits of the encoder Q2

_{n}' and Q1

_{n}'. These expressions are obtained by minimizing with charts of Vaca full functional dependency, due to the count of transitions and destination bits YI

_{n}I 0,1,4 signal points of the ensemble of signals. Transition graph displays the progress of the convolutional encoder as a state machine with memory.Each transition out of a single current state and leading to the subsequent, is assigned a set of signal points of the ensemble sinarest [1, 2, 4] is consistent splitting the original extended signal set (alphabet signals) nested subsets and the distance between the elements of the subset (signal points) at each step of partitioning is increasing, and the number of elements decreases. As the source of the extended signal set is applied triazacyclohexane cross constellation (32-CR), shown in Fig. 2. It is advanced because transmission m 4 unencrypted data bits over the channel during the interval modulation method quadrature-amplitude modulation (QAM) would be enough to have an ensemble of signals (Fig. 3), consisting of 16 pixels (16-QA). The use of convolutional coding to the input information bits Q2

_{n}'Q1

_{n}' leads to the appearance of additional excess fifth bits Y0

_{n}. Therefore, the ensemble of signals must have M 2

^{m+1}32 points. In this case, it is the ensemble of signals 32-CR with 90-degree symmetry, which is necessary to ensure the insensitivity of a generated sequence of signals to the jumps of phase by a multiple of 90

^{about}. The study approach is based on partitioning the original signal is VA on 2

^{m+1}=2

^{3}=8 ( 2 number of input bits of the convolutional encoder) nested subsets A, B, C, D, E, F, G, H (Fig.2).The splitting is performed in the (+1) 3 steps. In the first step of partitioning obtained two subsets (Fig.2): A U B U C U D E U FU G U H ( U - sign associations) with the minimum Euclidean distance

_{1}= = 2 where

_{about}the minimum Euclidean distance to the original signal set

_{o}= In the second step, break out subsets of A U B C U D E F U, G U H

_{2}=

_{1}= 2 the last step of partitioning are eight subsets A, B, C, D, E, F, G, H

_{3}=

_{2}=4 When the rotation signal set clockwise 90

^{about}subsets A, B, C, D, E, F, G, H, go, respectively, the subsets E, F, G, H, C, D, A, B. When rotating 180

^{about}subsets A, B, C, D, E, F, G, H pass, respectively, C, D, A, B, G, H, E, F, and at 270

^{about}in G, H, E, F, A, B, C, D.A graph of transitions was based on the following rules [3, 4]

(a) transition graph must be symmetric and all transitions should occur with the same frequency;

b) the transitions that start in one state and leading in different States, it is necessary to match the signals of one of the subsets obtained in the first step of partitioning;

g) if we denote q of States of the encoder through i 0,1,q-1, so that the encoder and, therefore, the sequence of signals are transparent to the phase uncertainty in the communication channel, a multiple of 90

^{about}must exist functions one correspondence f

_{l}:0,1,q-1} _0,1,q-1} l 1,2,3 such that running the following statement. For each transition from state i to state j, i

_{n}j 0,1,q-1} denote by X0 the group of signal elements of one of the resulting partitioning subsets, and through X1, x2, X3 groups of signal elements obtained from X0 by clockwise rotation, respectively, at 90, 180 and 270

^{about}. Then each transition from state f

_{l}(i) the condition f

_{l}(j), (l 1,2,3) is assigned to a group of signal elements X

_{l}(l 1,2,3), respectively.Transition graph shown in Fig.4. Features one correspondence have

f

_{1}: 1110 f

_{2}: f

_{3}:

For the transition graph of the squared free distance equal to 12. Indeed, if the transmitted sequence of signal points belonging, for example, the subset A (zero state), the nearest to it is the sequence of signal points belonging under taking into account the minimum distance between points of the subsets a and b, A and D

_{AB}2,

_{AD}2, figs.2) the squared free distance between the observed sequences is equal to d

_{free}

^{2}

_{AB}

^{2}+

_{AD}

^{2}= 12. If the correct sequence to select another, then there is a sequence, separated from her at a distance .Free distance allows to estimate AMC compared to the unencrypted transmission method QAM-16. Then, taking into account the normalization by the average power for AMC have [2, 4]

G 10lg 10lg 4,771 dB.C output of the convolutional encoder output bits, denoted as Y0

_{n}, Y1

_{n}and Y2

_{n}do respectively on the fifth, fourth and third input unit 11, the second and first inputs of which are served noncoding information bits, denoted by Y3

_{n}, Y4

_{n}. In accordance with an input bit sequence YI

_{n}I 0,1,4 unit 11 selects for transmission over the channel, one of the points of the alphabet signals (Fig.2).To ensure the insensitivity of the signal elements of the ensemble of signals to the jumps of the phase of the carrier wave, a multiple of the 90

^{about}without the operation of the differential encoding and reducing the complexity of building a convolutional code is) each group of four signal elements, obtained by rotating one of them by 90, 180 and 270

^{about}clockwise assigned the same bit combination Y4

_{n}Y3

_{n}Y2

_{n};

b) the signal elements in each of the eight subsets A, B, C, D, E, F, G, H are assigned the same bit combination Y2

_{n}Y1

_{n}Y0

_{n};

Subset Y2

_{n}Y1

_{n}Y0

_{n}Subset Y2

_{n}Y1

_{n}Y0

_{n}< / BR>

A 0 0 1 E 0 0 0

B 1 0 1 F 1 0 0

C 0 1 1 G 0 1 0

D 1 1 1 H 1 1 0

C) for each current state of the encoder and each input bit combination device will denote by V 0 the signal element corresponding to the bit pattern Y4

_{n}Y3

_{n}Y2

_{n}Y1

_{n}Y0n. Then we denote by V1, V2, V3 signal elements received when V0 is rotated 90, 180 and 270

^{about}clockwise, respectively. Then the signal elements corresponding bit pattern Y4

_{n}Y3

_{n}Y2

_{n}Y1

_{n}Y0

_{n}at the current state of the encoder f

_{l}(W1

_{n}W2

_{n}W3

_{n}W4

_{n}) (l 1,2,3) and when the same input bit pattern Y4

_{n}Y3

_{n}Q2

_{n}'Q1

_{n}' are respectively V1, V2, and V3.In accordance with the input bits YI

_{n}(I 0,1,4) in block 11 is uniquely determined signal point and the outgoing signal point.Unit 11 permanent memory stores the value of signal elements. Input bits YI

_{n}(I 0,1,4) for unit 11 form an address code signal element in ROM. Examples of implementation of block 11 in Fig.5.17, 18, S. 182, 283 [7]

The simulation results of the proposed device for forming surtace-coded signals showed that, compared with the prototype in channels with additive white Gaussian noise and when the races phase carrier wave that are multiples of 90

^{about}when small and medium-sized relations With/W (15-20 dB) it provides a significant increase noise immunity of the transmitted signal sequence by increasing the free distance between the signal sequences. DEVICE FOR CODING CONVOLUTIONAL CODE containing serially connected first delay element, the second delay element and the first adder, the third delay element whose output is connected to the first input of the second adder, the output of which is connected to the first input of the third adder, the fourth adder, the output of which is connected to a second input of the first adder, the multiplier, the output of which is connected to a second input of the third adder, the fifth adder and block constant paimen the input device, the third input of the unit's permanent memory and the second input of the fourth adder are combined and the third input device, the first input of the multiplier is the fourth input device, characterized in that, to improve the noise immunity of the device, it introduced the sixth adder, the fourth delay element and an inverter, the output of the first adder connected to the input of the third delay elements, the first and second inputs and the output of the sixth adder connected respectively to the fourth input device, the output of the third delay element and the fourth input of the unit's permanent memory, the second input of the fourth adder and the first input of the fifth adder connected respectively to the output of the third adder and the fourth input device, the output of the fifth adder through the fourth delay element is connected to the input of the first delay element, the second inputs of the second and fifth adders and the input of the inverter, the output of which is connected to the second input of the multiplier and the fifth input of the unit's permanent memory.

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