SU1736008A1 - Device for decoding nordstrome-robinson code in discrete channel - Google Patents

Abstract

The invention relates to computing and can be used. The aim of the invention is to increase the correcting ability and speed of the device by adding the input code word to the generators of adjacent classes and decoding the received code words by truncated Reed-Muller code decoders. The device contains 7 blocks of addition with the generators of an adjacent class (1), 8 truncated reed-Muller decoder codes (2), a block of keys

Description

h 17

The invention relates to computer science and computing, specifically to decoding devices of the Nordstrom-Robinson code, and can be used in the development of discrete information transmission equipment.

A Nordstrom-Robinson code decoding device is known based on breaking the code into biorthodial subcodes using the Walsh transform. This device is intended to decode a wide class of codes that are split into biorthogonal and for the Nordstrom-Robinson code is not optimal.

The device contains eight biorthogonal code decoding units based on the fast Walsh transform and the maximum element selection scheme.

The closest technical solution is the decoding device of the Nordstrom-Robinson code containing

the comparison unit, whose outputs of the jj connectors are connected to the input of the same name with the control inputs of the comparison unit, the second outputs of the primary keys, as well as the received Joro word converter, the decoder, the detector

Chi-bok, four- and five-bit counters, two control units, a clock generator, two threshold elements, a Reed-Solomon code coder, a Nordstrom-Robinson code coder.

The disadvantages of the known device (is slow and more low compared with the maximum likelihood correction function

The purpose of the invention is to increase the speed and the achievement of a correcting ability for maximum likelihood.

The goal is achieved in that the first-eighth truncated Reed-Muller code decoders, the output buffer register and the first-seventh addition blocks with generators of the adjacent class, whose inputs are entered into the device containing the comparison unit, the outputs of which are connected to the control inputs of the key block. and the inputs of the first truncated Reed-Muller code decoder are respectively combined and are the inputs of the device, the outputs of the first to seventh blocks of addition with the generators of the adjacent class are connected to the inputs of the second respectively of the 7th truncated Reed-Muller code decoders, the first to fifth outputs of all the truncated Reed-Muller code decoders are connected

thirty

35

the third addition block is connected to the second information inputs of the key blocks of the same name, the outputs of which are connected to the inputs of the second to fourth addition blocks, respectively; the first output of the fourth addition block is connected to the input of the fourth comparison block and the first information input of the fourth key block, the second output of the fourth addition unit is subtracted to the second information input of the fourth key block, the first outputs of the first to fourth

The 4Q comparison blocks are connected to the first control inputs of the same key block and are respectively the first to fourth outputs of the decoder, the inverse outputs of the first to fourth

45 comparison units are connected to the second control inputs of the same key block, the output of the digit character determining block is the fifth decoder output, the output of the fourth key block is connected to the input of the digit sign determining block and is the sixth output of the block

FIG. 1 shows a block diagram of a device for decoding 55 of the Nordstrom-Robinson code; FIG. 2 hr. truncated Reed-Muller code decoder; in fig. 3 graph diagram.

A device for decoding the Nordstrom-Robinson code contains blocks 1

With the corresponding information inputs of the key block, the outputs of which are connected to the first inputs of the output buffer register, the second inputs of which are connected to the outputs of the comparison block, the sixth outputs of all the truncated Reed-Muller code decoders are connected to the inputs of the comparison block, the outputs of the output buffer register are device outputs .

In addition, in the device, the truncated Reed-Muller code decoder contains addition-subtraction blocks, sum- and module-world blocks, comparison blocks, key blocks and a digit sign determining unit, the inputs of the first addition-subtraction block are the decoder inputs, the first outputs of the first are the third addition-preamble blocks are connected to the first information inputs of the same-name key blocks and the inputs of the same-sum modules of the summation of modules; the output of each summation block can be

The modules are connected to the input of the same unit of comparison, the second outputs of the first

the third addition block is connected to the second information inputs of the key blocks of the same name, the outputs of which are connected to the inputs of the second to fourth addition blocks, respectively; the first output of the fourth addition block is connected to the input of the fourth comparison block and the first information input of the fourth key block, the second output of the fourth addition unit is subtracted to the second information input of the fourth key block, the first outputs of the first to fourth

comparison blocks are connected to the first control inputs of the same key block and are respectively the first to fourth outputs of the decoder; the inverse outputs of the first to fourth

Comparison units are connected to the second control inputs of the same key block, the output of the number sign determining unit is the fifth decoder output, the output of the fourth key block is connected to the input of the number sign determining unit and is the sixth output of the block

FIG. 1 shows a block diagram of a device for decoding a Nordstrom-Robinson code; FIG. 2 hr. truncated Reed-Muller code decoder; in fig. 3 graph diagram.

A device for decoding the Nordstrom-Robinson code contains blocks 1

the generator with the adjacent class, the truncated decoders 2 Reed-Muller codes, the 3 key block, the k comparison block, the output buffer register 5.

The block T of addition to the generator of the adjacent class is a set of six inverters inverting the elements of the original vector in accordance with

code distance (i), i.e. correcting errors of multiplicity three inclusive. The Nordstrom-Robinson code decoder will then correct all duplicate errors, as well as those triple and quadruple errors that are corrected when decoding to the maximum likelihood.

with the generators of this adjacent class 10 the number of decoding

The key block 3 is a device operating on a maximum of a set of keys which, at the output of a blisse, and a truncated device, pass five informational decoding simulations (decoding in preels from a truncated decoder of the code distance code) for vector-Reed-Nallera, having a maximum ditch with errors of multiplicity 0,1,2,3 one sum ne output ,, - -

The compare block C finds the truncated Reed-Muller code decoder that yielded the maximum amount, “encodes the number of this decoder Reed-Muller code in three binary symbols.

Register 5 is a 16-bit buffer register.

The truncated Reed-Muller code decoder (FIG. 2) is a 25-ThL1Pe decoder. When the Reed-Muller code decoder code is working, Muller decoding in Muller by maximum likelihood and limits of code distance, containing blocks 6 addition-subtraction, blocks 7 summation of modules, comparison blocks 8 (with eight), blocks 9 keys, block 10 determining the sign of the number,

The addition and subtraction block for the j-ro stage (,,. /,) Contains. adders and subtractors.

Block of the modules of the th stage

is a 2 J-input sum-35 items of length 16) mat. Example Let the line of communication

The comparison unit with eight represents the vector of length 16 v (1, 1, lt is a set of threshold logic circuits that are triggered when the threshold is reached (the threshold is eight) ”40

The key blocks are made on the basis of the AND, OR, and NOT logic circuits and serve to pass to the next stage the corresponding group of characters,

The block of determining the sign of the number passes the sign bit of the number to the output.

and the same and since vectors with five, six multiple errors in some adjacent class are vectors with multiplicity errors less than 2Q five, and since there is exactly a certain number of vectors in the column of the standard location table, the number decoded vectors with errors of the multiplicity of the truncated decoder will be the same. Therefore, a device for decoding a Nordstrom-Robinson code using a truncated Reed-Muller code decoder will be a maximum likelihood decoding device (this statement is verified on a computer by decoding in two ways all binary sequences.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

1, D.

On the receiving side, the vector w (-1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, - 1, 1, 1, 1) is received with errors on the first, sixth and the tenth positions of the elements of the received vector in pairs 45 we add and subtract, then we find the sum s of the modulus of the elements obtained

The operation algorithm is as follows. It is known that the coverage radius of the Nordstrom-Robinson code is four-, rem, while the coverage radius of the Reed-Muller code of length 16 is six, so there is no need to use a Reed-Muller code decoding device that works on maximum likelihood and corrects errors of six inclusive ,, It is enough to build a device that decodes a Reed-Muller code of length 16 into a device that operates at maximum likelihood and a truncated decoding device (decoding within a code distance) for ditch with multiplicity errors 0,1,2,3 one - -

5 TL1RE When the decoder of the Reed-Muller code works at maximum likelihood and

and the same, and since vectors with five, six multiple errors in some adjacent class are vectors with multiplicity errors less than Q five, and since there is exactly a certain number of vectors in the column of the standard layout table, the number decoded vectors with errors of multiplicity CHET1RE when the decoder of the Reed-Muller code works on the maximum likelihood and

16) Example Let the line be

The work of the truncated decoder will be the same. Therefore, a device for decoding the Nordstrom-Robinson code using a truncated Reed-Muller code decoder will be a maximum likelihood decoding device (this statement is verified on a computer by decoding in two ways all binary sequences).

sent a vector of length 16 v (1, 1,

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,

1, D.

On the receiving side, the vector w (-1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, - 1, 1, 1, 1) is received with errors on the first, sixth and the tenth positions of the elements of the received vector are added in pairs and subtracted in pairs, then we find the sum s by the modulus of the elements obtained

adding m, and comparing it with eight, Sat g, 8, then for further decoding we skip the elements obtained by adding, if s & C, then for further decoding by transmission elements obtained by subtracting, while at each step we get the next information symbol (1 if s 8, 1

if a ). In the last step, we determine the sign of the element (obtained by adding, if), obtained by subtracting, if) —this gives the fifth in71736008В

formation symbol. We take this from — since the Reed-Muller code is linear, by the power of a graph scheme (FIG. 3).

that a vector consisting of

Let us prove that the device will be is -s -s s of one units. Then in steps 1 ,, .., 4 we correct all errors of multiplicity 1,2,3, respectively;

in | - | a, +% | | a, + a4 | + 0 .. aC, - “- ay + a4 | + .. „+ a, 3 + a, 4 + a, 5 s | a, + a2 + ..„ + av | + .. a1o + .., + a, 6), + a +, 0. + A , b |,

where & i +1 are the characters that came from the channel. It is easy to see that the distortion of the 1st symbol entails a decrease in any amount by 2 (if no symbols were distorted, then all the sums are equal to sixteen), the distortion of the symbols leads to a decrease in any amount, tsa. if no more than three characters are distorted, then any amount will be more than eight and decoding will be correct. Thus, it can be seen that the truncated decoder is guaranteed to correct any three errors. At the same time, the number of adders is reduced in a single decoder of the Reed-Muller code from 6b to 1, and in the entire decoder of the Nordstrom-Robinson code from 512 to 312. In the decoder, you need to find the maximum element of 16 elements for maximum likelihood; in the Reed-Hallerian code decoder and 120 comparison operations in the Nordstrom-Robinson code decoder, in a truncated Reed-Muller code decoder, four comparison operations with a constant and 32 comparison operations with a constant in the Nordstrom-Robinson code decoder are possible. estimate the decrease in hardware costs 1.5 times.

The device works as follows.

The code vector of length 1b comes from the communication line and arrives at the inputs of blocks 1 of addition to generators of adjacent classes, from the outputs of which the results go to inputs of truncated decoders 2 Reed-Muller codes (since one of the generators of adjacent classes consists of only zeros, this In the case of a decoded vector, you can immediately apply to the truncated decoder 21 Reed-Muller codes). At the outputs of the truncated decoders 2 Reed-Muller codes, we have five information symbols and the maximum correlation coefficient. In block C, compare subcodes

five

five

0

five

0

five

0

five

find the larger of the correlation coefficients, which gives three information symbols that arrive at the second inputs of register 5 of the decoded word record, S. truncated decoder 2, which gives the highest correlation coefficient, skip five information characters to the first inputs of register 5 of the decoded word record.

Thus, we obtain a device for decoding the Nordstrom-Robinson code, containing a smaller number of logic elements as compared with the known device, working as a combinatorial circuit in contrast to the known device and providing a single correction for all possible errors.

Claims (1)

1. A device for decoding the Nordstrom-Robinson code in a discrete channel containing a comparison unit, the outputs of which are connected to the control inputs of a key block characterized in that, in order to increase the correction ability and speed of the device, the first to eighth truncated Reed code decoders are introduced into it -Mallera, the output buffer register and the first - seventh blocks of addition with generatrix of an adjacent class, whose inputs and inputs of the first truncated Reed-Muller code decoder are respectively combined and are inputs devices, outputs of the first to seventh blocks of addition with generators of the adjacent class are connected to the inputs of the second to eighth truncated Reed-Muller code decoders, the first to fifth outputs of all truncated Reed-Muller code decoders are connected to the corresponding information inputs of the key block whose outputs are connected to the first the inputs of the output buffer register, the second inputs of which are connected to the outputs of the comparator unit, the sixth outputs of all the truncated readings of the Reed Naller code are connected to the inputs of the comparison unit, the outputs of the output buffer register are the device outputs 20 The device according to claim 1, that is, that the truncated Reed-Muller code decoder contains addition-subtraction blocks, module summation blocks, comparison blocks, key blocks and a number sign identifier block, the inputs of the first addition-subtract block are the decoder inputs, the first outputs of the first and third addition-subtraction blocks are connected to the first information inputs of the m-and key blocks of the same name and the inputs of the modules of the same summing modules, the output of each module's summing blocks is connected to the input of the same block compared to and second outputs of the first - third blocks -vychitani adder coupled to the second 0 five 0 five the information inputs of the same key blocks whose outputs are connected to the inputs of the second to fourth addition and subtraction blocks respectively, the first output of the fourth addition and subtraction block is connected to the input of the fourth comparison block and the first information input of the fourth key block; the second output of the fourth addition and subtraction block is connected to the second information input of the fourth key block, the direct outputs of the first to fourth comparison blocks are connected to the first control inputs of the same key blocks and are respectively the first to fourth outputs of the decoder, the inverse outputs of the first to fourth comparison blocks are connected to the second control inputs of the same key blocks, the output of the number sign determining unit is the fifth output of the decoder, the output of the fourth key block is connected to the number sign input and is the sixth decoder output w i irf I T . J 91 №1Г 71 “And H 0 | J Have J ) W5 one AND FW