RU43420U1 - DECODING DEVICE OF REED CODE - SOLOMON - Google Patents

Abstract

The Reed-Solomon code decoding device relates to the field of communication technology and can be used to decode the Reed-Solomon error-correcting code in digital information transmission systems. The Reed-Solomon code decoding device contains an input unit, a buffer storage unit, a syndrome calculation unit, a Galois field element generator, a received symbol polynomial calculation unit, a key equation solving unit, an error locator calculation unit, an inverse Fourier transform calculation unit, a switch, an information recovery unit, erroneous decoding decoder and OR circuit. Moreover, the first input of the inverse Fourier transform calculation unit is connected to the output of the input unit, the second input of the inverse Fourier transform calculation unit is connected to the output of the Galois field element generator, the output of the inverse Fourier transform calculation unit is connected to the input of the syndrome calculation unit, the outputs of the buffer storage unit and the error locator determination unit connected to the input of the switch, the output of which is connected to the input of the information recovery unit, the first output of the information recovery unit is connected to the input ohm of the erroneous decoding decoder, the second output of the information recovery unit is the information output of the device, the output of the error locator calculation unit is connected to the first input of the OR circuit, the second input of which is connected to the output of the error decoding decoder, and the output of the OR circuit is the output of the decoding signal of the code decoding device Reed - Solomon. The technical result achieved by using a Reed-Solomon code decoding device is to increase protection against erroneous information decoding.

Description

The utility model relates to the field of communication technology and can be used to decode the Reed-Solomon code in digital information transmission systems.

At present, the Reed - Solomon noise-resistant code is widely used to protect information from errors that occur in digital information transmission systems. The interference-resistant Reed-Solomon code provides high information reception characteristics in communication channels of various quality, however, the protection of the received information from erroneous decoding is relevant. In case of erroneous decoding of the received information, the number of errors in the Reed-Solomon code exceeds the detecting and correcting ability of the code, and the code decoding device gives out information with errors.

To correct t errors in the Reed - Solomon error-correcting code, 2 · t redundant code symbols are required. When decoding the Reed-Solomon code, t error locators are calculated that determine the location of errors in the code. After the removal of t erroneous symbols in the Reed - Solomon error-correcting code, t excess symbols remain. In the proposed device, these t redundant symbols are used to protect against erroneous decoding of information.

It is known a Reed-Solomon code decoding device comprising a syndrome calculation unit, a key equation solving unit, an error locator computing unit, an error value calculating unit, a buffer storage device and an error correction unit, the inputs of the syndrome computing unit and the buffer storage being connected to the input of the decoding device, output the block for calculating the syndrome is connected with the input of the block for solving the key equation, the output of which is connected to

the input of the error locator calculation unit and the input of the error value calculation unit, the outputs of which are connected to the inputs of the error correction unit, the third input of which is connected to the output of the buffer storage device, the output of the error correction unit is the output of the decoding device (V. Mutter Fundamentals of noise-resistant information transmission of information. L Energoatomizdat, 1990, p. 244).

However, this device has insufficient protection against erroneous decoding of the received information, due to the fact that an incorrect determination of error locators in the error locator calculation unit or error values in the error value calculation unit leads to erroneous information decoding.

Closest to the proposed device is a Reed-Solomon code decoding device (prototype) containing an input unit, a buffer drive, a syndrome calculation unit, a Galois field element generator, a received symbol polynomial calculation unit, a key equation solution unit, and an error locator calculation unit, the input the block is connected to the information input of the decoding device, the first output of the input block is connected to the input of the buffer storage, the second output of the input block is connected to the input of the calculation unit locators received symbols, whose output is connected to the input of the syndrome calculation unit, an output unit is a syndrome calculating unit solutions key input equation, the output key equation solving unit connected to the input calculation block error locators. (USSR author's certificate No. 1309317, class 4 N 03 M 13/00, publ. 1987).

The disadvantage of this device is the lack of protection against erroneous decoding of the received information. When the number of errors in the Reed - Solomon code exceeds its correcting ability, the error locator calculation unit incorrectly determines the error locators,

which is not controlled and leads to erroneous decoding of information.

The purpose of the utility model is to increase protection against erroneous decoding of received information by controlling the values of error locators in the information recovery unit and in the erroneous decoding decoder.

To achieve the goal, a Reed-Solomon code decoding device is proposed, comprising an input unit, a buffer storage unit, a syndrome calculation unit, a Galois field element generator, a received symbol polynomial calculation unit, a key equation solving unit, and error locator calculation unit, the input unit being connected to the information input decoding device, the first output of the input block is connected to the input of the buffer storage device, the second output of the input block is connected to the input of the block for computing the locators of the received symbols, you od is connected to the input of the syndrome calculation unit, an output unit is a syndrome calculating unit solutions key input equation, the output equation solving unit key input unit connected to calculate the error locators. What is new is that the inverse Fourier transform calculation unit, the switch, the information recovery unit, the erroneous decoding decoder and the OR circuit are introduced into the decoding device, while the first input of the inverse Fourier transform calculation unit is connected to the output of the input unit, the second input of the inverse Fourier transform calculation unit connected to the output of the Galois field element generator, the output of the inverse Fourier transform calculation unit is connected to the input of the syndrome calculation unit, the outputs of the buffer storage ator locators and error detection unit coupled to the input switch, whose output is connected to the input of data recovery unit, the first output data recovery unit connected to the input of the decoder decoding error, the second output of block

data recovery is the information output of the device, the output of the error locator calculation unit is connected to the first input of the OR circuit, the second input of which is connected to the output of the erroneous decoding decoder, and the output of the OR circuit is the output of the decoding signal decoding device of the Reed - Solomon code decoding device.

The drawing shows a structural diagram of the proposed device.

The Reed-Solomon code decoding device contains an input block 1, a generator of Galois field elements 2, a buffer storage device 3, an inverse Fourier transform calculation unit 4, a syndrome 5 calculation unit, a polynomial calculation unit 6 received symbols, a key equation solving unit 7, a switch 8, a block computing error locators 9, information recovery unit 10, erroneous decoding decoder 11, and OR circuit 12.

We will consider the operation of the Reed-Solomon code decoding device using the example of the Reed-Solomon code correcting triple errors.

The proposed device operates as follows.

Reed - Solomon code decoder receives t bit code symbols belonging to the Galois field GF (2 ^m ). The total number of characters of the Reed-Solomon code received at the input of the decoding device is

k1 = k + 2t,

where k is the information length of the Reed-Solomon code,

t is the number of errors corrected by the code (t≤3).

The input block 1 to which these symbols arrive transmits non-erased symbols to the inputs of the buffer storage 3 and the inverse Fourier transform calculation unit 4. In addition, the input block 1 transmits the numbers of the received symbols (locators) to the input of the polynomial calculation block 6 received symbols. The numbers of the received characters are counted in order from the beginning of the Reed-Solomon code to its end.

The buffer storage 3 is a serial - parallel shift register, which stores the characters of the Reed - Solomon code.

The Reed-Solomon code consists of characters obtained as a result of the direct Fourier transform of the source information. When decoding the Reed-Solomon code, the inverse Fourier transform of the characters of the Reed-Solomon code is calculated. The inverse Fourier transform is carried out in the inverse Fourier transform calculation unit 4. To calculate the inverse Fourier transform, we use the Reed - Solomon code symbols r _i from the output of input block 1 and the elements of the Galois field d _i from the output of the generator of elements 2 of the Galois field.

The Galois field element 2 generator is a sequential m-bit shift register with feedbacks.

Inverse Fourier transform calculations are performed using recurrence formulas:

where a _i are the symbols of the inverse Fourier transform,

r _i , r _j - Reed - Solomon code symbols,

d _i , d _j - Galois field elements,

i, j are the variables of the cycles.

An example of the implementation of the inverse Fourier transform is described in the source (V. Shabanov. On the Estimation of the Achievable Speed of PC Decoding Devices with Correction of Erasures. Communication Technology, Ser. TPS, 1983, issue 7, p. 27).

In the block for calculating the polynomial 6 received symbols from the output of the input block 1, locators of the received symbols of the Reed - Solomon code are received. In the block for calculating the polynomial 6 received characters calculate the polynomial with (x) the received characters according to the formula:

where j (q) is the locator of the qth received symbol,

α is a primitive element of the Galois field.

In a recursive form of a record, calculations are represented as

where c _i are the coefficients of the polynomial c (x).

An example implementation of a device for computing the polynomial of locators of received symbols is given in the source (USSR Author's Certificate No. 1481902, class 4 N 03 M 13/02, publ. 1989).

Symbols a _i i = 0 ... k ₁ -1 of the inverse Fourier transform from the output of the inverse Fourier transform calculation unit 4 are fed to the input of the syndrome 5 computation unit, the coefficients c _i i = 0 ... k _{1 of the} polynomial characters from the output of the polynomial computing unit 6 received characters. In the unit for computing syndrome 5, a polynomial of s (x) syndrome is obtained. The syndrome polynomial s (x) is calculated as the ratio of the polynomial a (x), the coefficients of which are the symbols a _i i = 0 ... k-1 of the inverse Fourier transform, and the polynomial of the received symbols c (x):

s (x) = a (x) / c (x).

The coefficients of the polynomial syndrome s, calculated by the recurrence formulas:

In the proposed device, the decoding of the Reed-Solomon code is carried out with the correction of no more than three errors. The triple errors in the Reed-Solomon code are corrected by solving the key equation for the coefficients of the polynomial of error locators. The coefficients of the polynomial of error locators σ _i and the coefficients of the polynomial of the syndrome s _i are interconnected by a key equation (a system of linear equations), which is written as:

The coefficients of the polynomial of error locators σ _i through the components of the syndrome are expressed in the form

where Δ, Δ _i are determinants of a system of linear equations.

For the case of three errors t = 3, using the last formula, we write the coefficients of the polynomial of error locators in the form:

Where

At the input of the block for solving the key equation 7, the coefficients of the syndrome s ₀ ... s ₅ are received from the output of the block for computing syndrome ₅ . The block solving the key equation 7 calculates the coefficients of the polynomial of error locators in accordance with formulas (4).

Next, the coefficients of the polynomial of error locators from the output of the block for solving the key equation 7 are fed to the input of the block for computing error locators 9.

Error locators are the roots of the error locator polynomial.

x ³ + σ ₁ x ² + σ ₂ x + σ ₃ = 0.

Using substitution

we reduce the last equation to the form

where is the coefficient

The error locator calculation unit 9 first calculates the coefficient r by the formula (7), determines the roots of equation (6), and then calculates the error locators by the formula (5).

As an example of the implementation of the unit for computing error locators 9, we consider the implementation of the unit using read-only memory (ROM).

The solutions of equation (6) in the Galois field GF (2 ^m ) are determined using a pre-programmed ROM. The address input of such a ROM is the value of the coefficient r, having m bits, and the contents or output of the ROM are the roots of equation (6). Equation (6) for some values of the coefficient r may not have solutions in the Galois field GF (2 ^m ), in this case, in the ROM at the address determined by the value of the coefficient r, when programming the ROM, forbidden combinations are written. Forbidden combinations can be binary combinations whose values do not belong to the Galois field GF (2 ^m ), for example, binary combinations whose value is greater than 2 ^m -1. The presence of a forbidden combination at the output of the ROM will mean that an unrecoverable combination of errors has occurred in the Reed-Solomon code and decoding of the Reed-Solomon code should be abandoned. In this case, the unit for computing error locators 9, by decrypting this forbidden combination, generates a decoding rejection signal, which is then fed to the input of the OR circuit 12.

In the event that equation (6) has solutions in the Galois field GF (2 ^m ), the error locator calculation unit 9 calculates the error locators by formula (5). Next, the error locators that determine the location of errors in the Reed-Solomon code come from the output of the error locator calculation unit 9 to the control input of the switch 8.

The information input of the switch 8 from the output of the buffer drive 3 receives the characters of the Reed-Solomon code. Switch 8 passes the Reed-Solomon code symbols to their output, whose numbers do not match the values of the error locators. Therefore, at the output of switch 8 there will be only those Reed - Solomon code symbols in which no errors were detected.

Further, from the output of switch 8, the Reed - Solomon code symbols are fed to the input of the information recovery unit 10. Of the total number of k + 2t characters of the Reed - Solomon code, switch 8 passes only k + t characters to the input of the information recovery unit 10. Of these characters, only k characters are enough to restore the original information of the Reed-Solomon code, at characters are redundant characters. The information recovery unit 10 performs the inverse Fourier transform of k + t symbols. The reed-Solomon code symbols, by definition, are a direct Fourier transform of the original information symbols, supplemented by zero symbols to the block length of the code. Therefore, with the inverse Fourier transform, k + t characters will be obtained, of which, if the information is correctly decoded, k characters will be informational, and t characters will be zero. In the case of erroneous decoding with a high probability of approximately 1-1 / 2 ^mt , redundant characters will be nonzero. The criterion for determining erroneous decoding of information is the difference from zero at least one of t redundant characters in the inverse Fourier transform, calculated after deleting the erroneous characters in the Reed-Solomon code.

The implementation of the information recovery unit 10 is similar to the implementation of the inverse Fourier transform calculation unit 4.

From the output of the information recovery unit 10, information symbols of the Reed - Solomon code are sent to the output of the decoding device. From the other output of the information recovery unit 10

redundant characters are fed to the input of the decoder 11 erroneous decoding. In the event that the redundant symbols are non-zero, the erroneous decoding decoder 11 generates an erroneous decoding signal, which is input to the OR circuit 12.

The OR circuit 12 performs the function of a logical OR of two signals indicating the refusal of decoding. The first signal comes from the error locator calculation unit 9. It appears if the polynomial of error locators has no solutions. The second signal comes from the information recovery unit 10. This signal appears if the redundant Reed - Solomon code symbols, after the inverse Fourier transform, are non-zero.

The resulting decoding rejection signal from the output of the OR circuit 12 is supplied to the output of the decoding device.

In the proposed utility model, redundant Reed-Solomon code symbols that remain in the codeword after deleting the erroneous symbols are used to determine erroneous decoding of information. This greatly reduces the likelihood of erroneous decoding of information.

For example, the Reed - Solomon error-correcting code (22, 16) defined over the Galois field GF (2 ⁸ ) with a minimum code distance d _min = 7 allows correcting triple errors. After determining the location of the three errors and removing them from the codeword, we obtain the shortened Reed - Solomon code (19, 16). To restore information, the inverse Fourier transform of the shortened code is performed (19, 16). As a result, we get 16 characters of information and 3 redundant characters that are used to protect against erroneous decoding of information. In the event that at least one of the 3 redundant symbols is non-zero, a decoding reject signal is generated. In this case, the probability of erroneous decoding will not exceed 1/2 ²⁴ .

We also note that the proposed decoding device of the Reed - Solomon code can be implemented both in hardware and in software - in hardware. In the latter case, the inclusion of existing individual computer components (adders, memory devices, registers) in the proposed device gives a gain in the amount of equipment. The greatest reduction in hardware costs is provided by the software implementation of the inverse Fourier transform calculation blocks 4, syndrome 5 calculation block, polynomial calculation block 6 received symbols, key equation solution block 7, error locator calculation block 9, and information recovery block 10. In these blocks, the formulas are calculated (1) ... (5). Software implementation using high-level algorithmic programming languages (Pascal, C, and so on) makes it easy to perform calculations using formulas (1) ... (5), and calculations using recurrence formulas (1) ... (3) should be performed using loop operators. Moreover, the amount of memory for the implementation of the decoding device is an insignificant part of the total computer memory resources.

The technical result of the proposed decoding device of the Reed-Solomon code is to increase the protection against erroneous decoding of information.

Claims (1)

A Reed-Solomon code decoding device comprising an input unit, a buffer storage unit, a syndrome calculation unit, a Galois field element generator, a received symbol polynomial computing unit, a key equation solving unit, and error locator computing unit, the input unit being connected to the information input of the decoding device, the first the output of the input block is connected to the input of the buffer drive, the second output of the input block is connected to the input of the block for computing the locators of the received symbols, the output of which is connected to the input b lock syndrome calculation, the output of the syndrome calculation block is the input of the key equation solution block, the output of the key equation solution block is connected to the input of the error locator calculation block, characterized in that the inverse Fourier transform calculation block, a switch, an information recovery block, an error decoding decoder are inserted into it and an OR circuit, wherein the first input of the inverse Fourier transform calculation unit is connected to the output of the input unit, the second input of the inverse transform calculation unit The Fourier is connected to the output of the Galois field element generator, the output of the inverse Fourier transform calculation unit is connected to the input of the syndrome calculation unit, the outputs of the buffer drive and the error locator determination unit are connected to the input of the switch, the output of which is connected to the input of the information recovery unit, the first output of the information recovery unit is connected with the input of the decoder erroneous decoding, the second output of the information recovery unit is the information output of the device, the output of the calculation unit l error okator is connected to the first input of the OR circuit, the second input of which is connected to the output of the decoder erroneous decoding, and the output of the OR circuit is the output of the reject signal from decoding the decoder of the Reed-Solomon code.