KR100220694B1 - Modified syndrome polynomial generator - Google Patents

Abstract

The present invention relates to an implementation circuit for processing extended syndrome polynomial operations in a channel decoder. The extended syndrome polynomial T (X) expansion apparatus according to the present invention is characterized in that it comprises a laser resistor for sequentially providing this laser polynomial of the laser polynomial, a laser diode provided from the laser resistor and a syndrome of each order of the syndrome polynomial The first through (n + 1) -th arithmetic operators are operated to calculate the coefficients and generate the arithmetic result. Each of the arithmetic operators includes: a multiplier for multiplying the laser beam provided from the laser register by a coefficient of the syndrome polynomial; An adder for adding the syndrome coefficient to a result multiplied by a multiplier in a preceding stage of the multiplier; And a syndrome register for temporarily storing the syndrome coefficients and providing the stored syndrome coefficients to the multiplier and the adder; And the syndrome coefficient stored in the syndrome register is updated as a result of being added by the adder.

Therefore, the number of multipliers and adders can be greatly reduced compared to the prior art, and a simple circuit can be realized.

Description

Extended syndrome polynomial expansion device

The present invention relates to error correction in a channel decoder, and more particularly to an implementation circuit for processing an extended syndrome polynomial operation in a channel decoder.

Typically, noise that occurs during the process of transmitting, storing, or retrieving data may cause errors in transmission, storage, or retrieval of data. Accordingly, techniques have been developed that can correct such errors in various techniques for decoding data to be transmitted or stored.

One such decoding technique is to add a set of check bits to a group of message bits or information bits to form a codeword. These check bits are determined by the encoder and are used to detect and correct errors. In this regard, the encoder processes the message bits as a coefficient of the binary message polynomial and derives the check bit by computing the generator polynomial for the message polynomial through a multiplication or division operation.

One class of error correcting codes is the Bose-Chaudhuri-Hocquenghen (BCH) code containing well-known Reed-Solomon codes.

Reed-Solomon code is an error correction theory developed for digital communication applications. It detects and corrects errors generated or introduced in a transmission channel by the receiving end to obtain original transmission data.

When information data such as "d" is generated from the information source and transmitted to the encoder, the encoder generates a codeword corresponding to the information data one-to-one based on the prescribed code format. The generated codeword is modulated according to the characteristics of the channel and transmitted through the transmission channel. In the transmission channel, a signal transmitted by noise and disturbance is altered and reaches a demodulation unit. The value to be altered is defined as an error "e" e "are considered to be present.

That is, r = c + e. The decoder determines whether an error is included in the received word based on the prescribed code format. If the error is included, the decoder calculates an error value e, Components are removed and restored to the original source data and transmitted to the information receiver.

A decoding process for generating a codeword from the source data and a process for determining whether or not an error has occurred in the received word and obtaining and correcting an error value is performed by a complicated and difficult mathematical calculation.

Further, when it is assumed that a codeword is configured as n symbols (a basic unit constituting a codeword), when it is found that i (1 <i <n) th symbol of this codeword is wrong, The position of the symbol is referred to as the erasure position, and the symbol representing this is called the laser. When such a position estimated as an error is known, an error correction code can be used to correct the laser or to correct the error and the laser simultaneously.

In the process of receiving or retrieving a transmitted or stored codeword, some additional noise components may be converted into an error pattern of the codeword. To process the error pattern imposed on the Reed-Solomon code, the following procedure is used. Prior to the description, the Reed-Solomon code is made up of n m-bit symbols, k symbols among the n symbols are data symbols, and the remaining n-k symbols are check symbols.

As a first error correction step, the syndrome coefficients (or values) S ₀ , S _1, ... of each order of the syndrome polynomial "S (X)" of the Reed Solomon code as shown in the following equation , And S _2t-1 are calculated.

In Equation (1), t denotes an error correction capability.

The second step generates the laser polynomial "G (X) " using the generated laser as shown in the following equation (2). At this time, the root of the laser polynomial represents the position of the error.

In the above equation, k is the number of the laser, and E ₀ , E ₁ , ... , And E _k represents this laser.

The next step is to multiply the syndrome polynomial "T (X)" by the syndrome polynomial "S (X)" and this laser polynomial "Γ (X)" to expand the extended syndrome polynomial Develop.

Next, the root representing the error position in the received codeword is obtained using the Euclid algorithm and the chien serarch, and the error value is calculated using the error position and the syndrome value.

In the above process, a direct development method is generally used for developing the extended syndrome polynomial T (X) by multiplying the syndrome polynomial S (X) and the laser polynomial Γ (X) for this laser correction.

Figure 1 shows an arithmetic circuit for developing an extended syndrome polynomial using a typical direct expansion scheme.

As shown, this arithmetic circuit calculates the syndrome coefficient values S ₀ , S ₁ ... of the respective orders of the syndrome polynomial S (X) A first register array 10, and the second register array 20 which respectively store the laser near the laser polynomial Γ (X), the first resistor array 10 for each store the S _2t-1 and A plurality of multipliers 31 to 33 that multiply the syndrome coefficient values stored in the second register array 20 and the laser meandering values, a plurality of adders 41 to 43 that add the multiplication results of the multipliers, 43) as coefficients of each order of the extended syndrome polynomial. As a result, each register cell of each third register 50 stores the coefficient value of each degree of the extended syndrome polynomial T (X).

However, since the expansion apparatus of the prior art expanded syndrome polynomial implemented using the direct method uses 2t (k + 1) multipliers and 2t (k + 1) -2 multipliers, the hardware structure is complicated, There is a problem in that the size is increased when the circuit is implemented by an integrated circuit.

Therefore, it is an object of the present invention to provide an apparatus capable of developing an extended syndrome polynomial as hardware of a simple structure.

According to an aspect of the present invention, there is provided an apparatus for correcting errors included in a codeword that is encoded using a Reed-Solomon code and transmitted to a decoding system, includes an n-th order syndrome polynomial S (X) An extended syndrome polynomial T (X) expansion device which computes this laser polynomial G (X) representing the position is:

The laser register sequentially providing the laser beam of the laser polynomial; And a series of first to (n + 1) -th arithmetic operators for calculating a syndrome coefficient of each order of the laser beam and the syndrome polynomial provided from the laser register to generate an arithmetic result, :

A multiplier for multiplying the laser beam provided from the laser register by a coefficient of the syndrome polynomial; An adder for adding the syndrome coefficient to a result multiplied by a multiplier in a preceding stage of the multiplier; And a syndrome register for temporarily storing the syndrome coefficients and providing the stored syndrome coefficients to the multiplier and the adder; And the syndrome coefficient stored in the syndrome register is updated as a result of being added by the adder.

FIG. 1 is a circuit diagram of a prior art extended syndrome polynomial expansion apparatus.

FIG. 2 is a circuit diagram showing an implementation of the extended syndrome polynomial expansion apparatus according to the present invention. FIG.

DESCRIPTION OF THE REFERENCE NUMERALS

60: This laser register 71, 72, 73:

81, 82, 83: multipliers 91, 92, 93, 94:

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings.

Prior to the description, the laser polynomial G (X) and the syndrome polynomial S (X) are defined as shown in Equations 4 and 5, respectively, as described above.

In Equations (4) and (5), t is an error correction capability, and k represents the number of generated laser beams.

The hardware structure for developing the extended syndrome polynomial according to the present invention includes a laser register 60 in which the n-th order provides the laser roots of the laser polynomial G (X) sequentially, And a series of first to (n + 1) -th arithmetic operators 100, 110, 120, ... for calculating the syndrome coefficients of each order of the syndrome polynomial S (X) to generate the arithmetic result.

Each of the operators 100, 110, 120, ... according to the present invention includes multipliers 81, 82, 83, ... for multiplying the laser value provided from the laser register 60 by the coefficients of the corresponding syndrome polynomials, (71, 72, 73, ...) for adding the results multiplied by multipliers (81, 82, 83, ...) in the preceding stage of the arithmetic units 110, 120, 130, ..., and syndrome registers 91, 92, 93, ... provided to the adders 71, 72, 73, ....

At this time, the syndrome values stored in the respective syndrome registers 91, 92, 93, ... are updated as a result of being added by the corresponding adders 71, 72, 73, ..., And is provided to the preceding stage in-circuit syndrome register (91, 92, 93, ...) when this laser coefficient of the next order is provided from the register (60).

According to the present invention, the extended syndrome polynomial expansion apparatus adds the values stored in the temporary register 94 and the temporary register 94 to the result multiplied by the multiplier in the (n + 1) &lt; th &gt; And an adder (74). At this time, the value stored in the temporary register 94 is supplied to the syndrome register 93 in the (n + 1) th arithmetic operator 120 when the laser arc of the next order is supplied from this laser register 60, Lt; / RTI &gt;

The expanded syndrome polynomial expansion apparatus of the present invention configured as described above executes the operation according to the following steps.

In the first step, a zero value is first loaded into the flip-flop 94 in the arithmetic unit 130, and the flip-flops 91, 92 and 93 in the arithmetic units 100, 110 and 120 are supplied with the respective degrees of the syndrome polynomial S The syndrome values S ₀ , S ₁ ... , And S _2t-1 are respectively loaded. Then, the syndrome values S ₀ , S _1, ... of the respective orders of the polynomial S (X) stored in the respective flip-flops 91, 92, And S _2t-1 are provided to the corresponding multipliers 81, 82 and 83 and the first root of the laser polynomial Γ (X) is outputted from the nearest register 60 and multipliers 81, , 82, 83). Further, the root of each dimension of the laser polynomial G (X) from the nearest register 60 is provided to the adder 71 in the first calculator 100.

In the second step, each multiplier 81, 82, 83 in each of the arithmetic units 100, 110, 120 is connected to the root of the laser polynomial provided from the nearest register 600 and the flip flops 91, And provides the result of multiplication to the adder 72, 73, 74 in the next stage of operation. At this time, the adders 72, 73, and 74 receive the syndromes 81, 82, and 83, which are supplied from the flip-flops 92, 93, and 94 in the arithmetic units 110, .

In the third step, the results added by the respective adders 71, 72, 73 and 74 are stored in the flip-flops 91, 92, 93 and 94 in the arithmetic units 100, 110, 120 and 130, respectively.

In the fourth step, the values stored in the flip-flops 91, 92, 93 and 94 in the respective arithmetic units are transferred to flip-flops 91, 92 and 93 in the preceding stage, ) Is loaded with a zero value.

Then, in the fifth step, if there is another root of this laser polynomial Γ (X), it repeats from the second step, and if there is no other root, the end of the last stored in each of the flip-flops 91, 92, 93, 94 Value is determined as a coefficient of each order of the extended syndrome polynomial T (X) as follows.

In Equation (6), k denotes the number of the laser.

In order to facilitate the understanding of the present invention, the above calculation process will be described using the laser polynomial G (X) and the syndrome polynomial S (X) as follows.

ego,

.

Under this assumption, the roots of this laser polynomial G (X) ² and ⁴ , and the syndrome coefficient value of the syndrome polynomial S (X) is ¹ , ² , ³ , ⁴ . Thus, the syndrome value ¹ , ² , ³ , ⁴ requires four flip-flops and one temporary flip-flop to be loaded each, and each flip-flop has ¹ , ² , ³ , ⁴ , 0 are loaded.

The operation is performed as shown in the following table to obtain T (X) = ⁶X³+ ⁷X²+ 4X + ¹⁰

In Table 1, the first to fourth flip-flops represent four flip-flops for storing syndrome coefficient values, respectively, and Tmp represents a temporary flip-flop.

In addition, in the calculation process, the element {0, 1, 2, ³ , ⁴ , ⁵ ] for GF [2 ⁴ ] obtained using P (X) = X ⁴ + ⁰ , ¹ , ... , ¹⁵ } are defined as follows.

In this regard, only 2t multipliers and 2t + 1 multipliers are needed to develop the extended syndrome polynomial according to the present invention.

As described above, since the number of multipliers and adders used for developing the extended syndrome polynomial of the prior art can be remarkably reduced and can be implemented as approximately 1 / k + 1 as a whole, There is provided an advantage that a more efficient operation can be performed while reducing the number of operations.

Claims (3)

Order polynomial S (X) and the laser polynomial G (X) representing the error location of the code are computed in order to correct the error contained in the codeword encoded using the Reed-Solomon code and transmitted to the decoding system (X) expansion device, comprising: a laser register for sequentially providing the laser beam of the laser polynomial; And a series of first to (n + 1) -th arithmetic operators for calculating a syndrome coefficient of each order of the laser beam and the syndrome polynomial provided from the laser register to generate an arithmetic result, : A multiplier for multiplying the laser beam provided from the laser register by a coefficient of the syndrome polynomial; An adder for adding the syndrome coefficient to a result multiplied by a multiplier in a preceding stage of the multiplier; And a syndrome register for temporarily storing the syndrome coefficients and providing the stored syndrome coefficients to the multiplier and the adder; Wherein the syndrome coefficients stored in the syndrome register are updated as a result of being added by the adder. 2. The method of claim 1, wherein the updated addition result in the syndrome register is provided to the pre-computation intra-operative syndrome register when the next laser lobe is provided from the laser register. &Lt; Device. 3. The apparatus of claim 2, wherein the extended syndrome polynomial expansion apparatus further comprises a temporary register for temporarily storing a result multiplied by an (n + 1) -th operator multiplier in the computing unit, wherein the value stored in the temporary register Is provided to the syndrome register in the (n + 1) th arithmetic unit when the next laser beam is provided from the laser register, and is updated to a zero value.