JPS61216044A - Signal processor - Google Patents

Abstract

PURPOSE:To attain a highly efficient error correction by encoding information so as to transmit it through a communications line, calculating a syndrome of encoded data, introducing an error position and an evaluating polynominal, evaluating the error position and its size and decoding information through correction. CONSTITUTION:A histogram cell 107 is a perfect parallel processor generating a histogram and a vector converting cell 108 makes data from the cell 107 into blocks and converts them into a vector. An RS encoding cell 109 generates a reed solomon code. And cells 107-109 comprise an encoding part. An evaluating cell 110, the greatest common measure cell 111 and a syndrome cell 112 comprise a decoding part pipeline processor. An expanding cell 105 expands data compressed by the cells 107 and 108. Thus, in the signal processing tergeting the communications line, the processing employing a parallel processor can be possible, and necessary cells are arrayed in one-dimension in accordance with the ability of the code, whereby decoding processing can be made into a pipeline.

Description

DETAILED DESCRIPTION OF THE INVENTION [Technical Field] The present invention relates to the field of error correction, and also relates to a technique for performing parallel processing in signal processing for communication channels.

The present invention relates to a technique for performing syndrome generation, GCD (greatest common divisor) generation, and error in decoding BCH codes.

The present invention has three types of cells that perform the steps of generating a syndrome, deriving an error locator polynomial, an error evaluation polynomial, evaluating the error location and error magnitude, and performing correction in decoding a BCH code, Depending on their ability to sign cells.

This invention relates to a signal processing technique in which a necessary number of signals are arranged in one dimension.

[Prior art]

In recent years, the application of error detection/error correction codes (hereinafter simply referred to as error correction codes) has become widespread as a measure to improve the reliability of various digital systems including memory systems.

There are various types of error correction codes depending on the target system, but the most typical one is a class of linear codes called cyclic codes. These include BCH code suitable for random error correction, fire code suitable for burst error correction, and R S (Reed-solomon) code, which is a type of BCH code and suitable for byte error correction.
Includes symbols, etc. Among them, the RS code is a code that is extremely important in practical use because it has the characteristic of being able to reduce redundancy the most among linear codes with the same code length and correction ability. There are various decoding methods for RS codes that are widely used for discs (hereinafter referred to as CDs), etc., and it is relatively easy to implement a decoder for codes with a small correction ability of about 2 or 3. be. but.

In order to obtain high reliability, it is necessary to increase the correction ability and code length. In that case, problems arise in that the size and control of the device become extremely complex, and the calculation time required for decoding processing also increases.

For this reason, CDs are currently called CIRC.

Although it uses a type of double encoding, there are problems in using it in systems that require higher speeds.

For the decoding method of the BCH code, which is an error correction code.

There are two methods: Peterson's method and Berlekamp Matsusei's method. Conventionally, when decoding BCH codes, the correction ability is low,
Peterson's method is used because of the simplicity of the hardware. On the other hand, if Berlekamp Matsusei's method were to be implemented using hardware, the configuration and control would be extremely complex.

The current situation is that this has not been realized.

Similarly, signal processing for communication channels requires complex processing based on information theory, and depending on the communication channel,
Since high speed is necessary, it has been extremely difficult to achieve it in terms of hardware.

For this purpose, a simple method of hardening is adopted, or.

This was achieved by limiting their abilities.

For example, in channel coding, it was still at the stage of being able to realize double correction of R3 (Reed-Solomon) codes. Furthermore, in the conventional process, there is a problem that implementing the above-mentioned processing using software takes too much processing time and is not applicable.

In addition, parallel processing includes fully parallel processing, local parallel processing, pipeline processing, etc., but it is impossible to simply apply a parallel processor to a conventional serial processing section. The problem was that efficiency was sacrificed to keep it within a range that was easy to implement.

Due to the various problems described above, it has been difficult to realize a highly reliable R3 decoding method with large correction capability and code length.

〔the purpose〕

In view of the above points, the present invention aims to eliminate the drawbacks of the conventional communication channel by transforming the signal processing algorithm in the conventional communication channel into an algorithm suitable for parallel processing and using a parallel processor. .

In view of the above points, the present invention applies the idea of a systolic algorithm to the Berlekamp-Matsusay method and actually applies it to a BCH code decoder, a GCD (greatest common divisor) unit, or a syndrome generator. The purpose of this study is to study a specific algorithm for this purpose, and to design a dedicated cell that implements it in terms of hardware, especially for the error evaluation/correction section.

〔Example〕

Shadow Stop and 1 Bean IJ First, the principle of the R3 code will be described. The R3 code is a code of great practical importance, having the characteristic of having the lowest redundancy among linear codes having the same code length and correction ability.

The R5 code is a non-dual BCH code (Bose-Chav
This is a special case of the finite field (hereinafter abbreviated as GF) G
It is composed of elements of F(q). Here, q is GF (q
) is the original number of Using this q, various parameters characterizing the RS code are defined as follows.

・Code length: n (- symbol length in code n≦q −1
(2-1) ・Number of information symbols 2 k (-Information symbol button in code ・Test symbol a: n-k (-Test symbol button in code n-
= dmin-1 (2-2) - Correction ability: t (- Correctable symbol ω in the code
([X] Nygauss symbol . . . the largest integer not exceeding X) Here, dmin is called the minimum distance (Hamming distance). This means, for example, that two (n,k)R
5 code words (code length n, RS code word for the number of check symbols)
When F and G exist, F= (f o , f 1
, −−=−−−−−−f n−1) (2
-4) G = CgO, g 1, --------g n
-1) (2-5) (Each symbol means that the symbols at the corresponding positions of -DF and G of GF (q) for which the code is defined are different from each other by at least dmin times.

Also, when error E overlaps with code word F and it becomes received word R, E
= (eo * e i , -” e n-1)
(2-8) Rw(ro, rl, -----
-------rn-t) (2-7)=F
10E
(2-8) = (fo+eo, f1+et, -----
−, fn-ten-t) (2-9) Number of non-zero elements of E,
That is, if the number of errors that have occurred is t or less, R can be corrected by the decoding method described later and a correct code word F can be obtained.

however there is a possibility.

Example) dmin = 5 (t = 2) (7) If the number of errors occurring in the R3 code is 1, then if 1 = 1, two wheels - error correction is possible. 1 = 2: double error correction is possible. If ≧3: error detection possible (however, it may be considered a double error) If ≧4: error detection possible (however, it may be considered a single error) 1≧5 cases: error Detectable (but may be considered error-free) Therefore, when designing a code, consider how much error rate improvement is required for the system, and how far within the code's error correction ability. The design must take into account whether or not error correction will be performed.

First, polynomial expressions such as code words will be explained here.

For example, we want to encode the number of information symbols I= (i
o, f 1, -=-, i K-t)
(2-10), this is expressed as a polynomial as follows.

I (x) =10+11x+i 1x2+----+
1g-2xK-2+iK-1x1cm1 (2-
11) (n-k) check symbols C added in the same way
= (co, CI, ==C11-to-1)
(2-t2) is c (X)=CO-1-C
IX+C2X2+----Cn-to-1"X"-'
-' (2-13) Furthermore, the code word FF= (fO, f 1 , f2, -=----f n
-t) (2-14)=CO, C1, ---
-Cn- to -1, fo, tl, j2゜--==-i to-
1) (2-15) is F
(x)=f□+f1x+f2x2+-=-+fn-2x
It is expressed as a polynomial "-2+f, 1-1x"-1(2-18).

Next, as mentioned at the beginning, the R3 code is a type of cyclic code, but what characterizes the cyclic code is the generator polynomial 〇 (x) used during encoding/decoding. , the check symbols of the code must have a degree equal to the sky (n-k) and be divisible by (Xfi-1).

The R3 code uses the following formula.

G (x) (x-(X)(X-(R2)---(X-
a”-”) (2-1?)(G (X) = (
X-1) (X-a) --- (x-a"-"- is also acceptable)
(2-18) Here, α is a primitive element of the finite field GF (Q) whose sign is defined.

Using this (n-k) order generator polynomial, (n, k)R
To obtain 3 codes, follow the steps below.

i) Information symbol polynomial I (x) ((2-11)0
Multiply by zn″″ゞ.

u) I (X) *zn-K is generated by the polynomial G
(X) Let R(x) be the remainder polynomial divided by 't'.

I(x)-x''-'=Q(x)-G(x)+R(x)
(2-19) iii) Replace this R(x) with the test symbol polynomial 〇 (x), I (x)・x f
The codeword polynomial F (x) is added to i-IC
shall be.

F(ri = I (x) ・x”-” −C(ri = Q(
G(x) (2-20) As can be seen from equation (2-20), the codeword polynomial F (x) can be divided by the generator polynomial 〇 (x) that generated it. However, the generating polynomial of equation (2-17) is α, α2. ．．
Since it has the root fi−K, the codeword polynomial F (x
) by substituting this root, the following equation holds.

F (α') = 0 (i=1, 2, +, n
-K) (2-21) Expression (2-21) can be expressed as a matrix as follows (FT is the transposed matrix of F) Here, the matrix H on the left side is called the parity check matrix, and is also used in decoding. have important meaning.

As already mentioned, since the R3 code is a type of BCH code, it can be decoded using a general RCH code decoding algorithm. However, in that case, addition is required in the decoding process.

Symbol handling such as multiplication must be performed on the finite field GF (q) in which the R3 code is defined.

Considering the code of R3 with code length n = 2m-1 defined on GF (2m) (m: positive integer), the symbol is represented by an m-bit binary number, and the operation is performed on GF (2m). It will be done.

In addition, formula (2-17) is used for the generator polynomial, and the minimum distance between codes is d min = 2 t + 1 for simplicity.
I will put it as.

Now, the decoding procedure for such an R3 code is the general
As with the H code, it is divided into the following four steps.

Stella 7'l) Syndrome calculation.

Step 2) Calculate error locator polynomial and error evaluation polynomial.

Step 3) Estimation of error location and error value.

Step 4) Execute error correction.

Among these, in the syndrome calculation in step 1, C. As will be described later, only the operation of simply substituting the root of the generator polynomial into the received word polynomial and finding its value is performed. On the other hand, steps 2 and 3 are the most complicated steps in decoding the R3 code, and there are two main algorithms for this: Lecambe Φ Matussy's method and Beaterson's method.
There is a street.

In the present invention, the idea of systolic algorithm is applied to each step, and three basic types of cells that execute each step are: syndrome cell, 5tapl each)
2) GCD cell.

5step 3, 4) Realize as an EVAL cell.

Step l Syndrome First, similarly to (2-4), (2-6) to (2-9), the transmitted codeword is F:F= (fo, fl, -
-fn-1) The error that occurred is E :E=(eo,
et, ---en-1) the received word is R:R=
(r□, rl, -rn-t) = F+E = (fo+eo, f1+el, --f, -t+
en-1), the polynomial representation R(x) of the received word is as follows.

R(x) =F(x)+E(x)=(f □+
e□) + (f 1 +e 1) x+−−+ (f
n-1+efi-t) xfl-1(2-23) However, as shown in 2.2, the root α1(i =1
．． -1-9n-k), equation (2-21) (F(
α1)=O) holds, so if we similarly substitute α1(i=1,-+,n-k) into the received word polynomial R(x), we get R(αk) F (αk)+E(α1)- 0+E
A value determined only by the error E is found, such as (αk)−E(αk) (2-24).

This is called a syndrome, and once again S = (So, s t, +++++, 5fl-
-t) (2-25) S1=R((E'
10=E(Qi+su(i=0.1.−−−+n −
K −1). This syndrome contains all the information about the error (location and size of the error).

(Since the syndrome is 0 if there is no error, it is possible to detect the presence or absence of an error.) Moreover, its polynomial expression is as follows.

5(x)=so+slx+--+56-g-1x"-"
-1 (2-27) Furthermore, similarly to the case of equation (2-22), the syndrome ((2-25) and equation (2-26) can be expressed as a matrix as follows.

S-H・8 guns (RT: for H transposition row)
(2-28) Next, FIG. 4, FIG. 5, FIG. 6, FIG. 7 mentioned above, and FIG. 8 described later will be further explained. Fourth
In step 1 of the diagram, command tn (
command input), coefficient data r L fl *, and calculation result yln.

In step 2 command In is s t,
If yes, in step 3, as shown in FIG. 5, enter coefficient data 7J (
S”rtn), data output (yout=7).

Import the next data (y=ysn).

Also, in step 2.4 command 1n)
C If it is “calc” instead of “5tart”,
Proceed to step 5! ! = 511

Also, if No in step 4, command H is "end", so in step 6 s=s・X
+rifi, output the syndrome value L (w45 [i1$ (2t -1) output from no cell) by Yout=S, and perform the next input V = V in.

In step 7, the data is output as is (r out
= r in) L, command (command)
) is also output as is (command out (co
mmand out)=command rn), and further outputs in step 8.

On the hardware, rin■, rout@ in Figure 6.

ROM 15 is a table for selecting the coefficient α.

(Cell array multiplier) Cellular A
rrayMultiplierO is the part that calculates the syndrome in FIG.

rout, yout, cOmmand Out are actually finally output.

On the hardware, rin■, rout@ in Figure 6.

command in■, command out■
,yfn■.

yout■ corresponds to the input/output in FIG. Also.

ROM 15 is a table for selecting the coefficient α.

(Cell Array Multiplier) Cellular Ar
rayMultiplierO is the part that calculates the syndrome in FIG.

In step 2 of 1. Step 1, the error locator polynomial and error evaluation polynomial are calculated using the syndrome of the calculation result of step 1. First, here, the error E = (e O, e 1-- −
-e n -t), the number of non-zero likelihoods, that is, the number of errors, is set to 1 (1≦t).

Also, the position where the error occurs is determined by ju(u=1゜2-1-
-1) (j u=o , 1-------n-1)
year.

Let the error at position ju be eju. Furthermore, (2-2
), (2-3) equation as n-k = dmi n-1 = 2t
(2-30), then (2-26), (2-
The syndrome and syndrome polynomial in equation 27) are expressed as follows.

51 = E (10 for α = Σe j u ((X' +
l) j u (i!0, 1.----.2t-1) U abuse 1 Also, a new S. (x) Soo (X) =Σs i
By setting x 1 (2-33) 1 depth 0, the following equation is obtained.

S (x) − [Soo (x) co mod
x2 t (2-35
) Now, the error locator polynomial σ(X) is defined as follows. This polynomial has an error order of 21ju (
u=1.2. -----． 1) (ju=o.

1, ----n -1), GF (2m)
is a polynomial whose root is the element α-ju.

cr (x) = (1-aj l x) (1-aj
2x) ---(1-aJ ux)=■(1-aj
uX) (2-38) U-to 1 Next, the error evaluation polynomial ω(X) is defined as follows for σ(x) and Sco(x) described above.

ω(x) = σ(X) ・5ctz (X) = Σe
juαjuU厘1 Then, from equations (2-34), (2-35), and (2-37), the following equation holds true.

cr (x) @S (x) = [(+> (X)
] mod dx2 t(2-38) Therefore, using an appropriate polynomial A (X), σ(X).

The relationship between S (x) and ω(X) is expressed as follows.

A (x) −x2 t+cr (x) ・S (x)
= (1) (x) (2-39) By the way, since the number of errors 1 is (1≦t), ω(X
) and cr (x) are de gω(x) < de gcr (x)≦t
(2-40), and further ω(X
) and σ(X) are relatively prime (the greatest common difference (GCD) polynomial is a constant), (2-39), so ω(x) and σ(x) that satisfy equation (2-40) have constant coefficients. Since 0 or more is uniquely determined except for ω(x) and cr (x) are x2t and 5
It can be obtained through the process of Euclid's algorithm for finding the greatest common denominator (GCD) polynomial of (X). Here, a method for calculating the greatest common difference (GCD) polynomial using Euclid's algorithm will be briefly described. First, let us express the greatest common denominator polynomial of two polynomials A and B as GCD[A, Bl.

Also, for A and B, the following polynomial and 10*degA
In the case of ≧degB A=A −IA4 B−IJ ・B
(2-41) ■= B (2-
42) When *degA≧degB, X=A
(2-43)■2B-LB・A-14
ΦA (2-44) (i, X-Y-IJ: 5
If we define M), which is the circle divided by Mr.
D[A, Bl and GCD [χ, 100] satisfy the following formula.

GCD [A, Bl = GCD [A, U]
(2-45) Therefore, the above A and B are rewritten as A and B, and the respective orders degA and degB are
Depending on the magnitude of When it becomes a zero polynomial, the other non-zero polynomial is obtained as the greatest common polynomial of A and B.

Note that finding the greatest common polynomial of polynomials A and B is no different from finding the following polynomials C and D.
eg is the order.

GCD [A, Bl = C-A+D-B
(2-48) Then, in the process of executing the above iterative step and finding the greatest common polynomial of polynomials A and B whose degree is expressed as i=degA≧degB, polynomials C, D, and W that satisfy the following equation are obtained. You can ask for it.

The problem of finding such a polynomial is called the extended GCD problem.
Therefore, the error locator polynomial σ(X) and the error evaluation polynomial ω(
In equation (2-47), X) is the polynomial A)(2t
, extended GCD when polynomial Bt-3(x)
Determined by solving problems.

Step 3 In step 3, the error location and error value are estimated from the error location polynomial σ(X) and error evaluation polynomial ω(x) obtained in step 2. First, the received word R= ( ro, r
1+---, rfi-t), the symbol position i=
element α- of GF (2m) according to o, 1----1-1
Iteratively assigns i to the error locator polynomial σ(X). At this time,
From equation (2-36), if σ(α″″L)=O holds true, it can be seen that α−1=α−ju holds true for i at the error position ju. (ju=o, 1--1-n-1,
(u=1, 2--1, l≦t) Further, the value of the error evaluation polynomial ω(X) for such α-1=α-ju is as follows.

Furthermore, if σ゛ (X) is the differential of σ(X), then the following holds true. Therefore, from equations (2-48) and (2-49), the error value eju at the error position ju can be obtained from the following equation.

From equation (2-9), the received symbol rju at the position ju where the error occurs is the symbol fj of the original code word.
It is expressed as follows from u and the error size eju.

f J u= rju−eju
(2-51) Therefore, in step 4, it i(
t = O1l + ----n 1), subtract from the received symbol ri < (GF (2m) J:) f t = r t
-e t (2-53) Perform error correction at position i.

Figure 1 shows a model of a coded communication system.

100 is an information source, lot, 102 is an information source.

This is a part that encodes a communication channel, and 103 is a communication channel.

104 and 105 are decoding parts of the information source 9 communication path. 106 is the destination of communication.

FIG. 2 shows a block diagram for performing parallel processing by a parallel processor to which the present invention is applied. The same parts as in FIG. It is a fully parallel processor.

108 is a vector conversion cell, and a histogram cell 107
For example, data from "1, 2, 3, 4° 5.6" is converted into blocks such as a and b, respectively, and vector-converted. Further, 109 is a cell for creating the above-mentioned R5 code. The histogram cell 107, vector conversion cell 108, and R3 encoding cell 109 correspond to the encoding section in FIG. Also, 110. ill and 112 are the aforementioned Eva l cell and GCD cell, respectively.

This is a syndrome cell and a pipeline processor corresponding to the decoding section of FIG. Reference numeral 105 denotes an expansion cell, which expands data compressed by the histogram cell 107 and vector conversion cell 108. This makes it possible to use a parallel processor in signal processing for communication channels, and only the necessary number of cells can be used depending on the code capacity.
By arranging them dimensionally, the decoding process can be pipelined.

Syndrome Cell Next, the syndrome cell for calculating the syndrome t6 in step 1 above will be explained.

As shown in the explanation of syndrome calculation, in step 1 of decoding, the received sequence R(rn-1---r 1 .
r o) to the coefficients of the syndrome polynomial used in step 2 (s 2 t −1−−−5t ).

SO) is derived based on equation (2-29). The function required for the 7 rays of the syndrome cell to realize this is input data (r n -1---1 rl, ro)
From, S2t −1−−−−sl , sQ are G in this order.
The answer is to pass it on to the CD cell side.

By the way, as can be seen from equation (2-29), the specific calculation of the coefficients of the syndrome polynomial is based on the value of the variable
The coefficients (received symbol rn
-1, ---1, r1. ro), and the value of 7 can be replaced with ice, which is solved by an iterative algorithm as shown in the following equation.

si= f・4rn-1mαi + I +rn-2)
aα"'+rn-3]-αi + r+---
+r1) mat ” l+r□ (5-1
0) This algorithm has the same form as the systolic algorithm for solving DFT (Discrete Fourier Transform), but since the coefficients are not known in advance, it cannot be applied as is.

Therefore, in order to solve this algorithm, the coefficient s 1 (i=0
, l , ----, 2t-1) must be assigned.

In this Figure 3, X corresponds to Si, αi+1
(value to be substituted into the polynomial), intermediate result of s calculation Cs
s), and y is the delay required when transferring the calculation results. Also, rtn”ou
t is coefficient data (r n-1, +++++,
rt, ro) of! / 0 boat, Y in r Out represents the I10 boat of the calculation result, and COm m & m d in・o
ut represents the I10 port of the command for informing the cell of the start and end of data.

Here, each cell has data rn-t, ----9ri.

It receives rQ one after another and repeats the product-sum calculation of formula (5-10), and outputs the calculation result after n repetitions. In addition, co
Three types of "mmand" can be considered. First, "5t
"art" represents the beginning of input data, and upon receiving this, the cell initializes the "S" register. Also, "calc"
Then, the product-sum calculation is performed once, and at "end", the product-sum calculation is performed and the calculation result is output. This function is illustrated in FIG. 4. The details will be described later.

Syndrome cell Each syndrome cell shown above has the coefficients s i (i = O, t , -1--12t) of the syndrome polynomial.
Since one calculation of -H is assigned, the total number of required syndromes is 2t ([1. Also, GCD
Considering the interface with the cell array, each Si must output from the high-order term, so the syndrome cell is connected in one dimension from the cell that calculates the low-order (#O) term as shown in Figure 5. I have to.

At this time, rn-1 begins to enter the leftmost cell.

Calculation result from the rightmost cell (s2t-t,

There is a delay of 2t) symbol cycles before the 511SO) starts to be output. ■Symbol cycle: rj (input cycle of j = n-1, ----, 1, O)) Note that the output only needs to be output from cell #2t-1 in the end, and the first input is You must continue to input "MO" in ytn of the leftmost syndrome cell (so) with the value of .

Also, as can be seen from the form of equation (5-10).

For the syndrome cell array, the received symbol rj (j=
n-1, ---1, t, o) must be input from the higher-order terms of the received word polynomial.

Syndrome cell - Here, we will explain the design of a dedicated cell that implements the functions of the syndrome cell described above in hardware.The function of this syndrome cell is very simple compared to the GCD cell described later. Basically register and GF
Although it consists only of the above multiplier/adder, it also requires a control section for synchronization, a register for output transfer, etc.

Taking the above into consideration, FIG. 6 shows a concrete design of a syndrome cell that handles the R3 code on GF (21m). Further, when considering the operation of the cell within one symbol cycle as in the case of the GCD cell, the flow of processing is represented by a timing chart as shown in FIG.

(Also, the l symbol cycle is divided into 16 internal cycles.) Also, the multiplier on the GF has a “Cellular-Arraymul” as in the case of the GCD cell.
It is assumed that the scale will be approximately as follows, and the number of pins of Ilo is 48 pins, so it can be easily implemented as an LSI.

Next, the characteristics of this syndrome cell can be summarized as follows.

-The constant αi+1 refers to the ROM table by "se 1ect" from the outside so that one cell can be used for calculation of any 51i.

-Data other than “command” is GF (28)
It is handled as the above vector-expressed symbol (8-bit parallel).

- Each cell is controlled only by the ``synchronization signal 5YNC'' and the reference clock ``CLOCK'' (corresponding to an internal cycle).

Note that the "C0NTR0LL" portion in FIG. 6 may be realized by a horizontal microprogram ROM.

Also, ``■'' is a counter that counts 16 bits of a clock, ``2'' is a control section that outputs a predetermined control signal in response to input of commands, etc., and ``2'' is a latch. 0 is a register in which data during calculation is stored, and MUX@ is a multiplexer that switches whether or not to output the syndrome SiO.

Also, [stock] and ■ are gate parts for performing coefficient addition and O calculation processing.

As mentioned above, commandln has 5tart''.

There are "calc" and "encf", and their timings are shown, for example, as shown in FIG. 1,2.3
---n indicates the number of symbol cycles, #Q, #l, -
-- indicates the cell in FIG. 5, and the explanation will be centered on the cell #O.

Now in symbol cycle l, the command “5tart”
” is input, there is a delay of one cycle and the next #l is input from out.
The command “5tart” is output to the cell. Furthermore, in the same way, the above command “
5tart" is output. Also, in synchronization with "5tart", data rn-1--- is inputted. Also, as mentioned above, in the 0th and 2nd symbol cycle where YLII is inputted, "ca, When the ``tc'' command is input, the above-mentioned syndrome calculation is performed, and continues until n-1 symbol cycles.Finally, in n symbol cycles, the ``end'' command is input and one syndrome is calculated. ,
” OL fl * ” 00 ut * ” 10
Processing progresses with a delay of one symbol cycle for each uL.Finally, if the cell ends with #1, if you want to finally output, output 31 with the "end" command, and then s□
Output.

The 7th rM is a detailed explanatory diagram within one symbol cycle of the timing chart shown by #81N.

This 16 count is performed by the counter ① in FIG.

''' Command input/output is a 0.1 clock line, register■
and is passed to the clock register 11 at 14.15.

Also, in FIG. 7, the output y is input to the yin register 2 at the 2.3 clock, and stored in the y register 0 at the 1415 clock. However, the command 'end'
', the value of the Si register (2) is passed to the yout register (2) under the control of the MUX 16 (7). Also, SEX
+rin is calculated at the 2.3rd clock, and Si is set in the register (2) at the 4.5th clock.

Next, calculation of the error locator polynomial and error evaluation polynomial shown in step 2) will be explained.

When applying the systolic algorithm to decoding the RS code of a GCD cell, the biggest problem is the decoding step 2), that is, the error locator polynomial σ(x) and the error evaluation polynomial ω(X
) is derived.

Here, we will discuss the algorithm for step 2 of this decoding and the dedicated cell (hereinafter referred to as GC) that implements it in hardware.
The design of the cell (referred to as D cell) will be explained below.

This Algorithm First, as mentioned above, the algorithm for deriving σ(X) and ω(X) can be reduced to an extended GCD problem. i.e. )(
2t as polynomial AO, syndrome polynomial S (X)((
2-32)) as a polynomial BQ, (degAO=
2t, degBo=2t-1).

GCD [If polynomials 〇 and W that satisfy AO and Bol are found, D represents the error locator polynomial σ(x) and W represents the error evaluation polynomial ω(x), respectively. It is known that there are vehicles in which σ(X) and ω(X) are uniquely determined except for the difference in constant coefficients. Therefore, the following polynomials A, B, U, V, L for AQ and BO.

Define M and set its initial value as U=M=l; L=V=0; (A=AO, B
= Bo) and repeat the steps in Figure 9, and when degA (degB) < t, A(B)
is found as ω(x), and L (M) is found as σ(x), respectively.

In addition, in the method shown in FIG. 9, the division on GF in the iterative step is omitted by multiplying A and H by the highest degree coefficient α of polynomial B and the highest degree coefficient β of polynomial A, respectively. . (See formulas (2-41) and (2-43))
Even in this case, no woody problem occurs in the values of σ(X) and ω(X).

FIG. 9 will be explained. First, in step 1, U
=M=l, L=V=O, A=A□.

Set the initial value by setting B=BQ. In step 2, determine whether degA≧degB, and in step 3, multiply A and B by the highest order coefficients β and α of polynomials A and H, respectively, and repeat equations (2-41) and (2-43). Division on GF in the step is omitted.

If degA and degB become smaller than the predetermined order in step 4, proceed to step 5.6, and ω(x)
=A, cr (x) =L, (1) (x) =B
, cr (x) =M is calculated.

Next, when applying the Sistry concept to the repetition step in FIG. 9 and having one GCD cell process one repetition step, the financial model of that cell becomes as shown in FIG. 10.

In Figure 10, the polynomial is input from the left side of the cell,
Polynomials processed according to the orders of A and H are output from the right side. Here, λ.

, T:, s represent output polynomials for input polynomials A, B, L, M, respectively.

(Polynomials U and V t* are not directly necessary for decoding the RS code, so they will not be discussed hereafter.) As shown in FIG. 10, the GCD cell that executes the iterative steps in FIG. Three execution modes are required depending on the order, and these will be referred to as modalities from now on.

i) degA, degB≧t and degA≧degB-
-1 “reduceA” ii) degA, degB≧t
and degA≧degB---“reduceB”ii
i) degA<t or degB<t −
=-nopGCD Cell Moll If we construct a cell array in which cells are arranged one-dimensionally as shown in Figure 10 and repeat the steps in Figure 10, we can derive σ(X) and ω(X). pipelined. However, the problem here is that the length of the polynomial changes during the process. The order of (the length of A) decreases, and the order of L (the length of A) decreases, and the order of L (
L length) increases.

・If the cell mode is “reduceB”: The cell reduces the order of B (length of B) and increases the order of M (M
length) increases.

In order to make the functions of cells correspond to such changes in the length of the input polynomial, extremely complicated processing is required for each cell. In that case, the amount of calculation for each cell in the cell array becomes uneven, resulting in inefficiency.In order to solve this problem, the systolic algorithm for solving the extended GCD problem of KungN et al. The input is divided into individual coefficient data and the order difference of A and B, but
In order to actually apply the method to decoding the R3 code, specific degree data of each polynomial is required in order to distinguish between the above three modes. (The degrees of L and M are also required as the degrees of the error locator polynomial.) Furthermore, the coefficient data is input into each cell in order from the highest degree by aligning the terms corresponding to the degrees of the polynomials on the sides. Data processing and each order processing must be performed separately. At that time, in order to equalize the amount of calculation for each cell, the change in the degree of A or B in one cell must be kept to at most the first order.In this way, degA, degB of A and B However, the next term is not necessarily proportional.

If the term next to degA (degB) of TeA (B) in "reduceA"("reduceB") is zero, there is no problem if you simply shift A to a higher position.

In addition to these coefficient data and order data, data "5tart" representing the beginning of the data is required.

At this time, when each cell receives "5tart=1", it recognizes the start of the data, and the type of processing (st
ate) and processes the coefficient data to calculate a new order for sending to the next cell. Further, each cell repeats the same process according to 5tate until it receives "5tartxl" next time.

Note that in order to deal with the change in the length of the polynomial described above, a buffer delay may be provided in each cell and the following processing may be performed.

, and the color is one color faster than λ.

L transfers one step later than i.

In the case of (α”bJ+β=a%) → Transfer λ one faster than color.

As can be seen from this example, calculations such as multiplying xdegA-66g8 are not necessary in actual data processing.

Considering the basic model of the GCDE cell that realizes the above, it becomes as shown in FIG.

In this Figure 11, ・ain・Out+bin+Ou
t+l in, Out, min out is A,
It represents the I10 port of coefficient data of each of the B, L, and M polynomials.

Further, S t & r t i fl + Out sets the I10 port of “5tart” representing the beginning of data as deg A L fL * Out .

de gBl n -Out -degLl n , O
ut, degMtnIout represents the I10 port of the degree data of each polynomial. In addition, a, b * 11+ 12 + m 1 + m shown in the cell
2. degA, degB, degL, degM are each
This shows the delay for the '777. Also, α, β
5tate is a register that stores constants necessary when executing the iterative step shown in FIG. 9, and 5tate is a register that stores the mode of each cell during the iterative step.

Next, this basic GCD cell model in FIG.
The processing flow as shown in the figure is
By repeating from the input of "=1" to the next input of "5start=1", the process corresponding to one repetition step in FIG. 9 is performed. In this FIG.
1”, the cell recognizes the beginning of the data and reads “5t
Mode “set” for setting “ate”, α, β, etc.
5tate". Also, if "5tart≠1", perform the process according to "5tate" ° "caf
e" mode is executed. Detailed processing flows in each mode are shown in FIGS. 13 and 14.

What you need to be careful about above is "Start" added to the beginning of the data, the degree degA of each polynomial,
When degB, degL, and degM pass through one cell, they always pass through a delay once. Therefore, it takes two symbol cycles (l symbol cycle is a data input cycle) for data to pass through one cell. On the other hand, in order to align the beginnings of the coefficient data of each polynomial in response to changes in length, the number of delays used when transferring data changes depending on the type of processing. As shown in FIG. 11, one delay for A and B and two delays for L and M are facilitated. ) Here, in order to clarify how the delay is used, "'5tart"
Based on the speed at which the cell array passes through the cell array,
Table 1 summarizes the passing speeds of coefficient data of polynomials at
) has the following meaning.

GCD cell Actually execute the compound step 2) and AQ=X2t.

In order to obtain cr (x) and ω(x) from B□=S(x), it is necessary to configure a cell array in which GCD cells are connected in a one-dimensional manner as described above. At this time, each cell reduces the degree of A or B by at most one (but σ(X),
In order to find ω(x), initial value A=AO(degA=
2t) , B=BO(degB=2t-1) +7) The iterative steps of FIG. 9 must be performed until either order becomes (t-i), thus.

A maximum of (2t + 1) cells are required. This is illustrated in FIG. 15 (#0 to #2t). Here, the following initial values are input to the left end of the cell array.

Furthermore, as described above, it takes two symbol cycles for data to pass through one cell. Therefore, the delay from the start of input to the left end of the cell array until the start of output of the result to the right end is 2 (2t + 1) symbol cycles. Note that when the 151iij connection is used, the result output from the rightmost cell is always degA=t'-1(
degB=t-1), and the coefficient data of A (B) is output from the next term (t-1) (not necessarily non-zero).

However, L (M) (7) order degL(degM
), the number of errors in the received word is 1 (1≦t), and the output of coefficient data also starts from a linear term (non-zero), so it is variable depending on the number of errors.

Furthermore, whether the rightmost cell output is degA=t-1 or d
Since the data to be passed to step 3) of the combination differs depending on whether e gB=t -1, some interface is required between the GCD cell array and the cell array that executes step 3).

(degAzt-1+σ(x) =L, (1) (x)
=A:degB=t-1+cr (X), =M, (1
)( This model is an improved version of the model proposed by Kung et al. for solving the extended GCD problem in order to actually apply it to the decoding of R3 codes. This model is sufficient when implemented in software, but if it is implemented directly in hardware and one cell is made into one chip, the number of I10s is too large, making it unrealistic.

What should be noted here is that the coefficient data and order data of polynomials A, B, and M do not necessarily have to be input and output at the same time. Therefore.

The coefficient data of each polynomial is “war”, and the degree data is “d”.
By time-sharing input/output as "eg", the number of I10 bins required for one cell can be significantly reduced.Also, the number of multipliers on the GF required for processing coefficient data is reduced to one.
Considering the area occupied within one cell, it is desirable that the number be only one.

Note that the configuration of the adder on this GF can be considered as a species, but the R5 code on the GF (28) can be handled by taking into account the velocity, occupied surface, product, and specificity of the configuration. The figure shows a specific design of a GCD cell. Also, considering the operations necessary for the cell configuration in Figure 16 in correspondence with Figures 12, 13, and 14 representing the operations of the GCD cell basic model, the flow of processing during one symbol cycle (Startn input cycle) is expressed in a timing chart as shown in FIG. Here, the l symbol cycle is divided into 16 internal cycles. In addition.

Preset”, “deg compu” shown in the figure
te” is the line hh only if “5tartil=bi,”
” am ti゛@ 11, -β・bi
The calculation of "n" is performed only in the case of "5tartln#l".

Next, the characteristics of this cell configuration can be summarized as follows.

+1 Coefficient input/output data in Figure 11 (lLth hO
ut, btn, Out, fin, Outlminlou
t>, V & rth hVlr011t, order input/output data (degALn, Out-degBln, Ou
t , degLtn, out , deKNb, n, ,
The input/output is multiplexed using deg in and aegout to reduce the number of I10 bins required for one cell. - Coefficient data is treated as a vector-expressed symbol (8-bit parallel) on GF (213), and first-order data is treated as '119 (8-bit parallel) expressed in 8-bit binary.

・The delay required inside the cell as shown in Figure 11 is set to FI.
An example of replacing with FO and pipelining internal data processing in accordance with input/output multiplexing, for example, "α" atn - β"bitl" required for processing coefficient data.
- Calculations such as "α@1tn-β@m%n" can be efficiently performed using one multiplier on the GF. In addition, degAsn-1″′, which is necessary in processing order data,
, “degBt n-”, “degLtn+degg
in-degAtn”, “d e gMl B+de
Integer operations such as gA in-de g13tn'' can be performed efficiently using one ALU.

- The size t of the error correction capability required to set "5tate" can be input by "5select" from the outside so that it can be used for combining any RS code on GF (28).

・Each cell has a synchronization signal “5YNC” and a reference clock “
CLOCK" (corresponding to an internal cycle).

9. The procedure for setting data into each FIFO buffer is as follows:
It is determined in the same way as No. 12, 13, and 14 depending on the value of .

Note that the "C0NTR0LL" part in FIG. 16 may be realized by a horizontal microprogram ROM, and
ate generate” portion is atn.

It may be configured with a combinational circuit consisting of a comparator whose inputs are bin, defAin, degB, n, and "se 1ect".

Next, the hardware and flowcharts shown in FIGS. 11 to 17 will be explained in detail, focusing on FIGS. 16 and 17.

As explained in FIGS. 6 and 7, first, in one non-pol cycle, 5tartFIFo■ is set and at the same time data A, B, L, M, degA, B are set.

First aL of L9M, b J I I K l mK
l l , J + k + 1 are input. To explain in more detail, a start signal is set in the 5tarttn register O, C0NT, and its 4-bit output is input to the address of the control unit O (ROM).

The 33 bits output from the control section 0 are latched every clock and sent to each section to control 16 internal cycles.

In FIG. 12, if 5tart=1 in step 3, set 5tate is entered in step 4, and a mode for setting α, β, etc. is executed. In addition, steps 1 and 2
．． 5 is a step of inputting or outputting data.

13th rl! J is step 4+7) set in Figure 12
5tate flowchart. d in step l
Determine whether egAHor degBtn<t, ye
In the case of no, the state becomes "nop" and the process returns. Also, if no in step 1, step ML n + d e g A s n +
deg Bx n is calculated, and in step 5 deg
Find L or de gM.

Figure 14 shows the "calc" shown in step 6 of Figure 12.
”Explain the mode.

In step 1, the previous step 5 in the flow of Figure 12
Determine whether or not tate is “nap”. If yes, proceed to step 5, or if no, proceed to step 3.
It is determined whether 5tate="reduceA" or not, and the process advances to step 4.

Also, the states shown in Figures 12, 13, and 14
(state) generate (
Cellular Array Multiply
r) It is carried out at @. 0 to 0 are FIFO buffers, respectively. 0 is a delay register.

is performed (start=1), and a, b from 2 to 9 clocks.

1, the value of m is input. Also, the clock and r: 1 92 and 12. Set m2 to var2FIFO31. Initially 12=m2=0 0 then 11, ml
Set in varFIFO30.

degA11=t, degB1n=j, degL1B=
Since degM4no, degA□ut=o,
degB□ut=0. degLOut=0. degMO
u1=0. Also, VaroltFIFOse
t 32 also aout, bout, 1out
+mOut=0.

Next, Ce1luar Array Multi
Calculate a fist al, β・bJ from plier, and Drag
@) to calculate α'l&i-βbj, and Tempre
Set gQ.

And Latch (a), (b), (c) and the MUX, ALU, Lamah connected after that
(d) , Latch (e) de g L
i n, de gM t n + & b F I
Set FO@, and let a=al, b and bj.

Next, to explain the second symbol cycle, var
2 FIFOQ, 5tartF engineering FoQ, war I
F I FOQ, var inF I F oQ, de
g 1npxFoQ set was performed in the same way. However, 12=a*l k-β*mh, 012
=Inl +=Q, start=o, i,
xjlk, ml = mh, ain = ai-
1, bin=by-1, JLin-JLk-1,
minxmh-1, deg AgaBIL=LIL=N
IL=0.

Next, since it is 5tartO, enter the calc mode and perform the STATE in the first symbol cycle.
Calculations were made accordingly. Here, 5tate=
Since we are thinking about reduce, we calculate α・ai−1,β・bj−1 using cell array multiplier,
Calculate α*ai-1-β-bj-1 using D rag and set it to 7smpreg (D. Also, use the same method to set aajLk-1sβ・mh-1 to TempregQ. Then, deg out F I F.O.Q.
, var out F I F OQ,
deg Aout = deg A, d@g B
out s deg R, deg Lout=deg
L, deg Mout wdeg m, aa
ut = a −at−1s β −b j−1, b
out = b7. JLout! cz
Set *lh-β*mh, mout=0.

Since 5tart=0, from Figure 7 degCosp
The ute is the last ahpzFoQ performed a x &
Set i-1, b = b j-1.

In addition, deg F I F oQ, var 2 F
The value to be set to IF oOlvarout FI FOQ is determined by the MUX.

Similarly, in the third symbol cycle, degOut, deg
Bout, degrout, de mout, ao
ut, bout, 10ut, and nJut are output, resulting in 2 symbol cycles of W[.

Evaluation' Cell Next, the EVAL cell in steps 3) and 4) of decoding will be explained.

The systolic algorithm for estimating the error position and error value in steps 3) and 4) of decoding will be described, taking into consideration the interface with the GCD cell. In addition, a dedicated cell (hereinafter referred to as an evaluation cell) that executes the algorithm in hardware
We will explain the design of

AlgorithmAs mentioned above, in step 3) of decoding, step 2
) is the error locator polynomial σ(X).

Error evaluation polynomial ω(X) and differential σ′ of σ(X)
Element α-j (j=n-1, ---
-, 2, l, 0) must be sequentially substituted to obtain the values. (Here, the received symbols are input from higher-order terms of the received word polynomial.

That is, it is assumed that rj is input in the order of j=n-1, ---, 2, 1, O. Therefore, in the explanation for step 3), α-j(j = n-1, -----.

It must be noted that the order of assignment in 2.1.0) is reversed. Therefore, the Evaluat that realizes this
The functions required for the i on cell array are σ(X), ω(x), (σ”(x
)) in order from the highest order, and α
-j (j=n-1, ---2, 1, 0) is sequentially substituted and the value is output. Here, the concrete calculation required is simply substituting a variable into a polynomial and finding its value, so an iterative algorithm similar to equation (5-10) can be used.For example, if the degree polynomial f (x) is The calculation of is developed as follows.

f (x) = f t xt+ft-1x″-1+ −
−−−+ f , x + f 0 (5-11) = [
-----[(f t X+ ft-1)X+ ft-2
]X+ −−1−+ f 1 ) x + f o
(5-12) However, in the syndrome calculation, each cell has X to be substituted in advance, and a coefficient is given to each cell, but here the coefficient is known in advance, so the DFT
The systolic algorithm for solving can be used as is. However, σ passed from the GCD cell array side
(X), ω(X).

The coefficients of each polynomial of (σ'(X)) are given from higher-order terms. To deal with this problem, (5-11), (5
-12) Instead of the equation, the following equation may be solved.

f (x) x = f t + ft-1x-'+
------Meeting 1) +f, x +f, x (5-13)=
(-----[(f ox-'+ f ,
) x −1+ f 2] x” +−−−
-+ f t-1)x-'+ f t
(5-14) This is a polynomial f (x) in which each coefficient of f (x) is inverted.
+ft-1x+ f5 (5-
This corresponds to substituting x-1 into 15). Even if σ(X), ω(x), and (σ'(X)) are solved in this way, the estimation of the error position and the calculation of equation (2-50) described in the explanation section of step 3) will not work. There are no wood problems.

In this case, the order of σ(X) is always t, the order of ω(X) is (t-B), (the zero term is treated as zero, and the order of σ°(X) is also (1-1) Let's keep it as follows.) In order to solve the above algorithm, the 18th
Repeat operation 1 of formula (5-14) in one cell as shown in the figure.
You must allocate the product sum calculation times.

In FIG. 18, fl represents a register that stores the i-th coefficient of the polynomial f (x), and xin,
out represents the I10 port for data on the GF that is input to the polynomial, f in and out represent the I10 port for transferring the results of one product-sum calculation, and command in.

out represents the I10 port of the command given to the cell, where there are two possible types of "command".

- First, before starting calculation, the coefficients of the polynomial f (x) must be loaded into each cell of the 7 rays of the evaluation cell, so a command "1oad" is required. In addition, this “1oad” includes:
The number of the cell to load must be included to tell which cell to load the data into. Furthermore, since the cell can start the sum-of-products calculation as soon as the data loading is finished, the command "calc" for that purpose is necessary. It becomes like this.

・Here, when the command is "load" for each cell,
Load the necessary coefficient data, and in the case of "calc", Xin, fin and f.

One-time product-sum calculation of equation (5-14) from “fin・x i
n+f 1” and transfer the result.

In one Evaluation cell shown above, (5-
14) Since we are performing one product-sum calculation of the formula, in order to solve the following f (x), we need to divide this cell into the second
They must be connected in a one-dimensional manner as shown in figure 0.Here, it takes t symbol cycles (one symbol cycle is a data input cycle) to load f t#f into each cell of the bond. After the loading is completed, α'(j=n-1
, +++++, 2, 1, 0) is started and the first result f(α-1)@(αJ) starts to be output. There is a delay of t symbol cycles. Note that xin has no meaning while loading coefficient data, and the value output from the right end of the cell array during the t symbol cycles after loading is completed until the first result is output is meaningless. .

Therefore, xin-α' (j= n-1*----*
2 ml, 0), enter the valid value after loading is completed. Also, during repeated calculations, the leftmost f in
fO must always be input.

Furthermore, since there are a plurality of cells, "load" is performed with a shift of about one symbol cycle depending on the cell.

Evaluation cell Here, we will design a dedicated cell that implements the functions of the evaluation cell described above in terms of hardware.
As mentioned above, you need to be careful at this time.
σ(X) (t order including zero term), ω(X) ((1-1) order including zero term), σ'(x) (including zero term (
1-1) The following calculations can all be solved using the same algorithm. Therefore, the evaluation in Figure 18 (Evalua
tion) It is possible to specifically design a cell basic model and configure a cell array for each polynomial. However, since the function of this Evaluation cell is very simple, data The input and output of σ(X) and ω(X) are multiplexed in a time division manner.

It is desirable to be able to perform sum-of-products calculations for the same order of σ°(X) in one cell.
An i on cell can basically consist of only a register for storing coefficient data and a multiplier/adder on the GF, but it also requires a control part for synchronization and a register for transferring calculation results. FIG. 21 shows a concrete design of the evaluation cell that handles the R3 code on GF(28). Also, as in the case of GCD cells and syndrome cells, if we consider the operation of a cell within one symbol cycle (l symbol cycle is a command input cycle), the flow of processing can be expressed in a timing chart as shown in Figure 22. . (Here, too, one symbol cycle is divided into 16 internal cycles.) Note that the multiplier on the GF has “C” as in the case of the GCD cell.
e l l u l ar-Arraymultipl
ier" is assumed to be used.

・In order to perform product-sum calculations of the same order of σ(X), ω(X), and σ°(X) in the same cell, change f in and out in Figure 18 to the coefficient data of the three polynomials. I am sharing it with you.

(respectively cr (x) in, out, (1) (
X) in, out.

σ'(x) in, out s ) ・Data other than “commana” is handled as vector-expressed symbols (8-bit parallel) on CF (28) ・Coefficient data shown in Figure 18 Three registers for storing fl are prepared for the coefficient data of the three polynomials. (Respectively σi, ωi, σ“i) ・In line with input/output multiplexing, registers for storing input/output data are configured with FIFO, and one multiplier on the GF performs product-sum calculation for each polynomial. Do it efficiently.

・In order to use it for decoding any R3 code on GF(2B), the degree to which the cell is assigned is set to “5” from outside.
You can input with "elect".

・Each cell has a synchronization signal “5YNC” and a reference clock”
CLOCK” (corresponds to an internal cycle).

Note that the "C0NTR0LL" part in FIG. 21 can be realized by a microprogram ROM, and the specific "command" can be realized by the order handled by the cell, which can be realized by using a comparator. It can be determined by −(
2command=0"→"calc","comm
and#0"→" lo ad (Ce l
1#) Fig. 19 will be explained. In the case of "1 oad" in step l, a cell with a predetermined number is selected from the select signal that comes after the "1 oad" signal (step 2
), set fi=fin in step 3, and step 4
Output with .

If no in step l, that is, the command calculates (c
a l c), in step 5 fout=fin@
Perform xin+fi and proceed to step 6 to output.

Note that the calculation in step 5 is performed in the cellular array multiplier shown in FIG. As mentioned above, FIG. 22 is a detailed explanatory diagram in which the l symbol cycle is divided into 16 clocks.

We have studied the systolic algorithm for executing the three steps of decoding the R3 (Reed-Solomon) code in more than one place, and developed a dedicated m-cell ``GCD cell'' that implements each step in hardware. Syndrome Cell”, “Evaluation”
When a decoder system is actually constructed using these cells, it becomes a one-dimensional cell array as shown in FIG.

(Defined on GF (28). Code length n = 28-1
, error correction capability t (arbitrary), and the received symbols rn-1, ---, TI, ro are input in this order. ) Here, Evaluat 1on-t=nil(t-1
) output is the circuit “ErrorPattern g” for realizing error pattern calculation and gate function.
"enerate &GATE" is input. (
This part is composed of individual TTL and the like. ) This is σ
Calculation of (X) requires t EvaIuation cells, while calculation of σ'(X) and ω(x) requires (
Only t-1) EvaluationOn cells are required,
While #t's Evaluation cell is performing the next product-sum calculation for cr (x), this circuit calculates (2-5
0) means a car that only needs to be calculated by the formula "-ω(X)・σ'(X)-'".

Note that the received symbol (rn-11--1r I + r6) input to the left end of the syndrome cell array
are simultaneously stored in the buffer memory in this order.

Also, these are σ(No. 6)・(α')(j=n-1゜---,1,0) from Evaluation cell #t
When it starts to be output, it will be output one after another in this order. At this time, if “σ(α−i)・(αj)t=0”, as explained in the section of the decoding method, there is more error in rj−(ω(α−j)・(αj)t− +) ・ (σ°
(α~J)・(αj)t−+) −r=−ω(α−j)・σ°(α−j)' (
5-18) has occurred, so the correction can be made by opening the gate and adding this calculated value to rj.

Another feature of this system is that each cell operates synchronously in l symbol cycles consisting of 16 internal cycles, and all decoding processing can be pipelined. Here, some interfaces (consisting of individual TTLs, etc.) are required between each cell array, but the overall control is as follows:
Basically, “5YNC” and “CLOC” control each cell.
In addition, depending on the interface configuration, the delay time required for the decoding process (after rn-1 is input to the left end of the syndrome cell array,
luat f on (evaluation) From cell #t σ(α−j
)・(αj)t(j=n-1) is output and the time from when rn-1 can be corrected) changes, but the delay in the cell array itself is N+2t+2 (2t+1)+2t
=N+8t+2 (symbol cycle)
(5-17).The functions required for each interface are briefly described below.

Conflict syndrome → GCD; Determine the beginning and end of the syndrome from the output "commandout" from the syndrome cell #(2t-1), and pass the data to the GCD cell #O based on the output from "y out". Sta
r t in”.

“varin” and de g in” are generated in a time-sharing manner.

eGcD+Evaluat 1onH#2t G CD
output from
”, the start of output of ω(X) is determined, and “degout
”, select σ(X) and ω(x), and calculate the Ev of #O.
aluat i'on (evaluation) Data to be passed to the cell "c"
ommandin”.

“fin” is generated in a time-division manner. At the same time, GF
x in data TABLE (ROM)
Request in.

In addition, in order to perform continuous decoding processing, Evaluat
ion (evaluation) cell (the first σ(α−j)
(αj)” (t symbol cycles until the output of jan-1, ---) starts) can be ignored.

Also, as described in the section on the configuration of the syndrome cell, here the received symbol power r n-1, ---.

Since rl+ro are input to the syndrome cell in this order, and corrections are made in this order, the last rt-1, ---.

The correction processing of rl+ro will be ignored, but this part is a check symbol part as explained in the encoding section, so there is no problem here. We evaluate trick algorithms, cells, and an R3 code decoder system constructed using them.

First, the three cells "GCD cell" that handle the R3 code on CF (2") shown in the previous section, 'sindoel-mu-t
In order to evaluate the feasibility of 'AI' and 'Evaluation Cell', the number of gates required for each configuration, the capacity of the horizontal microprogram ROM for control, the number of I10 pins, etc. are summarized in Table 2.

臘W處蝮□ All of these are large enough to be made into an LSI of 1 chip. The reason why the scale of each cell has become relatively simple in this way is that the symbols on the GF are expressed as vectors.
It is treated as bit-parallel data, and the multiplier is
This is because the internal processing of each cell is pipelined and the internal processing of each cell is pipelined. (Addition is realized by bit-wise exclusive OR). Figure 16, 6th
Although not shown in FIG. 21, a synchronization circuit and a FIFO initialization circuit are actually required at the start of operation. Table 2 also includes these items.

Next, we evaluated the processing speed by considering that each cell operates synchronously in one symbol cycle, each consisting of 16 internal cycles (see Figures 17, 7, and 22).
However, among them, the one with the longest processing time is “GCD
This processing time varies depending on how the cell is actually created, but for example, 5 (Shot
ky) type TTI, one internal cycle would be approximately 50 (ns) at most.

(The ROM is assumed to be a bipolar ROM.) In that case, the l symbol cycle is "800 (ns)", so the data transfer rate (including redundant data) in the decoder system shown in Fig. 23 is "IOMBPS (Mega Bit ROM)".
Per 5econd)".

Note that the decoder system in FIG. 23 has a code length n=28-1. It deals with R3 codes with an error correction capacity t (arbitrary), but its characteristics are that the decoding process is pipelined with simple control, and that the number of cells required for the system configuration is reduced only by the error correction capacity t. It was decided.

However, if processing speed is not so much of an issue, it is not necessary to use all of these cells (GCD: 2t+1, syndrome: 2, Evaluat fan: 2), and the buffer memory etc. If the same cells are used repeatedly, it is possible to construct a decoder system with fewer cells and therefore at a lower cost. Furthermore, each cell designed this time can be used as is for a shortened code as long as it is an R5 code on GF (28). (Because the number of required cells is determined only by t) Furthermore, in the explanation of the system configuration, when performing continuous decoding, correction of the check symbol part (see the section on encoding) can be ignored, but # Xin to be input into the Evaluation cell of 0 is “GF data TABLE (ROM)”
” by changing the order in which they are requested, it is possible to correct any symbol in the received word.

In the present invention, the configuration of the R3 code decoder and the algorithm therefor were studied from two approaches.

First, in the first approach, a decoder with a high speed and as simple configuration as possible that can be realized with a normal TTD and ROM is used.
We designed and manufactured a decoder for magneto-optical disks. At that time, we adopted a product code configuration that combines two extended R3 codes on a simple GF(2') to simplify the decoder at each stage, and at the same time to simplify the decoding at each stage including erasure correction. As a result of extending and applying the direct decoding method, high-speed decoding became possible. The data transfer rate of this decoder including redundant data corresponds to IOM BPS.

In addition, in the first stage (C2) decoding, double error correction,
In the decoding stage (C2), in addition to single error correction, two
By performing double and triple erasure correction, it was possible to achieve a high error correction ability that improved the pit error rate from about 10-3 to about IQ-12. This decoder uses LS type TTL, bipolar ROM, and static RAM.
This is a sufficiently practical design that was realized using . (A future problem with this approach is that when realizing a decoder that applies the direct decoding method to erasure correction, it will be possible to consider ways to reduce the number of ROMs and make it possible to implement the decoder system into an LSI.) ) Next, in the second approach, we considered the application of the systolic algorithm as a decoder configuration that takes advantage of the characteristics of VLSI, assuming the future introduction of VLSI. At that time, we improved the algorithms proposed for solving the extended GCD problem and DFT in order to actually apply them to RS code decoders, and performed syndrome calculations, derivation of error locator polynomials and error evaluation polynomials, error locators and values. We considered a systolic algorithm that performs three steps of decoding, such as estimating . Also, assuming that any RS code (shortened code is also possible) on GF (28) is handled,
We designed a dedicated cell to implement each systolic Φ algorithm in hardware, but by pipelining the internal processing, we were able to simplify the configuration of each cell. It was confirmed that the number of cell gates and the number of I10 bins were large enough to be integrated into a 1-chip LSI. Furthermore, we showed that by configuring a decoder system as a one-dimensional cell array and sending data in one direction, the entire decoding process can be pipelined with simple control. In addition,
The number of cells required in this case is determined arbitrarily depending on the error correction ability of the code being handled, but if processing speed is not an issue, a small number of cells can be used repeatedly using a buffer memory. For example, an economical decoder system configuration can be expected. In addition, in order to have a certain degree of versatility and be able to apply it to codes other than R5 on GF (28), it is possible to create a flexible system configuration by converting part of the cell configuration into software. Needless to say, it's a good thing.

Note that the fully parallel processing (histogram cell 107) in FIG.
) are arranged in a matrix, and histogram calculation using fully parallel processing is well known, but it is a process in which the image density and the density are determined using this method, and then the histogram is converted into the required signal space using a ROM, etc. A vector transformation is performed at . The systolic algorithm described in the present invention is an algorithm in which a desired result is obtained by repeating the same operation.

〔effect〕

As described in detail above, the present invention transforms the conventional algorithm for signal pairing and logic in communication channels into an algorithm suitable for parallel processing, and uses a parallel parallel processor to eliminate the drawbacks of the conventional system and achieve high efficiency. As explained above, it is possible to provide a signal processing device that is capable of making errors, when applying the idea of the systolic algorithm to the Bahrkamp-Massey method and configuring a decoder in which the syndrome generation section is made into a dedicated cell. By arranging the necessary number of syndrome cells in a one-dimensional manner according to the code capability, the entire syndrome generation process can be pipelined. Another advantage is that cell control requires only a reference clock and a synchronization signal.

By pipelining the decoding process in this way;
Although some interfaces are required between the cell arrays that execute each step, the overall control has the advantage of requiring only a reference clock and synchronization signals.

Furthermore, all the cells operate synchronously in the same symbol cycle, and the l symbol cycle can be up to 800 ns, so when considering the code on CF (2r), the data transfer rate can be 104 BPS.

Furthermore, since each step is composed of the same cell, it is suitable for LSI implementation.

Furthermore, since the correction capability increases simply by increasing the number of identical cells, it has the effect of being suitable for mass error correction.

As explained above, by applying the idea of the systolic algorithm to the Berlekamp-Massey formula 5,
When configuring a decoder in which the 0 part is made into a dedicated cell, by arranging the necessary number of GCD cells in one dimension according to the code capability, the process for deriving the error locator polynomial and error evaluation polynomial can all be pipelined. I can do that. Another advantage is that cell control requires only a reference clock and a synchronization signal.

[Brief explanation of the drawing]

Figure 1 is a block diagram showing a model of a coded communication system, Figure 2 is a block diagram showing parallel processing by a parallel processor, Figure 3 is a block diagram showing one of the syndrome cells, and Figure 4 is a block diagram of a command. FIG. 5 is a block diagram showing the connection of multiple syndrome cells. FIG. 6 is a block diagram showing the configuration of the syndrome cell. FIG. 7 is a timing chart of the syndrome cell (S+). Figure 9 shows the mode timing of each syndrome cell, Figure 9 is a flowchart for deriving σ (lack) and ω (X) by the extended GCD problem, Figure 10 shows the conceptual model of the GCD cell, Figure 11 The figure shows the basic model of the GCD cell, and Figure 12 shows the GCD cell.
Figure 13 is the set state mode processing flowchart of the basic model of the GCD cell. Figure 14 is the processing flowchart of the GCD cell calculation (cafe) mode. Figure 15 is the specific design of the GCD. Block diagram when performing. FIG. 16 is a detailed block diagram showing the specific configuration of the GCD cell. FIG. 17 is a timing chart within one symbol cycle of a GCD cell, FIG. 18 is a block diagram showing a basic model of an evaluation cell, and FIG. 19 is a flowchart showing functional processing of the basic model of an evaluation cell. Fig. 20 is a block diagram when evaluation cells are connected, Fig. 21 is a block diagram showing the configuration of the evaluation cell, Fig. 22 is a timing chart of the evaluation cell, and Fig. 23 is RS code decoding based on the systolic algorithm. FIG. OlO is a cellular array multiplier O is a state generator OlO is a control 103 is a communication path 112 is a syndrome cell 111 is a GCD cell

Claims (1)

[Claims] Encoding means for encoding information from an information source; a communication channel for transmitting encoded data by the encoding means; and a communication channel for transmitting the encoded data transmitted by the communication channel. It has a decoding means for decoding, and the decoding means has (1
) Syndrome calculation, (2) Derivation of error position polynomial and error evaluation polynomial, (3) Evaluation of error position and error magnitude, and execution of correction. Device.