JPS6165531A - Code converting method - Google Patents

Abstract

PURPOSE:To obtain easily a DC free code not obtained by a conventional sys tem, for example, d=2, k=9, M=4, N=4 and TW=0.5T by deciding the unique rule to the combination of code words in case k-d+1>N-d' not in existence in a conventional general rule. CONSTITUTION:When an inequality I is established, connection rules a1-a4 of the general rule are applied as they are and an excellent (d, k) DC free code which had not been attained by the conventional general rule is established by introducing a new connection rule a5. In the connection rule a3, the part L of two code words with DPnot equal to 0 is not always '1' below d-1 in the range where equation I is established. However, when both are (d) or over, it is inclu sive of the conventional connection rule a4, and when they are both d-1 or below conversely, since it is included in the conventional connection rule a3, the new connection rule a5 is the combination of a code word with Pnot equal to 0 and l<=d-1 and a code word with DPnot equal to 0 and l>=d, and the ¦DSV¦ is not increased by using the code rule a5 and the d, k limitation is satisfied.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to a code conversion method for converting an M-bit data word into an N-bit code word, which is applied when transmitting and recording digital signals.

Conventional configurations and their problems In general, the following four points are known as properties necessary for communication channel codes used when magnetically recording digital signals.

(1) Maximum number of consecutive bits: If either “O” or 1” continues for too long, it will be difficult to extract the clock information and the self-clock function will not be available. In order to avoid this, it is desirable that the above value is small.
A code in which 11+ changes occur frequently is not suitable. Therefore, it is desirable that d be a dog.

(3) Detection window width TW: This is a measure of the phase direction margin against time axis fluctuations such as jitter of the reproduced signal and peak shift due to waveform interference, and the larger the value, the better. If the signals are coupled by a rotary transformer and the DC component is blocked, it is desirable that the code be a DC-free code that does not include the DC component.

Hereinafter, codes subject to the above constraints (1), (2), and (4) will be referred to as (d, k) DC-free codes.

Conventionally, various (d, k) DC-free codes have been developed from the above point of view, and a general rule for systematically obtaining (d, k) DC-free IJ- codes was previously proposed (Japanese Patent Application No. 1983-
207938) 0 Next, we will show the general rules and clarify the problems,
Before that, we will briefly explain DC-free codes.

(I) For DC-free codes, the value obtained by assigning +1 to 1" in the code word and -1 to "o" is calculated as the disparity of the code word - (
(hereinafter referred to as DP). In addition, in a pit string generated by connecting code words, the added value of +1 and -1 from the start of the bit string to an arbitrary focus is calculated as DSV (Digital Sum Va) at that pit.
riation) 0 This DSV is +■ or -
■If it is always finite without divergence, its sign is DC
Becomes free.

(II) About the general rule This general rule states that for d of 2 or more, in order to satisfy the restriction on d by connecting code words and to keep the DSV finite, the connection end of the usable code words is Conditions are uniquely determined for given d and k, and a unique connection rule between code words is introduced.

The connection end conditions and connection rules for code words are shown below.

First, when DC-free, that is, DSVi is kept finitely, and the codeword length is finite, the disparity of the codeword is
Since DP is also finite, the next codeword to be transmitted will have a disharity DP with the opposite polarity to DSV, depending on the sign of DSV at the last pick (LB) of the codeword transmitted before.
to have the following. By doing so, divergence of DSV can be prevented.

Next, in addition to the above-mentioned connection rule for limiting the DSV to a finite value, code word connection end conditions and connection rules for satisfying the restriction on cl will be specifically shown.

(■-1): For d greater than or equal to 2, when d' is the largest integer not exceeding d/2, a series of "1" at the beginning of an N-bit code word starting with "1" The number of bits l and
The number of consecutive bits τ of 0" or '1" in the terminal R part of the code word belongs to either of the ranges shown in the following equations (1) and (2), and b = N-l-r bits. middle B of codeword
In 'FiVI, d bits or more are bi, /) or less consecutive ff. L such that OI+ and 1' appear alternately.
, B and Rrrr +---r M+ m −'r −
h Z, a 8 m (”! (:○For all bits of J-CCO, Q OII is 1°l, !l
Select the back pattern CCO of CCO in which 111 is reversed to II OII.

-d+1 for N-bit codeword N-bit codeword d'≦l≦, -d+ for cl-&<, r≦
1 −・−−−−(j) d−d′ (−d+1 for 7≦,
d′≦r<, −d+1 =−−−@) Below,
It is assumed that l and r belong to formula (1), but the same applies to formula (2).

(ll-2): Code word CCO selected in (II-1)
Among them, the above! A code word CWO with DP=O where d-1 or less is paired with its back pattern CWQ, and a data word is associated with each pair.

Further, the code word CW1, DP-〇, where l is greater than or equal to d
and its back pattern CW1 are paired, and a data word is associated with each pair.

(U-3): Code word CC selected in (ll-1).

Among them, code words CW2 and DP (where l is less than or equal to d-1), code words CW2 and DP (code words CW3 and their back patterns CW2 and CW3, respectively) are combined into one set, and a data word is assigned to each set. correspond.

(It-4): Code word CC selected in (It-1).

Among them, the code word CW, DP)o, in which l is greater than or equal to d
The code word CW5 of 4 and DP(o and their back patterns CW4 and CW5 are made into one set, and a data word is made to correspond to each set.

Next, it will be shown that the correspondence between code words and data words shown in (n-1) to (It-4) above satisfies both the restriction on d and the restriction that DSV is finite. However, 1=1
Consider the connection of a first code word W1 with 1 and r=r1 and a second code word W2 with 1=12 and r=r2. Note that in the following, the final bit of Wl will be referred to as LB.

(al): Since both CWO and CWo have DP=O, connecting either of them as W2 will not increase ID5v1, so only d and k are constraints. Therefore, the following connection rule is established. That is, when either CWo or CWO must be used for W2, (al, 1) When LB is 1111+, W2=CWO (al, 2) When LB is ff OII, W2=CWO. This is because when LB is "1", W2 is "o 11" which is less than d-1 bits.
At the connection between Wl and W2=CWo, there is an O of d-1 bits or less.
” occurs, which violates the d restriction, so in this case, W2=CW
O is not appropriate. Conversely, when W2=CW○, R of Wl
The maximum number of consecutive focuses of "1" in the L part of CWo is -d+1, and the maximum number of consecutive focuses of n1n in the L part of CWo is d-1. The maximum number of consecutive focuses is k. Also, Wl
In the R part of the
", and in the L part of W2=CWo, there is at least the d' bit of 1", so Wl and W2=CW.

There will be more than d bits of “1” at the connection point,
d satisfies the restriction.

The above description also applies to (al, 2).

(a2): Since DP=O for both CWl and CWl, only d and k are constraints, as in the case of (al).

Therefore, the following connection rule is established. In other words, C in W2
When either Wl or CWl must be used, (a2.1) When the number of consecutive bits of "1" in the R part of Wl is d or more, W2 = CW1 (a2.2) "1" in the R part of Wl W2 = W1 (a2, 3) When the number of consecutive bits of "○" in the R part of Wl is d or more, W2 = CW1 (a2.4) R part of Wl When the number of consecutive bits of noll in is less than or equal to d-1, W2 = less than or equal to CW1, (a2.1
) and (a2.2) will be explained. First (a2
．． Regarding 1), W2 = 0'' at the above mentioned part of CW1
The number of consecutive bits is greater than or equal to d and less than or equal to -d+1. On the other hand, W
Since the R part of 1 is "1 pa" with more than d bits and less than -d+1 bits, in the connection of Wl and W2 = CW 1,
d, satisfies the restriction.

Next, regarding (a2.2), 0 “1” in the R part of Wl is d
-1 focus or less, and 11" of the L part of W2=CW1 is less than -d+1 bits, so it satisfies the k restriction. On the other hand, 1" of the R part of Wl has at least d - d' bits, and W2 = Since the "1 pa" in the L portion of CW1 also has at least a d' pit, it also satisfies the d restriction.

As mentioned above, (a2.1) and (a2.2
), it can be seen that the constraints on d and are satisfied. Note that (a2.3) and (a2.4) are the same as in (a2.1) and (a2.2), so they will be omitted.

(a3): CW2, CW2, CW3 and CW3
are all DP+O, and "ol" in the above mentioned part is DP+O.
Since the number of consecutive bits of l or 1" is greater than or equal to d' and less than or equal to -1, the following connecting agent is required in order to satisfy the restrictions on d and without increasing ID5V l. However, DSV is the value up to the last bit of W2.

(a3.1) When DSV≧0, (a3.1.1) When L B is 1”, W2=CW
3 (a3.1.2) When L B is 0”, W2=CW
2 (a3.2) DSV (When O, (a3.2.1) When L B is 1”, W2=CW
2 (a3.2.2) When LB is 0”, W2=CW3
shall be. When DSv≧0, use CW3 or CW2 with DP〈0, and when DSV (o, CW2 with DP〉0)
Alternatively, CW3 is used in order not to increase ID5v1. Furthermore, the reason why such a connecting agent satisfies the limitations on d and d is for the same reason as stated in (al).

(a4): CW4, CW4, CWs and CWs
are both DP←0, and “0” in the above-mentioned part is DP←0.
Since the number of consecutive bits of "or 1" is greater than or equal to d and less than or equal to -d+1, the following connecting agent is required in order to satisfy the restrictions on d and without increasing l DSV l. However, DSV is the value up to the last bit of Wl.

(a4.1) DSv>oo,! : Ki (a4.1.1) When the number of consecutive bits of 1" in the R part of Wl is d or more, W 2 = CW 4 (a4.1.2) When the number of consecutive bits of 1" in the R part of Wl is W2 = CW5 when d-1 or less (a4.1.3) When the number of consecutive bits of "0'° in the R part of Wl is d or more, W2 = CW 6 (a4.1.4) R part of Wl When the number of consecutive bits of noll in
) When the number of consecutive bits of "1" in the R part of Wl is d or more, W2 work CW5 (a4.2.2) When the number of consecutive bits of "1" in the R part of Wl is less than or equal to d-1, W2 work CW4 ( a4.2.3) When the number of consecutive bits of "o" in the R part of Wl is d or more, W2 = CW 4 (a4.2.4) The number of consecutive bits of "o" in the R part of Wl is d- When it is 1 or less, set W2 = CWs. When DSV≧0, use CW4 or cws where DP<o, and use CW4 where DP (when O, DP') is 0.
-4 ft CW 5 Il tDIri, ID5V
This is to prevent a total increase in I. Furthermore, the reason why such a connecting agent satisfies the limitations on d and d is for the same reason as stated in (a2).

(11-1) ~ (El-') and (
By the code conversion method specified in al) to (a4), 2
For the above d, a (cl, k)DC7ri-one code is obtained.

The above is the general rule for creating a conventional (d,k) DC-free code, but a drawback in this general rule occurs when the code word length N is equal to or less than the maximum number of consecutive bits.

That is, if we exclude codewords in which all N bits have the same binary value, the codewords CCo and CC.

If the maximum value of the number g of consecutive bits of the same binary value in the L part of is 'm &
aw is given by equation (3) and equation (4), respectively.

'ma = N-(d-d') ・・・・・・・・・-
@) r=N-d' ・Yamakawa... (4) dx Here, 'maw is the formula (5), and 'meLX is the formula (6)
Assume that the following is satisfied.

d<, 1ma<k-d+1 ・・・・・・・・・
・(6) d<r <k−d+1 −−−−(6) m
aw In this case, equation 0) can be expressed as equation (7).

d'(/riN-(d-d'), d-d'≦r≦N-d
/ . . . . . . When formula (a) holds true,
Among the connecting agents (al) to (a4), the problematic one is (
This is the case of a3).

In the case of (a3), both the L parts of CW2 and CW3 must be 1", which is less than or equal to d-1 bits. This means that when 'max=k"1 and rma=k-d+1, Since this is a condition for satisfying the restriction, if equation (7) holds, it is not necessary that both the L parts of code words CW2 and CWs be 11'', which is d-1 bits or less.

Object of the Invention The object of the present invention is to eliminate the drawbacks of the conventional example and to have performance higher than that of the conventional example (d,
k) To provide a code conversion method to systematically obtain DC-free codes.

Structure of the Invention The present invention solves the conventional general rule by applying the connecting agent (al) to (a4) of the general rule as is and introducing a new connecting agent (a5) when the formula (force holds). This is a code conversion method that can obtain an excellent (d, k) DC-free code that could not be obtained with the previous method.

Next, the new connecting agent (a6) will be described in detail using Examples.

DESCRIPTION OF EMBODIMENTS As mentioned above, in the connecting agent (a3), the L parts of the two code words that are DP40 do not necessarily have to be 1'' below d-1 as long as formula (a) holds true. but,
If both are d or more, it is included in the conventional connecting agent (a4), and conversely, if both are less than d-1, it is included in the conventional connecting agent (a3), so the new connecting agent (a5) is DP+o or ＃＜
: The code word of d-1 and the code word of DP~0 and l≧d,
This is what happens when they are combined.

Here, a code word with DP40 and l <, d −1,
There are the following two combinations of code words with DP40 and l≧d.

(i) Code word C'W2 of DP>○ and l d-1, its back pattern CW2 and DP (o d<l≦-
N+d' code word CW s' and its back pattern C
W5/゛ - This is made into one set, and a data word is associated with each set.

(ti) D P <O?”:)l<, d-1(7
) Code word CW3 and its back pattern CW, s and D
P) The code word CWd of o and d <, l <: k −N + d' and its back pattern CW4'i are made into one set and made to correspond to the data word.

Next, it will be shown that the correspondence between code words and data words shown in (i) and (ii) above satisfies both the restriction on d and the DSV finite condition.

Note that l=g1. The first code word W1 with r=r1, and 1=
12. Let us consider a second code word W2 where r=r2, and the last bit of Wl is called LB.

First, regarding the above (1), the following (05, 1), (a6
．． 2) Use a connecting agent.

(a5.1) When DSV≧0(7), (a6.1.1) When L B is “1”, W2=C
W6' (a5.1.2) W' when L B is “○”
2=CW2 (a5.2) DSV (when o, (a6.2.1), when L B is 1", W2=CW2
(as, 2.2) When LB is "0°" w2 = δπ
7 In (as, 1) above, since DsV≧o, the code words CW2 and CWm with iDp<oy are used for W2, and in (as, 2), since DSV<o, W
21/C D P ) Ofl code 'fFM CW
2. CWT' is used to prevent ID5VI from increasing. On the other hand, regarding the restriction on d, when (as, 1.1), the "1 pass" of the rl bit in the R part of Wl and W 2
= 12 bits '1'' in the L part of CW s'
At r 1+ 1" of 112 pits, d
Since d'< r 1 and N d', and from the above (1), d≦g2≦N - d', d(r1+12<:
Then, d, satisfies the restriction.

(as, 1.2) if d'<12<d-1<k
Since N + d1', d≦r1+12k, which satisfies the restriction on cL.

Second, regarding the above (11), when (as, 3) DSV>O, (as, 3.1) L section 3 is throbbed by "1" W2
=CW3 (as, 3.2) W when L B is “0”
2=CWa'-(as, 4) When DSV<00, (as, 4.1) When L B is 1''', W2=C
W4' (as, 4.2) When LB is 0'', W2=C
W3 In the above (as, 3), since DSV≧0, W2 has DP(o code word CW s , CW4
', and in (as, 4), the code word CW3 is DSV(o, so W2 is DP).

CW 4' is used to prevent ID5v1 from increasing.

The restriction to d is the same as in (1), and (
Both as,3) and (as,4) satisfy the restriction on d.

As mentioned above, when formula (7) holds true, a new connecting agent (as) can be introduced, so the number of code words that can be used increases compared to the conventional general rule.

Table 1 shows the code words CWO to CWs, CW4' and CWs'.
Table 2 shows the characteristics of the connecting agents (al) to (as
) is shown. However, DV in Table 2 is DSV>o
Then DV=”o°’, DSV (If o then DV==”
1”, and P is DP-〇 of the second code word, then P=″0
”, DP+o, then P=“1”. Also, E is the first
The number of consecutive bits of the same binary value in the R part of the code word (() is d
If it is less than or equal to -1, E="o".

If it is greater than or equal to d, E=“1”. F is defined as shown in Table 2.

Note that °×'' in Table 2 is a mark indicating that there is no relationship.

The codes shown in Table 3 are obtained according to the invention (d, k)
This is an example of a DC free code, M=4°N=8, d
=2, k =9, Tw =0.5 T's (2,
9) It is a DC free code.

As is clear from Table 1, Table 2, Table 3, and Table 3, it is possible to correspond to 16 data words, so M=4 pinto data words can be converted into N=8 bit code words. Therefore, Tw=100T=0
．． 5 T.

Note that in Table 3, the back pattern is omitted, and the combination of code words A10-/Fy, 16 is an example.

By the way, the conventional general rule is d=2 and k=9.

When N=s, the combination of code words of 16 in Table 3 is not allowed, so the number of code words is 16, and only data words up to M=3 bits can be converted. Therefore, Tw=
qT: 0.375T.

On the contrary, according to the conventional general rule, ci=2, M=4°N=a
, Tw=0.5T, the minimum k is 10.

As described above, by introducing the new connection law (a6) according to the present invention, it is possible to obtain (d,
k) A DC-free code is obtained.

Effects of the Invention The present invention provides the advantage of −d+, which was lacking in the conventional general rules.
By establishing unique rules for the combination of code words when 1>N-d', for example, d=2°k=9. This is a code conversion method that can easily obtain DC-free codes such as M=4, N=s, and Tw=0.5T, and its practical effects are excellent.

Note that in this specification, equation (3) and subsequent equations have been derived and explained based on equation 0), but similar results can be obtained based on equation (2).

Claims (2)

[Claims] (1) When converting an M-bit data word to an N-bit code word larger than M, let d and k be positive integers of 2 or more with the relationship d<k, and let d' be d/2. If the largest integer that does not exceed k-d+1>N-d' holds, then out of 2^N code words obtained by N bits,
The number l of consecutive bits of "1" in the starting end L part is greater than or equal to d' and less than or equal to N-(d-d'), and the number r of consecutive bits of the same binary value in the ending R part is greater than or equal to d-d' and N −d′ or less, and both the number of consecutive “1” bits and the number of consecutive “0” bits in the middle part B of the code word of b=N−l−r bits sandwiched between L and R are d A code word composed of L, B, and R, which is greater than or equal to k or less, is defined as a CCO, and all bits of this CCO are changed from "0" to "1",
The code word that is the back pattern of the code word CCO in which "1" is replaced with "0" is @CCO@, and it is defined by the difference between "1" and "0" that constitute the code word in this code word CCO. A code word with disparity DP=O and a code word with DP=O among the code words CCO are paired, and the same data word is made to correspond to the pair, and among the code words CCO, DP>0 and l≦d− 1 code word and its back pattern, DP<0 and l≦d-1 code word, and its back pattern are made into one set, and a data word is made to correspond to each set, and the code word CCO is Of these, four code words are made into one set: a code word with DP>0 and l≧d and its back pattern, a code word with DP<0 and l≧d, and its back pattern, and a data word is associated with each set. , DP■0 and l≦d− among code words CCO
1 code word, its back pattern and DP ■ and d≦l≦k-
By forming a set of N+d' code words and the four code words of the back pattern, and associating data words with each set, even if the code words are connected, the resulting bit string will have the same binary value. A code conversion method characterized in that the number of consecutive bits is limited to d or more and k or less, and the added value of DP is kept within a finite value. (2) The code conversion method according to claim 1, characterized in that d=2, k=9, M=4, and N=8.