JPS63240154A - Partially responding channel signal system - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

DETAILED DESCRIPTION OF THE INVENTION Field of the Invention The present invention relates to modulation coding and partial response systems.

[Problems to be solved by conventional technology and invention]

In modulation coding, symbols are coded as signals drawn from one population such that only certain signal sequences are possible.

In recent years, many types of trellis
s) type modulation codes have been developed and have a high signal-to-noise ratio (SN
It has been used (eg, in modems) to achieve coding gains of 3 to 6 dB in IIF-limited channels such as voice telephone channels (e.g., in modems).

An early trellis code was Ungerboeck (U
Ngerboeck, “Channel Coding with Multilevel/Phase Signals” (IEEE Transact
ionson Information The'or
y, Vol. 1T-28, pp. 55-67, January 1982). The U-mouth gerboeck code for sending n bits per symbol is rate 172 or rate 273, which determines the sequence of subsets.
One-dimensional 4 to 8 subsets (RAM) or two-dimensional (Q
AM) is based on a 2°+1 point signal group. Yet another set of "uncoded" bits determines whether signal points within a particular subset are actually transmitted.

This delimiter and code provides some minimum mean squared distance j! between the permissible sequences of 13 points. l d”+++In
configured to ensure that Even after having an effect on the power cost of the extended signal constellation (a factor of 4 (6 dB) in one dimension or a factor of 2 (3 dB) in two dimensions), the increase in minimum mean square distance is For values of n that can be increased accordingly, from a factor of 2 (3 dB) for simple codes to a factor of 4 (6 dB) for the most complex codes.
dB).

Forney et al., “Efficient Modulation in Band-Limited Channels 4 ([EEE J, 5elecL8rea
s Com+sun.

Volume 5AG-2, pages 632-647, published in 1984)
devised a multi-dimensional trellis code based on 16 subset partitions of a 4-dimensional signal constellation combined with a rate 3/4 convolutional code. This 4-dimensional subset is 1
The paired two-dimensional signal population points consist of paired points from the two-dimensional signal population. For a simple 8-state code, the loss due to expansion of the signal population is approximately a factor of 2 (1,5d
B), resulting in a net coding gain on the order of 4.5 dB, but with a d 2+++In of 4 times the uncoded minimum mean square distance.

Similar codes are available on Calderbank and 5loan
``Four-dimensional modulation with an 8-state trellis code'' (8 Tk T Tcch, J, Vol. 64, 100
pp. 5-1018, 1985 [U.S. Pat. No. 4.58]
No. 1,601)).

Wei (U.S. Patent Application No. filed April 25, 1985)
No. 727,198) devised a number of multidimensional codes based on segmentation of populations in 4, 8, and 16 dimensions combined with rate-(n-1)/n convolution codes. Wei's multidimensional ensemble also consists of a sequence of points from a two-dimensionally configured ensemble. This code provides a performance (coding gain) versus code width advantage that minimizes population expansion in two dimensions and provides other benefits such as transparency to phase rotation over a wide range. "New Trellis Code J (IEEE Trans.

[nf, Theory March 1987] and “
"8-dimensional trellis code"(r'roc, IEEE,
74, pp. 757-759, 1986, also devised various multidimensional trellis-codes with roughly similar performance vs. width characteristics, and in some cases with relatively few states. .

All of the above codes are designed for channels where the main impairment (apart from phase rotation) is noise, especially channels where there is no inter-symbol interference.

It is an implicit assumption that the inter-symbol interference caused by the actual channel will be reduced to negligible levels by transmitting and receiving filters, or especially by adaptive linearization in the receiver. It is known that such systems work well as long as there is no significant attenuation within the transmission band +jJ, but in the case of significant attenuation ('zero' or 'nearly zero' level), noise The energy of can be greatly amplified in other domains (“noise enhancement”).

A well-known technique for avoiding such "noise enhancement" is to construct a signal system that provides controlled inter-symbol interference rather than no inter-symbol interference. The most well-known method of this kind is called a "partial response" signaling method (Forn
Maximum Likelihood Sequence Estimation Method for Digital Sequences in the Presence of Intersymbol Interference J (IHEHTra
ns, Inform.

Theory 1 Volume 1 T-18, 32, M is 63-37
8 pages, published in 1972).

In a partial response scheme (typically one-dimensional), the required output Yk at the receiving end is not Yk = Xk, but the difference between two consecutive inputs Xk, i.e. (Yb = Xm Xk-+
) and r, t6. In the sampled data representation using the delay operator RI, this means that the desired output sequence Y (D) is not X(D) but X(
D) (1-D), so rl-
It is called DJ partial response system. Impulse response (-
1, -D) is the spectrum of the S\L time channel with frequency? (DC), the transmit and receive filter combination with the actual channel must also be a DC zero to achieve this desired response. For channels with zero or near zero at DC,
A receiver configured to produce the desired (1-D) response will result in less noise enhancement than one configured to produce a perfect (i.e., no intersymbol interference) response. Dew.

Partial response signals can also be used for other purposes such as reducing sensitivity to channel loss near the band edges, relaxing filter requirements, tolerating pilot tones at the band edges, or reducing adjacent channel interference in frequency division multiplexed systems. It is also used to achieve

Other types of partial response systems are systems with zeros at the Nyquist band edge (1+D) and systems with zeros at both DC and Nyquist band edges (1-D).
2 systems.

A quadrature (two-dimensional) partial response system (QPR5) can be modeled to have a two-dimensional composite input, where the (composite) response (1+D) is both upper and lower in a carrier modulated (QAM) band pass system. This results in a QPRS system with zeros at the band edges. All of these partial response systems are closely related to each other, and a scheme for one can be easily adapted to the other, so that (1-
D) A system of responses can be constructed, and this can be easily extended to others, for example.

(:alderbank, Lee and Mazo(r
The baseband trellis code J ((EF, E Trans, Inf
, Theory vr (draft)) proposed a scheme for constructing trellis-coded sequences with spectral zeros at DC, a problem that is generally somewhat different, but particularly relevant to the design of partial-response systems. . Calderbank et al. adapted a known multidimensional trellis code using a multidimensional signal constellation to generate a begging signal sequence at spectral zeros in the following manner. A multidimensional signal constellation has twice the number of signal points as would be required in the non-partial response case, and consists of two equally sized disjoint subsets, i.e. a multidimensional signal constellation whose coordinates sum less than or equal to 0. Divided into a subset of dimensional signal points and those whose sum is greater than or equal to zero. The operating digital sum J (RDS) of the coordinates, which is initially set to 0, is adjusted for each selected multidimensional signal point by the sum of its coordinates. If the RDS at that time is not negative, then The signal point is selected from the signal subset whose coordinate sum is less than or equal to 0, and if RDS is negative, then the signal point is selected from the other subset. Thus, The RDS is kept constrained within a narrow range close to O, and this range is known to force the sequence of signals to have a spectral zero at DC.But at the same time, these signal points are For example, selected from the subsets in the same way as in non-partial response systems, the expanded multidimensional population is divided into some number of subsets with appropriate distance properties, and the rate −(n −
1) Composition of /n! 1 code has a minimum mean square distance between sequences of at least d2+min.
Determine the sequence of subsets such that it is guaranteed that . The coding gain is reduced by a factor of 21/2 or 1.5 dB in the 4th dimension, or by a factor of 21/2 or 0.75 dB in the 8th dimension, but otherwise similar performance is This is achieved as in the case of non-partial responses with a wide range of codes.

[Means to solve the problem]

One feature of the present invention is that the relationship between signal Xk and signal 72 is Yk
= Xk:tXi-b (k = 1.2, , ; L is an integer)
k and/or some sequence of digital signals Y
k (sequence Yk matches the given modulation code)
It is to cause. The encoder has five signals Yk (
J≧1) and select (Yk, YI%2, Yk+
J-1) with a sequence of representative values Ck (modulo M) of three related sets, where M is an integer, specified according to a given modulation code. The five symbols are selected from one of a plurality of J-dimensional populations, and this selection is based on the previous
'(k'<k). At least one of the populations includes both a point with a positive sum of coordinates and another point with a negative sum of coordinates. The encoder assumes that the signal Xk has a finite variance S,
It is configured to have l.

Another feature of the invention is that the encoder selects the signal Xk to correspond to a sequence of representative values Cm (modulo M) of alternating associated sets. However, in the case of Yk = Xk + Xk-L, C'h = Ck-C"h-b (modulo M) Yk =
If Xk It is within the string of No. 43 Yk to obtain, and that the encoder is in the sequence Yk 2
Minutes smaller than 30! ks.

and the sequence Xk has 5,274 (S, -
3o) Let's have a molecule ILsX with no greater than %, and So is approximately the minimum signal power required to represent n bits per signal with a string of characters spaced Δ.

Another general feature of the invention is that the encoder causes the signals Xk and Yk to have a selected variance Sx and Sy within a predetermined range.

In the preferred embodiment, this range is the parameter β
Sx is approximately 50 (1-β'), and sy is approximately 2S0/(1+β).

Another general feature of the invention is an apparatus for generating a sequence in a given N-dimensional modulation code by generating a one-dimensional sequence of signals based on coded bits and uncoded bits. The modulation code is based on an N-dimensional population partitioned into code-related subsets, each subset having a plurality of N
represents a dimensional signal, and the device calculates, for each N-dimensional symbol, a one-dimensional related set of N M values corresponding to the match type of each N coordinate (modulo M) of the symbol. an encoder for obtaining a representative value Ck, where the representative value of each associated set represents a subset of the one-dimensional values in the one-dimensional population of possible coordinate values for each N dimension, and each one-dimensional signal in the sequence is selected from possible coordinate values based on uncoded bits.

In a preferred embodiment, the sequence of Xk or Yk can be taken as output, L=l, Yk
= Xk , k' = −1,
J is 1, each group is a one-dimensional range of values centered on βXk-1 (0≦β<1, preferably β>0),
There is a finite number of sets (eg, two disjoint) J-dimensional populations, and Yk and Xk may be real or complex values.

Another general feature is the sequence zk=Yk+nk (k
=1.2, , , ) into a decoded sequence Yk, where the sequence of signals Yk is: (a) the sequence is due to a given modulation code; Digital sum Xk=Yk+Yk-,+
Y k-2y 1, has the variance S, l of the batting limit, (c)
The signal ■k falls within a predetermined tolerance depending on Xk.(k'<k), and the sequence nk represents noise. The range violation monitor configures the expected operating digital sum Xk = Yk + y, -, +, , frf;
The decoded sequence Yk is compared with a predetermined tolerance range based on the expected operational digital sum Xk.(k'<k), and an indication is made whenever k is outside the tolerance range.

Another general feature of the invention is that the sequence Zk=Yk+n
k (k = 1.2, , ), where the sequence of signals Yk is such that (a) this sequence is due to a given modulation code and this code is a finite number Q (b) Yb = XkfXk-L(L
is an integer), where the sequence Xk has a finite variance 58
, and the sequence nl, represents noise.

The decoder corresponds to an encoder in which each sequence is (a) in the code up to time, (b) in a given state at time K, and (c) a finite number M of integerly spaced values (
For each combination of a finite number Q of states and +f+r It includes a modified maximum likelihood sequence evaluation means for finding for each of the marked values.

The present invention is adapted to known modulation codes, in particular trellis codes, for use in partial response systems;
Achieving substantial coding gain for any large number n of bits/symbols with reasonable decoding width parity, the same advantage that the code has in non-partial response systems. The present invention also provides that the design of the trellis code for partial response systems requires relatively small human signal energy S.

and a relatively small output energy Sy, and allows these two quantities to be smoothly exchanged with each other. Furthermore, high dimensional trellis codes can be adapted for use in essentially low dimensional partial response systems.

Other advantages and features will become apparent from the following description of the preferred embodiments and from the appended claims.

〔Example〕

According to FIG. 1, the present invention provides a method for generating a signal sequence to be used as an input to a partial response channel 10, which is a one-dimensional (real) 1-D partial response baseband system, e.g. zero at DC. including methods of (
In what follows we briefly show how to modify such a design for other types of partial response systems. ) Each output signal Zk of such a system is given by the following formula.

That is, Zk=Yk, +nk However, nk sequence (n(D)) represents noise,
The Yk sequence (y(D)) is a partial response coding (PRC) sequence defined by the following equation. That is, Yk :Xk -Xk-1 However, Xk sequence (X (D)) is a sequence of channel input.

Since Xk = Xi+-t +Yk, the Xk sequence can be recovered from the PRC sequence by forming a working digital sum of values Yk (given the initial value of the Xk sequence), and thus: The Xk sequence is called an RDS sequence. RDS sequence x(D)
and the sample variance of the PRC sequence y(D) is
Denoted as Sx and Sy, respectively.

The discrete-time partial response (1-D) (represented by block 12) is a well-known method for obtaining a composite partial response for a noise energy P (of the noise sequence n (D)) that is small compared to the PRC energy Sy. This is a composite response of a transmission filter array made up of , an actual channel, a reception filter, an equalization amount, a sample circuit, etc. This may require sending out a relatively large number of bits n per channel input. The detector (not shown) is X(D) (or, because of the one-to-one relationship between them, y(D)
)) is computed on the noisy PRC sequence z(D). If the detector is a means of evaluating the maximum possible sequence and the secondary f is for the first order, then the objective is to allow the allowed PRC sequence y(
D) The minimum mean square distance between 1f! The goal is to maximize I d21n.

In some applications, the design constraint is simply to minimize the sample variance Sx of the RDS (human input) sequence. In other applications, the constraint is on Sy. In still other applications, there is an effective energy constraint near the middle of the composite filter array, and it is therefore desirable to keep sx and Sy small, and in fact to provide a smooth design alignment between them. Would.

A related problem lies in the design of sequences with spectral zeros, e.g. O at zero frequency (DC). The aim is therefore to represent n bits per sample, have spectral zeros, have as small a sample variance S as possible, but have a large minimum mean, squared distance Ill d between the possible y(D) sequences. ``We will design a sequence y (D) that can have atn.

A common auxiliary objective is the operational digital sum (R
DS). The sequence of working digital sums x(D) is, for example, y(D)/(1-D)
Since the sample molecule lLS x is a measure of its dispersion, the invention is also applicable to the design of sequences with spectral zeros.

A number of design principles are effective in achieving these objectives. The first principle is the output (PRC) that takes N values at once.
The sequence y(D) belongs to a subset of an N-dimensional ensemble determined by a known N-dimensional trellis code.
The input (RDS
) to design the sequence x(D).

Therefore, Q@small mean square distance between PRC sequences is 11! l
d"mln will be at least greater than d"1n guaranteed by the trellis code. Furthermore, maximum likelihood sequence evaluation means for trellis codes may be easily adapted for use with this system and result in substantially the same, if not optimal, decoding as in the same trellis conid in a non-partial response system. One would achieve the same reasonable value d 2w1n for vergence.

One embodiment of the invention is based on a known 8-state two-dimensional trellis code similar to that of Ungerboeck as described in Reference No. 11, which transmits 6 bits per (20-dimensional) signal. (This also requires 14.4 kbps of data.)
It is similar to the code used in the CCITT Recommended Specification for Modems v.33. ) FIG. 2 shows the encoder 20 for this code. For every 6-bit symbol 21 sent from data source 23, two of the six input bits to encoder 20 are input to rate-2/3 eight-state convolution encoder 22. The three output bits of this encoder are used in the subset selector 24 to select one of eight subsets of the No. 18 population of 128 points shown in FIG. 3, with 16 points in each subset (
Points in the eight subsets are designated A to H, respectively).

The remaining four "uncoded bits" 26 (FIG. 2) are used in a signal point selector 28 to select from the selected subset the (two-dimensional) signal points to be transmitted. This code achieves a gain in d'+++in of a factor of 5 (7 dB) over the uncoded system, but using 128 points instead of a cluster of 64 points results in a loss of about 3 dB. The net coding gain is approximately 4 dB.

(One-dimensional form of a two-dimensional Ungerboeck code) The sequence of symbols xh sent on the channel is (1-
D) is one-dimensional in baseband partial response systems. Therefore, this reduces the known trellis code to 1
Useful (though not required) to transform into dimensional form. This transformation has two characteristics. That is, the first is to characterize a two-dimensional subset as a component of a one-dimensional subset that is an element, and the second is to characterize the infinite two-dimensional group as a component of a one-dimensional group that is an element. Here, the two-dimensional υngerboec of the case
We show how such a decomposition is done for a k-code, and then we show how it is done in the general case of an N-dimensional trellis code.

The first step consists of eight two-dimensional subsets A, B1,
, , each of two smaller two-dimensional subsets, say A. and A, , Bo, and B1, etc., and show that a relatively small subset of 16 in this case can be characterized as follows. (
The possible values of each coordinate of point 8 are classified into four types a, b, and c.
, d, and then let this relatively small two-dimensional subset consist of points each whose two coordinates lie in a particular pair type.

If we prepare Figure 3 so that point 13 is one unit divided into each dimension (and the coordinates of each point are half-integers), a convenient mathematical expression for this decomposition arises. , then types a, b, c, d are equivalent types (modulo 4), and there are 16 sets A, , A, , B, 1 . each of is part 2
be the point whose coordinates coincide with a given pair (x, y) modulo 4, where X and y each have four values (a,
b, c, d), for example (±1/2.±372). These four values are called "representative values of a (one-dimensional) coset." The cluster points in FIG. 3 are labeled 0 and 1 to indicate one possible configuration of the 16 subsets described above.

For example, point 29 of Go is x = 5/2, y = 9/
2 coordinates, and the representative value of the related set is (5/2.
9/2) Modulo 4 or C-3/2. I/2).

Here, FIG. 2 can be modified as follows. In FIG. 4, the three output bits of encoder 22 and one of the uncoded bits 30 are output to subset selector 32.
, which selects one of <16 subsets based on the four input bits, 80 and A
, , or Bo and B, uncoded bit 30 selects. Accordingly, the original 8 subsets are encoded in encoder 2.
The three convolution coded bits produced by In fact, encoder 22 and bit 30 represent an 8-state rate-374 encoder whose output selects one of the 16 subsets even though the set of possible signal point sequences is unchanged. Next, each of the 16 relatively small subsets of stiffness is represented for each coordinate by a representative value 34 of a pair of one-dimensional related sets, where the representative value C3 of each related set is one of the four values. Let's assume that we can take one. The representative value of this pairwise related set is expressed as (cI k+ 02k).

One feature of the present invention is that all of the above-mentioned good codes, namely the Ilngerboeck code, the Gallager:
This means that the F-Code, Wet Code, and Calderbank and 5Loaner-Code can be modified in the same way. That is, any of these N-dimensional trellis codes can be generated by an encoder that selects one of 4N subsets, where the subset corresponds to the match type of each coordinate (modulo 4).
is specified by a representative value of a one-dimensional related set of four values. In some cases, 2N subsets are used, specified by the match type of the valley coordinate (modulo 2) and the corresponding representative value (e.g., (±1/2)) of a one-dimensional related set of N binary values. All you need is that.

For example, in the case of II n g cr b o e c k code, there is a 4-state 2D code, Gal Iage
r code (and similar (:alderbank and S 1oane codes) 8-state 4D code, W
The ei code is a 1B state 4D code, a 64 state 8D code, and so on. It has also been observed that many good lattice-shaped codes can be transformed in this way, e.g.
The lattice E8 of sset can be represented by a sequence of 4 or 8 binary one-dimensional associated set representative values (modulo 2), and can be
B and Δ, 2 and Leech's lattice Δ24 can be represented by a representative value (modulo 4) of a four-value one-dimensional related set.

The general form of all of these codes is shown in FIG. The encoder is N-dimensional and operates once for every N signals sent on the channel.

In each operation, p bits enter binary encoder C33 and are encoded into (p+r) coded bits. These coded bits are 1 of the N-dimensional signal population 2P1
Select (in the selector 35) one (N-dimensional lattice Δ
29+r related sets and corresponding subsets of the sublattices Δ'.

The population consists of a finite number of sets of 2n+1 points of translation into the grid, such that each subset contains 2°-p points).

Further (n-p) non-coded bits select one signal point from the selected subset (in selector 37). To this end, the code uses a 2 nor N-dimensional population of signal points N to send n bits to an N-dimensional symbol 1rk.

The encoder C and the grid divisions Δ/Δ' guarantee some minimum mean square distance 11id2n+in between any two signal points belonging to the possible subset sequences.

The above observation (about the deformability of all good codes) is the result of mathematical considerations for all of the good trellis and lattice codes mentioned above, and N lattices in integer multiples of 4. 42N (and in some cases 22N
N) becomes a sub-lattice of the lattice A'. Therefore, some integer q
In this case, Δ' becomes the union of 42N 29 related sets in this A'. The practical effect of such a consideration is that if n≧Q+P, then (p+r) coded bits and 9 uncoded bits can be combined into 42H related sets of 2 'I"l"r in Δ. These related sets can be further identified by a sequence of representative values (clks C2 +, *, cNk) of N four-valued one-dimensional related sets. where CJk represents the type of equivalence (modulo 4) spaced by an integer! Thus, FIG. 5 can already be modified to resemble that shown in FIG.

In this modification, a group of 21 point signals is divided evenly into 2qo light subsets, each with the same number of signal points (
2''-'I-p).

An example of an illustrated Ungerbock code is that N=
2, Δ=72, Δ'=2RZ2, p=2, p+r=3
, q=1 and n=6.

The second step is to transform the population into its elements 1)-1
It is a decomposition into groups of dimensions. For the population in Figure 3, the valley coordinates are 8 "inner points" (e.g., (±l/2.±3
72. ±572. ±7/2)) or one of twelve values that can be grouped as four "outer points" (eg, (±972.±1172)).

Each of these four one-dimensional homogeneity types has two inner points and one outer point (for example: if these three points coincide with +172 (modulo 4), then The type whose representative value is +172 includes these two inner points +1/2 and -772 and the outer point 9/2). Therefore, given the representative values of some related set, we can tell whether a point is an interior point or an exterior point, and if it is an interior point, which of the two interior points is it? It is only necessary to indicate which This can be done with two bits, for example b+11 (=inside or outside) and bzb (=which is inside) (ie one ternary parameter ah).

It can be said that the pair (b+h, bzk) is a range that identifies a parameter ak that takes one of three values indicating the following three ranges:

That is, (a) 0 to 4 (inner point, positive) (b) -4 to 0 (inner point, negative) (c) -6 to -4 and 4 to 6 (outer point) A certain real number ( The fact that each range straddles a portion of the solid line of the sum [11] containing exactly one point that coincides with modulo 4) means that the parameter ak that identifies the range, and the representative value Ck of the associated set are cl This means that it indicates a unique signal point for any value of .

Therefore, the signal point selector 36 of FIG. 4 can be broken down as follows. In FIG. 7, three uncoded bits 40 enter the range identification parameter selector 42 for every six pairs of coordinates.

One uncoded bit determines whether the outer point is sent. If so, the second bit determines whether the coordinates of and include the outer point, and the third bit selects the inner point at the other coordinates. If not, both coordinates are interior points, and the second and third bits select whether each coordinate has an interior point. Thus, in summary, element 42 converts the three uncoded bits into two pairs of output bits 44, namely al = (b++, b+2) and C2 = (b21
+b22) and the representative value C of the corresponding related set generated by the selector 46 of the representative value pair of the related set.
1 or C2. In this way, the entire encoder has 6 seats, 4 m
2 bits of k (4B) represent Ck and 2 bits represent ah
= (blkl bak) (in the coordinate selector 50).

All groups commonly used in the code above can be decomposed in this way. These principles are described in our U.S. Pat. No. 4,597,090 and in For n
This is similar to what was discussed in the paper "Effective modulation" by E y et al. (an N-dimensional population is constructed from a component two-dimensional population), and the same This configuration was used by Wei in conjunction with the trellis code in Wei's US patent application, cited above.

The general form of the encoder for an N-dimensional code is shown in FIG. For each N coordinates, P bits 51 enter the encoder 52, producing (p+r) coded bits 54, which together with q uncoded bits 56 are representative of N related sets. value (-b(6
0), and the remaining (n-p-q) uncoded bits 62 are selected into the sequence of range identification parameters ak(66) (selector 6
4), and this is transformed together with Ck (in point selector 68) to obtain the values Xk(
70). In general, the range identification parameter ak has possible values cl, (modulo 4
), and this function f(ck, ak) selects this element. In all the above codes, the string of representative values of the associated set can be taken as values spaced by four integers (modulo 4), and for some codes, the string of representative values of the related set can be taken as values spaced by four integers (modulo 4). It is taken as two integer-spaced values (modulo 2) (in this case the range would be 'I]2).

The size of the string ak is the size required to send n bits per N coordinates. The signal point sequence produced by this form of encoder is approximately the same as in the original code, and in particular, the signal point sequence is divided by the same minimum mean square distance 111d''min as in the previous code.

(Preliminary Coding of Related Sets) When an N-dimensional constellation point sequence generated by a known good trellis code is serialized into one-dimensional constellation points, - generally (due to inter-symbol interference) It cannot be used as an input to the partial response channel of FIG. 1 without reducing d2n+in. However, a technique called related-set preliminary coding can convert these known codes into S
It allows application to partial response systems without increasing k or decreasing d2min. This general method is shown in FIG.

Same as that used by known trellis codes,
A convolutional encoder 52, preferably having the configuration of FIG. 8, is used.

The (p+r) coded output bits 54 do not select the subset directly, but rather the subset selection/serialization device 7
N 1s corresponding to the selected subset in the non-partial response system (as shown in FIG. 8) at 0
It is transformed into a sequence ck of representative values c1, . . . cN of the related set of dimensions. These associated set representative values are then converted into another (i.e. "pre-coded") associated set representative value sequence Ck (pre-coding device 72).
) is "pre-coded".

where ekl=Ck-1'+Ck (modulo 4) (this preliminary coding measure can be done modulo 2 if it is possible to use representative values of the relevant set of modulo 2). Thus, The pre-coded sequence of associated set representative values 74 is the working digital sum modulo 4 (or 2) of the normal associated set representative value sequence. The pre-coded representative values ck of the associated set can then be classified N at a time in the classifier 75 (in the signal point selector/serializer 76) to indicate N-dimensional subsets; Point 13 can then be selected in the usual way (based on uncoded bit 78) and the resulting signal points can be placed on the partial response channel (in the same order as previously coded) by N can be sent as a sequence x (D) of one-dimensional signals Xk.

If ck is a half-integer, one is 172 from the other.
The values ck alternate between two sets of four value openings that are shifted by a certain amount. This has only a small effect, for example the alternating coordinates (0,1,2,3) and then C is always taken from the same character, e.g. (±172.±3/2). These offsets of Ck or ck are It does not affect d”min.

If the encoder takes the form of FIG. 8, then FIG. 9 can take the form of FIG. 1O, with the same blocks doing the same thing. In particular, the function f (cl, , ak
) is characterized as a function that selects a unique element that matches ck within the range identified by ak, so there is no problem even if preliminary coding changes the string Ck' to the string Ck, and in fact, Although perhaps useful in implementation, (modulo 4) in the precoder is unnecessary in principle.

In either Figure 9 or Figure 10, the PRC sequence (Yk = Xk for at least the same d2
It can be shown that it has min. The RDS sequence Xk has the same average energy Sx as in the original trellis code if the string ck' is the same as the string Ck, and still maintains the appropriate equivalence if not. (In the example, the average energy for each coordinate is +0.25 for signals with integer intervals.)
If Ok is an integer, then Xk is an independent random number with the same distribution, so (a) S, = 23x (b) The spectrum of the RDS sequence (Xk ) is flat (white) within its Nyquist band. (c) The spectrum of the PRC sequence (Yk) is the same as that of the partial response channel.

These descriptions are still approximately valid even if ck is not an integer.

The preliminary coding of related sets can be modified for other types of partial response systems as described below. (1+
D) For a (one-dimensional) partial response system, ck・=
Instead of being added in the precoding device 72, the ck-
The same system is used except that 1' is subtracted.

(1-D)' In the system, c 1. '=Ck-
Delay element 1 is replaced with delay element 2 so that L'+Ck'. In the case of a two-dimensional system of (1+D),
The manual input has paired outputs from the subset selector/sequential device, and the two outputs determine the real and imaginary (in the in-phase and quadrature quadrants) portions of the two-dimensional signal points to be sent out (1+D ) using precoding devices in parallel.

(RDS Feedback) Depending on the application, the average energy Sy of the PRC sequence may be increased at the expense of increasing the average energy Sx of the RDS sequence.
It may be desirable to reduce This is also R
PRC while increasing the low frequency content of the DS spectrum
Beating the trend down the spectrum. , 1uSLcs
[Information Velocity and Energy Spectrum of Digital Codes J (IEE [Trans, Inf.
orm, Theory.

Volume 1T-28, pages 457-472, published in 1982)
introduces the cutoff frequency Jf below which the PRC spectrum becomes smaller and flat, and shows that this f is approximately (S, /2Sx)f (however, , f is the Nyquist band edge frequency).

d'mi of trellis code in PRC sequence
A common way to achieve this trade-off while maintaining n is to extend the encoder of FIG. 9 or 10 as follows.

The PRC sequence can be calculated from the RDS sequence, and for a (1-D) channel, each PRC signal is just Yk=Xk-Xkt.

In FIG. 11, ('!i
) by feeding back a large PRC value Yk
The base of the signal point selector 80 is then set to the representative value ck of the associated set of P codes (calculated in the adder 84).

and Xk-1, and also the range identification parameter a.

It can also be placed in As long as the signal Xk is still chosen to match Ck' (modulo 4), the signal Y
k will be equal to Ck (modulo 4), thus preserving the d'mi mouth of the trellis code. (The idea is to calculate the PRC value Yk in advance, but what is actually fed back is the previous RDS value
k-1, so this is called RDS feedback. ) In an embodiment, this can be done as follows. As already mentioned, the normal selection function f (ck, ak) of the selector 80 has eight inner points between -4 and +4.
, but the four outer points can be characterized by being four half-integer values in the range -6 to -4 and +4 to +6. As long as the range of points inside the above spans eight signal points, two from each homogeneity type, and the range of points outside spans four signal points, one from each homogeneity type, the points inside this The range of and the range of outer points can be changed as a function of Xk-1.

A common way to do this is to define all ranges as
This is to perform parallel translation using a translation variable R(Xk-+) which is a function of -1.

That is, in the example, the range of inner points is -4+R(
X+t-+) to 4+R(Xk-+), and the range of the outer points ranges from 16+R(Xk-+) to -4+R(Xk-t), mata 4+R(Xk-+).
+) to 6+R(Xk-+).

The function R(X k-+ ) should generally increase with x, -1 so as to generally decrease Yk. We were able to show that the best choice is R(Xk-+) = βXk-1, where β is a parameter in the range 0≦β≦1. When β=0, RD flowing to element 82
The feedback of S disappears and FIG. 11 performs the associated set of precoding operations as in FIG. 1θ.

With this selection, if S. If is SK in the normal case (β=0), then the following is approximately valid. That is, (a) Sx=So / (1-β2) (b) S, = 2 So / (1+β) (-c
) RDS sequence spectrum S, (f) is 1/(
1-2β CO3θ+β2).

However, θ=πf/fN (d) PRC sequence spectrum S, (f) is 2
It is proportional to (1-CO8θ)/(1-2βcosθ+-β2). "The cutoff frequency Jfo is (1-β)fN.

(e) If the range of coordinates in the normal code is -M/2
to M/2, Xk is limited to the range from -M/2 (1+β) to M/2 (1-β), and Yk is -M
to M.

When β approaches 1, Sy becomes S. , S,(f) approaches a flat spectrum with an abrupt 0 at DC. On the other hand, Sx increases, and Sx (f) approaches a spectrum of 1/(1-D), except that it maintains a finite value near DC. We were able to show that this is the best compromise between Sx, S, and S0.

Figures 12, 13 and 14 are ck s a
Based on k and X k-1, Xk and/or Y
Three equivalent methods of generating k are shown.

In FIG. 12, since C' k-1 = Xk-, (modulo 4), -1 becomes Xk-1 in the feedback variable C' in the preliminary coding device 72 of the related set.
, and only the value of C'b (modulo 4) is used in the selector 80.

R(ak) indicates the range identified by ak, R(X
k-1) represents the range translation variable caused by the R-S feedback. Yk=Xk-X k-1miC”k
Xk-+C modulo 4) and c' @ Eic
Since k+Xk-+ (modulo 4), Yk
ECb (modulo 4).

Figures 13 and 14 show that if these are the same initial value
It is mathematically equivalent to FIG. 12 in the sense that having the same sequence of k-1 and human forces (cl, ak) produces the same set of outputs (Xk, Yb). In FIG. 13, Yk is in the range R(at+ >+ R(Xk-,)
-Xk-+ is chosen as the unique element matching ck in +, and Xk is determined from Yk as is a unique element in the range R(ak) +R(Xk-+) which also coincides with Co, (modulo 4).In Figure 14, the new variable i, is the unique element in the range R(ah) ″-Eck+Xk-
+ R(Xk-+) (Moshu-o 4)
2 is selected as the unique element matching the knee, and Xk
is determined from iI4, and C
′(modulo 4), the range R(a,, )
+R(x, -1) is a unique element.

FIG. 12 shows the delay elements in the precoding device as RD
In combination with the necessary delay element for S feedback, it is most effective if Xk is the desired output and C'k is always from the same string, e.g. (±l/2.±372). .

Figure 13 shows the preliminary coding device removed,
It is most effective if ■k is the desired output and Ck is always obtained from the same string, for example (±172.±372). Figure 14 takes a range translation variable R(Xk-+) outside the selector so that ik is always selected from the same range (the union of all R(ak)) and a new sequence i (D ) is a sequence of approximately independent and identically distributed random numbers ik (ignoring small deviations introduced by the coincidence constraints on c'), and this subsequence is defined as if X(D) or Y(D) This may be useful if a closely related white (spectrally flat) sequence is required.

Figures 15, 16, and 17 show X(D) and Y(
D), and i (D
) shows three identical filter structures used with the sequence. In FIG. 15, the RDS sequence X(D) is transmitted (signal s
(t)), the transmit filter HT(
f). In Figure 16, P
RC sequence Y(D) is transmitted filter H”r(f)
Since Y(D) has the value of DC zero, (in particular, It does not matter that the response of l/(1-D) is infinite at DC (if H'r(f) also becomes DC zero). In Figure 17, the new sequence i (D) is filtered in the output filter H''7(f) and its response is a cascade combination of the 1/(1-βD) sample data filter and HT(f). is equivalent to the case, i.e. if R(Xk-+) = β
If Xk-+ te, it is equivalent to the cases in Figures 15 and 16; otherwise, equivalent sample data filters are approximately nonlinear.Xk = ik + R (
This is a filter corresponding to Xk-+). Any of these equivalent forms is desirable if HT(f), R(Xk-1) and this implementation are used.

Certain modifications of the RDS feedback system described above are desirable in implementation. For example, it is desirable to change the form of range R(ak) from that used when R(Xk-+) = 0.

For example, in an embodiment, a simple configured RDS configuration is as described above. When X k-1 is positive, if ak indicates an inner point, Yk is usually selected within the range of -4 to 4, but if ak indicates an outer point,
Yk is a number that matches Ck within the range of -4 to -8,
If,X,-,is negative, use a range of 4 to 8 for the outer points. Therefore, (a) When there is no RDS feedback, the range of the PRC sequence Yk is −7 instead of −11 to It.
172 to +71/2.

(b) The dispersion of the PRC, s, is reduced from 20.5 to 13.25, resulting in a decrease of 1.9d B, and S 0 = 1
If it is 0.25 or more, it will be about 1.1 dB.

(c) If X k-1 is negative, the average of Yk is -372
As a result, the RDS sequence tends to wrap around 11 around zero. Although it is difficult to calculate Sx accurately, E [YkXk-+] = S, /2 and E
['ykXk-11=-(3/2)E[1Xk-11
According to the fact that the average absolute value of
is fairly well defined. (If there is no RDS feedback, the average absolute value of Xk will be 2.75)
(d) Given Xk-1, the variance of Yk is S. =32
, M is 1 and is approximately 0.3 d B higher than 50=IO,25 which would occur if no RDS feedback was present. When S, = +3.25, so = tt, the minimum Sx that can exist is Sx, = 19.5, and β: 0.6
Corresponds to 6. 5X=s, , +i: [IXl]", so Sx must be larger than (4,42) 2 = 19.5, so in such a simple way, Achieve quantity.

(e) Each Yk that may exist is a unique pair of values (ck r
ak). As discussed in more detail below, this means that the decoder does not need to keep track of the estimated working digital sum of the estimated PRC sequence, and also means that there is no error propagation at the decoder. .

In summary, although such a simple method does not achieve the best power and energy exchange between Sx and Sy, it does not effectively limit the peak values of not only S, but also Yk. This is to keep Xk in a relatively well constrained state and avoid error propagation on the receiver 3 side.

Thus, these methods (i) use the same energy S as would be required to send out n bits per symbol if the Xk sequences were uncorrelated and Sx was not a partial response;
0 and 5y=23, and (1i) the Yk sequences are uncorrelated and S,=S
, which allows 58 to S,(i) interactions in most cases where,S,l,becomes very large. Such energy exchange is possible in all of the trellis and lattice codes mentioned above.

(Decoding) The methods described in 1-1 are PRCs belonging to known good codes.
The sequence is successfully generated and therefore has at least the same d''min value as in the case of the code.

In FIG. 18, the appropriate detector for the PRC sequence Z (D) = Y (D) + n (D) that the noise receives is the maximum possible for a known good code adapted as follows. Sexual Sequence Evaluation Instrument (ViL
crbi algorithm).

(a) The first stage of decoding is the representative value CJk (modulo 4) of four one-dimensional related sets (where j = 1.2, 3
．． For each of the four types of real numbers that match 4), for each P reception RC value Zb = Yk + nl including noise, the element YJk closest to Zk in the valley type and its "distance" value m Jk = (YJk - 2k) 2 (square iI from zk
I! (block 92).

(b) In a code based on an N-dimensional lattice partition Δ/Δ′, the second stage of decoding consists of the related set 2 of Δ′ in Δ
per 17), the one-dimensional distance 1ull of the component
By adding the distances m and H and comparing these sums, we can find the best value (minimum distance!!) of the 42N related set 29 whose union is the related set of Δ' (Block 94).

(c) Decoding may proceed in the usual manner using the pawl distance determined in step (b) as the distance for each associated set of Δ' (block 96). The decoder can finally perform an evaluation of the sequence of related sets of A' and map this to a sequence of estimated related set representative values Ck, and this representative value can be replaced with the original ak and Xk can be restored (block 98). These last steps require tracking the working digital summation Xk-1 of the evaluation values Yk.

Since the PRC sequence is included in a known code, the error probability of this decoder is at least the same effective value d2m
It will be at least as good as the known code in terms of achieving in.

However, since a PRC sequence is actually only a subset of known code sequences, such a deco-da is not a true maximum likelihood sequence evaluation tool for a PRC sequence. As a result, the decoder may inadvertently decode a sequence that is not a proper PRC sequence. A proper PRC sequence must: - satisfy two other conditions:

That is, (a) The proper finite PRC sequence Y(D) is (1-I
)), that is, the sum of its coordinates must be 0.

(b) The :bll approximation of the range imposed by the signal point selection path is based on the reconstructed values of x,−1 of the RDS, Yk
(or similarly Xk or ik) must be satisfied for all.

If this decoder produces a normal decoding error corresponding to a short period of incorrect association set evaluation following a correct association set evaluation t(, then this corresponding finite PRC error sequence is non-zero. This will give rise to a member error in the decoder's estimated working digital sum Even if it is appropriate, Yk, ak,
Furthermore, there is a possibility that an accidental mapping error may be caused retroactively to Xk.

Therefore, the decoder must continuously monitor (block 99) whether the range constraints on the reconstructed Yk and Xk are satisfied. If this condition is not satisfied, it is known that the evaluated RDS Xk-1 is incorrect, and assuming that the sequence Ck of the related set is correct, the minimum value necessary for the range constraint to be satisfied is Xk-1 must be adjusted by the amount. If the probability is 1, then the result is that the evaluation RDS will eventually be resynchronized to the correct value, and normal decoding can be resumed. However, there may be a significant error propagation period.

(Error propagation times J!) Next, we describe a general method to avoid error propagation at the receiving end. works well, but is not limited to such cases; it can be seen as a generalization of the principle of an earlier precoding form (modulo M) used for coded sequences. can.

The basic idea is that when the code can be organized in a one-dimensional form such as in Figure 7, each possible PRC value
This means that k must correspond to a unique (ck, ak), and more generally, if a general N-dimensional signal point selection path as in FIG. 6 is used, then N The problem is that each group of Yk values does not correspond to a unique sequence of N cks, but must also correspond to an arbitrary set of uncoded bits. Therefore, the inverse map from Yk labeled 1 to coded and uncoded bits operates such that (a) the decoder does not have to track the RDS, and (b) error propagation does not occur. It is independent of the evaluation of the digital sum on the decoder side.

Therefore, block 99 in FIG. 18 can be removed.

, FIG. 19 shows how this can be done if the code can be represented in one-dimensional form, as in the illustrated embodiment. The signal point selector selects the value 5k=f (cb , a
Select l().

In the example, sk is one of 12 values, namely -6
Takes a half-integer value within the range of 6 to 6.

In general, sk will take one of the values from a string of integer intervals within the range 111 to M, and this range is denoted Ro. Next, as shown in FIG.
is chosen as a unique number that coincides with Sk (modulo M) in the range Ro + R(Xk-r) -Xk-1, where R(Xk-t) is the feedback transformation variable of the RDS and Xk -1 is the signal point of the previous RDS. At that time, (7)RD S Xk is (Yk+Xk-
+).

20 and 21, like FIGS. 12 and 14, are equivalent methods of generating Xk and/or Yk from the sequence S, such that Yk=sk (modulo M). In FIG. 21, an innovation variable ik is generated that is more or less white and evenly distributed within the range R6, so that its variance S0 is approximately M2/1
2, and therefore S in the embodiment. ! :t12, that is, a penalty of about 0.7 in the value 50=10.25 obtained without RDS feedback. As in FIGS. 12, 13, and 14, 3
The two total sequences Xk, Yk and ik contain the same information and can all be used as inputs to filters that shape the spectra for transmission, as in FIGS. 15, 16 and 17.

The penalty in the new reasoning is that if the coordinates of the original code are divided evenly over the range R0, then
That is, if the original group is surrounded by N cubes with one side of R8, it is excluded.

The same two-dimensional 8-state II n g a r as in FIG. 2 as in the illustrated embodiment involving a rectangular population, except in the case of the 128-point population of FIG. 22 instead of FIG.
b (using a l a c k encoder. This population consists of alternating points from a conventional 256-point (16X16) population, so that the coordinates are half-integer values of 16 (±l/
2. ±372, , , ±1572), but the sum of the two coordinates is an even number choice - i.e. (0, modulo 2)
There is a restriction that it must be. Therefore, the minimum mean square distance between signal points is! 2 instead of 2, and the code's d"min becomes 10 instead of 5. The variance of each coordinate is now 21,25, not 10.25, which is 2
After scaling L/, there is a loss of 0.156 dB associated with Figure 3, since the intersection is a circle rather than a square (in grating terminology, Z 8-like lattice partition RZ2/4Z'' instead of '/2RZ') where each of the eight subsets is Ct +c2 = 0
The representative value (cl, cz) of a unique pair of related sets corresponds to modulo 4 so that the value is modulo 2). Therefore, the three coded bits of FIG. 2 directly determine the representative value of a pair of related sets in the subset selector 24, without the aid of uncoded bits as in FIG. Then the four uncoded bits are
Select one of the 16 points in the selected subset. In this case, the uncoded bits can only be taken two at a time to determine one of four ranges: -8 to -4, -4 to 0.0 to 4, or 4 to 8. This is a 2-bit range identification parameter (al,
R2) each represents one of four values (±2.±6), so the coordinate selection function is simply 5k=f(ck,ak):Ck+ak. , the possible values for Sk are rl1M=16
Note that there are 16 half-integer values in the range -8 to 8.

Therefore, conventional precoding can be performed modulo 16. The entire encoder is shown in FIG. R.D.
The S value Xk is the sum (Sk+Xk-+) (modulo 16)
It is. In this case, the Xk values are essentially independent similarly distributed (white) random variables, and Yk=X@
-Xk-tmiSk (modulo 16).

As in FIGS. 12, 13, and 14, RDS
In order to exchange spectra through the feedback of Ideally βX as in
Let the RDS feedback variable be equal to k-1. Next, in FIGS. 24, 25, and 26, Yk =5. (
% juro 16), and S) as 50 = 21.25
Three equal ways of obtaining the sequences Xk and/or Yb=Xk-X k-1 are shown, such that l and Sy have the required interaction.

Here, Ro is in the range of -8 to 8.

In this case, the innovation variable ik has a variance 5o==16271 which is substantially the same as the variance of each coordinate in FIG.
2=21.3:l, so that the second figure instead of the third figure
No penalty of more than 0.16 dB occurs when using Figure 2.

As already mentioned, the decoder does not need to monitor the RDS, but it does not need to monitor the evaluated PRC sequence Yk,ck
and ak, and finally the original manual bit sequence is uniquely determined. However, if the decoder monitors the evaluated RDS and the corresponding range that k should fall in, it will detect that an error has occurred whenever the decoded Yk is outside the evaluated range. Can be done. Even if not used for error correction, monitoring of such range violations can yield predictions of the decoder's error rate.

(Augmented decoder) The true maximum possibility sequence evaluation means is
All states of the encoder and channel will be considered, including the value -1 (the state of the channel) and the state of encoder C.

Such a decoder detects the true d”mi of the PRC sequence.
n is ensured and there is no error propagation.

However, such a decoder is impractical since X k-1 generally takes on the value of a large number, perhaps an infinite number in the RDS feedback. Furthermore,
As will be explained in more detail below, when n is large the code/channel combinations become - far-fetched;
Obtaining the true d''min may require virtually infinite decoding delay.

However, it may be worth augmenting the decoder to at least ensure the true d"min of the code. Since every finite number of PRC sequences is divisible by (1-D), every finite number of PRC sequences is divisible by (1-D). The weighted error sequence must have an even weight, so the true d2min is always an even number. In the example, the true d2min is actually 6, not 5.

In such cases, a general method to achieve true d2a+in by simply doubling the effective state at the decoder is as follows.

Let us divide the decoder into two for each state of encoder C, one corresponding to even RDS and one corresponding to odd RDS. During decoding, two sequences coalesce into the same state if only their evaluated RDS have the same value (modulo 2). Therefore, it is impossible for two sequences with only an odd weighted error sequence to be combined, so that the effective value d2mi
n becomes the weight of the smallest even weighted error sequence in the original code.

Furthermore, if there is a decoding error that results in a consistent estimated RDS error as described above, this error must be at least 2, which will have a tendency to be detected sooner or later.

The decoder of FIG. 18 can be used by simply modifying it as shown in FIG. In the case of Hatonto code,
Each subset of the signal population (an associated set of 8 in 8) contains points whose sum of coordinates are all either even or odd. For example, in FIG. 3, four of the eight subsets include points whose coordinates sum to O (modulo 2), and four include points whose coordinates sum to 1 (modulo 2). In this way, each subset (A
The distance of the associated set of Δ' in 0 can be determined as before in blocks 92 and 94, and then the maximum likelihood sequence evaluation means 196 (a) included in the code and (b) Modified to find the best sequence of related sets with matching actuation digital sums (module port 2). The decoded related set sequence is again Yk in block 9B as before.
and Xk, and if necessary, the adjustment of Xk-, is performed by block 99 (if the adjustment is made, it is a multiple of 2).

However, this approach has disadvantages in addition to doubling the state space of the decoder. The two sequences are
Odd weighted error followed by a long string of zeros (no difference)
Only the sequence can differ. The decoder then follows the states of parallel pairs in the decoder's trellis code for a very long time without introducing ambiguity.

Such "quasi-anomalous" behavior can eventually be resolved by means of maximum-likelihood sequence evaluation, simply due to range violations due to different RDS parities in the two paths. Therefore, the decoding delay required to achieve true d2min can be very large.

For this reason, it is generally desirable to simply choose an encoder C with twice the number of states and use an unaugmented decoder for C.

For example, a two-dimensional Un of 16 states with d2min=6
A gcrbock code is preferred in implementation even though it has a slightly larger error factor than an 8-state code with an enhanced 16-state decoder.

4-state two-dimensional II n g cr b o e
Since the c k code has d"m1n=4 and the slightly weighted 4 error sequence is a - coordinate error of magnitude 2 and cannot be divided by (1-D), 01 IJngcr
The PRC sequence derived from the boeck code also has a true d2iin of 6. A 16-state decoder that monitors RDS modulo 4 can achieve this d"min. However, even when the error coefficient is large without deception, which is a quasi-anomalous code, the normal 16-state two-dimensional υn
The gerboeck code is a welcome break.

(Quadrature Modulation System) As mentioned in ``Quadrature Modulation System'', a complex (i.e., quadrature) partial response system (QPR5) is a complex-valued PRC sequence L
kodan) = (1 + D)
It can be modeled as a (1+0) sample data filter operating on a complex-valued RDS sequence (1+0) to yield X1-1. When used with double sideband quadrature amplitude modulation over a given band channel, such a system results in both band edges,
That is, it becomes 0 at fc+fN, where fc is the frequency of the carrier wave, and fN=1/2T is the width of one Nyquist band.

When N is even and 42N is a sub-lattice of A', as in all the good codes mentioned previously, a known good code can be converted into a QPRS system by using essentially the same principles as before. Can be adapted for use. 4
The 2'4 related set can be specified by the representative value Ck of the related set of N/2 complex number values, where the representative value of the related set is the real part of dan- and lJl, respectively.
Take one of 16 possible values corresponding to four integer interval values (modulo 4) for the number of items.

The overall diagram of FIG. 8 is valid except that the related set selector 58 and the range identification parameter selector 64 select the representative value Ci and the viewing identification parameter ai of the related set having a complex value of N/2. However, the signal point selector operates once for each quadrature signal to output a complex-valued signal X-.

Pre-coding of the associated set as in FIG. 9 is carried out by forming -1 (modulo 4) on the pre-encoded associated set of complex values once for each orthogonal symbol. It will be done. Figure 11, Figure 12, Figure 13
The RDS feedback as in the figure consists of one element from any of the 42" related sets and ideally βX
A function R(a
k).

If 2Z” or 2RZ2 is a sublattice of Δ′, the precoding is modulo 2 or (2+2
i) and step (a,) can identify a region of zone 4 or 8 that contains exactly one element from the relevant set of either 2Z2 or 2RZ2, respectively.

(Higher dimensional system) By feedback of the previous RDS value Xk-1 in signal units, the coordinates of the N-dimensional symbol are changed to
An example formed in the instep position is shown here. Similar performance can be obtained with systems that select signals based on higher dimensions. In such a system, the representative values of the pre-coded association set must be grouped as shown in Figure 9 to select a subset of the appropriate dimension, so that the signal points are selected in this dimension. and therefore the coordinates are also serialized again for sending out on the channel. If the order of related sets is maintained, such a system preserves the property that a PRC sequence is from a given code and has a specified d2n+in. In such a system, (RDS
) It is more natural to perform feedback in higher dimensions rather than signal by signal.

(N-dimensional code) Although code representation in one-dimensional form is desirable, this is not essential. In tree terms, the code is N as in
We show how it can be generated directly in dimensions. In one form, an N-dimensional code is completely equivalent to its one-dimensional counterpart. In other forms, simplified embodiments are obtained.

Also, for illustrative purposes, in addition to the two-dimensional 128-point group in FIG. 3, the 8-state two-dimensional Llnger
Use boeck type code. In this group,
Each coordinate takes a value from a string of 12 half-integer values in the range -6 to 6, and the two-dimensional population uses 128 of the 144 possible pairwise combinations of the elements of this string. .

As a first step, we expand the signal population to an infinite number of values as follows. The expanded population is the original (in Figure 3)
Let it consist of all pairs of numbers that match a certain point in the population (modulo 12). Thus, points in the expanded population consist of paired half-integer values.

If we consider the original population as a cell bounded by a 12x12 rectangle 98, the expanded population is defined by the second (infinite Consists of repetition.

Each cell holds only 128 of the 144 possible points, and there are 4x4 "holes" 99 in the expanded population.

The main characteristic of this expanded population 101 is that if 12X
If we place the 12 squares somewhere in the plane (with the sides oriented horizontally and vertically), the squares will contain exactly +28 points, each coinciding with each point in the original population.

A further generalization is also true, if we place a rhombus 102 (see Fig. 29) with horizontal rIJ 12 and vertical height 12 somewhere in the plane, this too each contains 128 points that match each point in .

In Figure 32, where M is 0, the RDS feedback can be configured in two dimensions as follows.

X k-1 is all Y preceding the symbol (in the current quadratic dimension)
Let k represent the operational digital sum.

Here, both the shape and position of this rhombus are made to depend on Xk-1, and R(Xk-+) represents a region of the surface corresponding to the 12x12 rhombus shapes as shown in Fig. 29. do. (YOok % yo l kya,) is,
With 3 coded bits and 4 uncoded bits according to the unconstrained code (Figure 2)
In the selector +04.105), let denote the point in the original population that is selected. Then (in the selector 10B) exists in the region R(Xk-t) and (Yo, k
, YO, as a unique point in a two-dimensional extended population corresponding to (Y
k, Yh+t), which become two coordinates Yk. As shown, Xk = Yk +Xk++,
k++ = Yk++ +Xkh") (Xk, Xk pass) can be obtained.

This two-dimensional system then produces the same output as the one-dimensional RDS feedback system shown earlier (modulo +2), with an optimal one-dimensional RDS feedback variable R(Xi,-+) = βXk-1. Show what you can get. In FIG. 31, in one dimension, Xk
−1 is given, ■k is selected as the unique value in the range (RO+βX h−+ −X k−+ ) that matches Sk (modulo 12), but here Sk
It is acknowledged that is the same as Yo. Therefore, it can be considered that the coordinates of one of the rivered diamonds in the two-dimensional system exist in the same range of 111, ie, 12. Next, if Xk-1 and ■k are given, and therefore x+, = Yk + Xk-1 is also given, then Y k+1 is in the range R, - (1 −β)Xk=Ro
-(1-β)Yk-(1-β)Xk-+. In this way, Yk, , is −(
Range R0-(1-β)Xk-+ shifted by 1-β)Yk
(similar to Yk).

Thus, with proper diamond selection, a two-dimensional system can mimic the performance of a one-dimensional (modulo 12) RDS feedback system. For this reason,
This provides the same advantages, including avoiding error propagation and best-neighbor interactions between Sx, S, and 30, and the same disadvantages, i.e., a significant increase in So to 12 over 10.25 that could otherwise occur. will have.

To further simplify the configuration, other two-dimensional RDS feedback variables (domains) can be selected and other benefits achieved at the expense of near-optimal power regulation.

For example, if x k-+ is positive, then R(X h-+
) is a rectangle 120 with 12 sides centered at (-2, -2)
, and when X k-1 is negative, it is a rectangle 122 centered at (+2, +2), which results in a system that is almost the same as the simplified one-dimensional system described earlier. . Thus, one of the two populations 124, 126 shown schematically in FIG. 32 is used.

As in the previous one-dimensional system, the interior points are Xk
-1 is always selected from the same set, but the outer points are changed to bias Yk in the positive or negative direction. The range of Yk is strictly limited to -71/2 to 71/2. In reality, this system is Yk+l
is the same as the previous simple system, except that is selected based on Xk-1 rather than Xk. In practice, all measurements of performance and spectra will be very similar.

Another modification is to add aldarbank to 1. e yields a system akin to e and Maxo type systems.

CLM-type systems are used when X k-1 is positive, and the other when X k-1 is negative.
We use an expanded signal population with twice the normal number of signal points, divided into two disjoint populations. for example,
Figure 33 shows a 16x matrix divided into two disjoint interpopulations of 0.112 every 128 points such that each population is evenly divided into 8 subsets of 16 points each.
16 square groups are shown. One group consists of points used when the sum of their coordinates is positive or zero and Xk-1 is negative, and the other group consists of points used when the sum of their coordinates is negative or zero and Xk-1 is positive. There are a number of points that are used when In two dimensions, doubling the population size doubles Sy, which does not result in good power exchange, but in higher dimensions there is a penalty for using two disjoint populations. becomes relatively small.

Such a concept can be generalized to N dimensions as follows. If there exists an N-dimensional form of the code with coefficients M as in Figure 8, then an N cube of edge M completely encloses the N-dimensional population, and the resulting cell is the original code. can be copied to encompass N spaces without compromising the least squares distance between the code sequences that match the sequence (modulo M). Therefore, the N-dimensional R-DS feedback relation % R
(X b-t ), but in this case for every X k-1, R(Xk-t ) is the third
In the N-dimensional analogue of the 0 diagram, there will be N spatial regions of volume M' that contain exactly one point in each equivalent type of N vectors (modulo M).

Other embodiments are within the scope of the following claims.

[Brief explanation of drawings]

FIG. 1 is a block diagram showing a (1-D) partial response channel, FIG. 2 is a block diagram showing an encoder for an 8-state Ungerboeck:ff-code, and FIG. 3 is an Ungerboeck code divided into 8 subsets. 4 is a block diagram of an equivalent encoder for the Ungerboeck code, FIG. 5 is a block diagram of a general N-dimensional trellis encoder, and FIG. 6 is a block diagram of a typical related set. Fig. 7 is a block diagram showing an equivalent one-dimensional encoder, Fig. 8 is a block diagram showing an example of modification.
10 is a block diagram showing a general N-dimensional trellis encoder, FIG. 9 is a block diagram showing a general encoder that performs preliminary coding of related sets, FIG. 1O is a block diagram combining FIGS. 8 and 9, and FIG. 12, 13, and 14 are alternative embodiments of FIG. 11; FIGS. 15, 16, and FIG. 17 is a block diagram showing three equivalent filter operation devices, FIG. 18 is a block diagram showing a general decoder, FIGS. 19, 20, and 21 are block diagrams showing alternative encoders, and FIG. 22 is a block diagram showing a general decoder. A diagram showing different signal populations,
FIG. 23 is a block diagram of an encoder used with the population of FIG. 22; FIGS. 24, 25, and 26 are block diagrams showing three peer encoders; and FIG. 27 is a block diagram showing a peer decoder. 28 is a schematic diagram showing an expanded signal group, FIG. 29 is a diamond diagram used for the group in FIG. 28, FIG. 30 is a block diagram of a two-dimensional RDS feedback encoder, and FIG. FIG. 32 shows a pair of groups, and FIG. 33 shows two disjoint groups. 10--Partial response channel, 20--Encoder,
22--Rate 2/38 bad convolution encoder, 23--Data source, 24--Selector, 28--Signal point selector, 33--Binary encoder C
135, 37... Selector, 42... Parameter selection device, 52... Encoder, 5a, 64... Sequence selector, 68... Signal point selector, 70-... Subset selection/sequential conversion device. Page 121 of Joa (no change in content) tυ IGI FIG, 10 FIG, /8 FIG, 19 G DaDGDGD AHAHAHAH BEBEBEBE FCFCFCFC GDGDGDGD FIG, 22 FIG, 26 FIG, 27 King Xk- k- to Yuu FIG, 32 Procedures Amendment 1. Case indication Patent Application No. 41783 of 1988 2, Name of the invention Partial response channel signal system 3, Person making the amendment Relationship to the case Patent applicant Address Name Codex Corporation 4, Agent 5, Subject of amendment

Claims (1)

[Claims] 1. The relationship between the signal X_k and the signal Y_k is Y_k=X
An apparatus for generating a sequence of digital signals X_k and/or a sequence of digital signals Y_k such that _k±X_k_-_L (k=1, 2, . . .; L is an integer), wherein said signal Y_k is a sequence in a given modulation code, J said signals Y_k (Y_k, Y_k, Y_k_+_1,,,Y_k
_+_J_-_1), a representative value of the associated set is specified in conjunction with the given modulation code, and the J symbols are selected from one of a plurality of J-dimensional populations. , the selection is made on the basis of the previous 2. A device comprising both, wherein said encoder is configured such that said signal X_k has a finite variance S_x. 2. The relationship between signal X_k and signal Y_k is Y_k=X
_k±X_k_-_L (k=1, 2, ,; L is an integer)
The digital signal X_k (k=1, 2, ,
.
A device characterized in that it is provided with an encoder for selecting said signal X_k to match a sequence of (modulo M). That is, when Y_k=X_k+X_k_-_L, c_k'=
When c_k=c^-'_k_-_L (modulo M), Y_k=X_k-X_k_-_L, c_k'=
c_k+c'_k_-_L (modulo M), and c_k is a representative value of the associated set specified according to the modulation code. 3. The relationship between signal X_k and signal Y_k is Y_k=
a sequence of digital signals X_k and/or capable of representing n bits per signal such that
Apparatus for generating a sequence of digital signals Y_k, said signals X_k and Y_k having variances S_x and S_y, wherein said signal Y_k is a sequence of possible signals evenly spaced at intervals Δ within a string. In a device in the string Y_k, the sequence Y_k has a variance S_y smaller than 2S_o.
and the sequence X_k has S_y^2/4
Apparatus comprising an encoder having a variance S_x not significantly greater than (S_y - S_o), S_o being approximately the minimum signal power required to represent n bits per signal in a Δ-spaced string. 4. Device according to claim 3, characterized in that the sequence Y_k is a sequence at a given modulation code. 5. The relationship between signal X_k and signal Y_k is Y_k=
An apparatus for generating a sequence of digital signals X_k and/or a sequence of digital signals Y_k such that Y_
an encoder which causes the signals X_k and Y_k to have selectable variances S_x and S_y within a predetermined range in the apparatus where k has variances S_x and S_y and said symbol Y_k is a sequence in a given modulation code; A device characterized by providing: 6. said signal sequence may represent n bits per signal, said signal Y_k being within a string of possible signals Y_k evenly spaced by an amount Δ, the range being controlled by a parameter β; S_x is approximately S_o/(1-
β^2), S_y is approximately 2S_o/(1+β), and S_o is approximately the minimum signal power required to represent n bits per symbol in a Δ-spaced string according to the code. 6. The apparatus according to claim 5. 7. An apparatus for generating a sequence in a given N-dimensional modulation code by generating a one-dimensional sequence of signals, the modulation code comprising an N-dimensional population partitioned into subsets associated with the code. and each subset includes N-dimensional constellation points, and the selection of the subset is based on coded and uncoded bits of the constellation points; From the encoded bits and uncoded bits, a set of N M corresponding to the match type of each of the N coordinates (modulo M)
An encoder is provided for deriving representative values of a one-dimensional related set having values, and the representative value of each related set is a subset of one-dimensional values in a one-dimensional group of possible coordinate values for each of the N dimensions. , wherein each one-dimensional signal in the sequence is selected from the possible coordinate values based on uncoded bits. 8. Device according to claim 1, 2, 3 or 5, characterized in that it provides an output to which the sequence Y_k is sent. 9. Device according to claim 1, 2, 3 or 5, characterized in that it provides an output to which the sequence X_k is sent. 10. Claims 1, 2, and 3, characterized in that L is 1.
or the device described in 5. 11. The relationship between the signal X_k and the signal Y_k is Y
6. The device according to claim 1, 2, 3 or 5, characterized in that _k=X_k-X_k_-_L (L is an integer). 12. The apparatus of claim 1, 2, 3, 5 or 7, wherein the modulation code is a trellis code. 13. The device according to claim 1, 2, 3, 5 or 7, characterized in that the modulation code is a lattice code. 14. Claims 1, 2, and 3, characterized in that M is 2.
, 5 or 7. 15. Claims 1, 2, and 3, characterized in that M is 4.
, 5 or 7. 16. Claim 1, characterized in that M is a multiple of 4,
8. The device according to 2, 3, 5 or 7. 17. The device according to claim 1, wherein J is 1. 18. The apparatus of claim 1, wherein J is the same as the number of dimensions N in the modulation code. 19. The device of claim 1, wherein k' is k-1. 20, J is 1, and each group is βX_k_−
2. The device according to claim 1, wherein the value is in a one-dimensional range centered on _1 (0≦β<1). 21. The device according to claim 20, characterized in that β>0. 22. The apparatus of claim 1, wherein there is a finite set of said J-dimensional ensembles. 23. The apparatus of claim 22, wherein there are two said J-dimensional populations. 24. Device according to claim 1, 2, 3 or 5, characterized in that the signals Y_k and X_k are real-valued. 25. Device according to claim 1, 2, 3 or 5, characterized in that the signals Y_k and X_k are complex numbers. 26. Device according to claim 25, characterized in that M is (2+2i). 27. The apparatus of claim 1, 2, 3 or 5, wherein at least two of the J-dimensional ensembles are disjoint. 28, sequence Z_k=Y_k+n_k' (k=1,
2, , , ) into a decoded sequence Y_k, the sequence of signals Y_k is such that (a) said sequence is from a given modulation code, and (b) an operational digital sum X_k=Y_k_− ＿１＋Y＿
k_−_2+, , has a finite variance S_x, and (c) the signal Y_k is defined by X_k' (start separation line; k'
<k), the sequence n_k represents noise, and the expected operating digital sum ■_k = ■_k + ■_k_
−_1+, , , and convert the decoded sequence ■_k to the expected working digital sum ■_k'
A decoder characterized in that a range violation monitor is provided for comparing the above predetermined tolerance range based on (k'<k) and generating an indication when the above-mentioned ■_k deviates from the tolerance range. 29. The expected operating digital sum ■_k is
29. The decoder of claim 28, wherein k is adjusted based on the indication so that k is within the tolerance range. 30. A decoder according to claim 29, characterized in that said adjustment is by a minimum allowed amount such that ■_k is within said allowed range. 31, sequence X_k=Y_k+n_k (k=1, 2
. (b) Y_k=X_k±X_k_-_L (L is an integer), provided that the sequence X_k has a finite variance S_x
and each sequence n_k represents noise, and each of said sequences (a) belongs to said code up to a certain time K, and (b) corresponds to said encoder being in a given said state at said time K. , (c) for each combination of states of the finite number Q, and the M, one for each value in an integer interval, up to a certain time K.
A decoder, characterized in that it is provided with modified maximum likelihood sequence evaluation means for finding Q partial decoding sequences. 32. The decoder of claim 31, wherein M is 2. 33. A decoder according to claim 31, characterized in that M is 4.