Partial response channel signaling systems

• US 5,040,191 A
• Filed: 07/10/1990
• Issued: 08/13/1991
• Est. Priority Date: 02/24/1987
• Status: Expired due to Term

• Current Assignee: CIF Licensing LLC
• Original Assignee: Codex Corporation (Motorola Solutions, Inc.)
• Inventors: Forney, G. D. Jr., Eyuboglu, Vedat M.
• Primary Examiner(s): Safourek, Benedict V.
• Application Number:
  US07/550,217
• Time in Patent Office: 399 Days
• Field of Search: 375/18, 375/25, 375/37, 375/39, 375/42, 375/54, 375/34, 375/58, 375/101, 375/59, 375/94, 370/30, 370/37, 371/43, 371/44, 371/45, 371/46, 371/55, 371/56, 364/514, 364/554, 364/734, 364/812, 332/103, 332/104, 332/106, 332/108, 332/115
• US Class Current: 375/263
• CPC Class Codes: H04L 25/497 by correlative coding, e.g. partial response coding or echo modulation coding transmitters and receivers for partial response systems transversal equalizers at the transmitter end H04L25/03343
• CPC Class Codes: H04L 27/3438 using an underlying generalised cross constellation

Abstract

Apparatus for generating a (running digital sum) sequence of digital signals X_k and/or a (partial response coded) sequence of digital signals Y_k, K=1, 2, . . . , such that Y_k =X_k ±X_k-l, L and integer, in which the Y_x signals are a sequence in a given modulation code. In one aspect, the signals Y_k are chosen to be congruent to coset representatives specified in accordance with a modulation code, a plurality of code constellations are used, and at least one constellation includes both a point with a positive sum of coordinates and one with a negative sum of coordinates. In another aspect, the signals X_k are chosen to be congruent to a sequence of alternate (precoded) coset representatives. In other aspects, the Y_k alphabet signals are evenly spaced, and a selectable, e.g., an optimal, tradeoff between S_x and S_y is made. An N-dimentional modulation code is generated as a sequence of one-dimensional signals. A maximum likelihood sequence estimation decoder reconstructs the estimated running digital sum, and generates a signal whenever the estimated running digital sum is outside a permissible range. In another aspect, the decoder includes a modified maximum likelihood sequence estimator adapted to find MQ partial decoded sequences, where Q is the number of encoder states, and M is an integer.

Claims

1. Apparatus for generating a sequence of digital signals x_k and/or a sequence of digital signals y_k, k=1, 2, . . . , such that the sequence of y_k signals is a partial-response-coded sequence derived from the sequence of x_k signals, said signals y_k being a sequence in a given modulation code, said apparatus comprising

a coset selector for generating coset representatives c_k in accordance with said given modulation code;

and

an encoder for selecting J said signals y_k, J≧

1, (y_k, y_k+1, . . . , y_k+J-1) to be congruent to a sequence of J coset representatives c_k (modulo Λ

_N), Λ

_N being an N-dimensional lattice, N being a positive integer, each of said J signals being chosen from a corresponding one of a plurality of J-dimensional constellations, said choice being based on a previous x_k'"'"', k'"'"'<

k, at least one of said plurality of J-dimensional constellations comprising both a point with a positive sum of coordinates and another point with a negative sum of coordinates, said encoder being arranged so that said signals x_k have finite variance S_x.

2. The apparatus of claim 1 wherein the relationship between the x_k signals and y_k signals is y_k =x_k ±

x_k-L, L an integer.

3. The apparatus of claim 2 wherein J is 1.

4. The apparatus of claim 2 wherein J is the same as number N of dimensions in said modulation code.

5. The apparatus of claim 2 wherein k'"'"' is k-1.

6. The apparatus of claim 2 wherein J is 1 and each said constellation is a one-dimensional range of values centered on β

x_k-1, 0≦

β

<

1.

7. The apparatus of claim 6 wherein β

>

0.

8. The apparatus of claim 2 wherein there are a finite set of said J-dimensional constellations.

9. The apparatus of claim 8 wherein there are two said J-dimensional constellations.

10. The apparatus of claim 2 wherein at least two of said J-dimensional constellations are not disjoint.

11. Apparatus for generating a sequence of digital signals x_k and/or a sequence of digital signals y_k, k=1, 2, . . . , such that the sequence of y_k signals is a partial-response-coded sequence derived from the sequence of x_k signals, said signals y_k being a sequence in a given modulation code, said apparatus comprising

a coset selector for generating coset representatives c_k in accordance with said given modulation code;

a generator of a sequence of alternative coset representatives c_k '"'"' chosen so that the sequence of coset representatives c_k is a partial-response-coded sequence derived from the sequence of c_k '"'"' signals, and

an encoder for selecting said signals x_k to be congruent to a sequence of alternative coset representatives c_k '"'"', where the congruence is modulo M if said coset representatives c_k are real, M being an integer, and modulo Λ

_N if said c_k signals are N-dimensional, Λ

_N being an N-dimensional lattice, N being an integer.

12. The apparatus of claim 11 wherein the relationship between the x_k signals and y_k signals is y_k =x_k ±

x_k-L, L an integer and wherein

c_k '"'"'=c_k -c'"'"'_k-L (modulo M), in the case when y_k =x_k +x_k-L,

c_k '"'"'=c_k +c'"'"'_k-L (modulo M), in the case where y_k =x_k -x_k-L.

19. The apparatus of claim 2, 12, 13, or 16 further comprising an output at which said sequence y_k is delivered.

20. The apparatus of claim 2, 12, 13, or 16 further comprising an output at which said sequence x_k is delivered.

21. The apparatus of claim 2, 12, 13, or 16 wherein L is 1.

22. The apparatus of claim 2, 12, 13, or 16 wherein the relationship between the x_k signals and y_k signals is y_k =x_k -x_x-L, L an integer.

23. The apparatus of claim 2, 12, 14, 16, or 18 wherein said modulation code is a trellis code.

24. The apparatus of claim 2, 12, 14, 16, or 18 wherein said modulation code is a lattice code.

25. The apparatus of claim 2, 12, or 18 wherein M is 2.

26. The apparatus of claim 2, 12, or 18 wherein M is 4.

27. The apparatus of claim 2, 12, or 18 wherein M is a multiple of 4.

28. The apparatus of claim 2, 12, 13, or 16 wherein y_k and x_k are real valued.

29. The apparatus of claim 2, 12, 13, or 16 wherein y_k and x_k are complex valued.

30. The apparatus of claim 2 or 12 wherein y_k and x_k are complex valued and wherein M is 2+2i, i=√

-1.

13. Apparatus for generating a sequence of digital signals x_k and/or a sequence of digital signals y_k, k=1, 2, . . . , capable of representing n bits per signal, such that the relationship between x_k and y_k is y_k =x_k ±

x_k-L, L an integer, said x_k and y_k signals having variances S_x and S_y, said y_k signals falling within an alphabet of possible y_k signals that are spaced apart within said alphabet evenly by a spacing Δ

, said apparatus comprising

means for receiving an input signal having n bits per signal; and

an encoder responsive to said receiving means for generating said sequence y_k and said sequence x_k such that said sequence y_k has a variance S_y less than 2S₀ and said sequence x_k has a variance S_x not much greater than S_y² /4(S_y -S₀), S₀ being approximately equal to the minimum signal power required to represent n bits per signal with a Δ

-spaced alphabet.

14. The apparatus of claim 13 wherein said sequence y_k is a sequence in a given modulation code.

15. Apparatus for generating a sequence of digital signals x_k and/or a sequence of digital signals y_k, k=1, 2, . . . , such that the sequence of y_k signals is a partial-response-coded sequence derived from the sequence of x_k signals, said x_k and y_k sequences having variances S_x and S_y, said symbols y_k being a sequence in a given modulation code, said apparatus comprising

means for receiving an input signal;

and

an encoder responsive to said receiving means for generating said x_k and/or y_k signals such that the ratio of variance S_y to variance S_x is selectable within a predetermined range.

16. The apparatus of claim 15 wherein the relationship between the x_k signals and y_k signals is y_k =x_x ±

x_k-L, L an integer.

17. The apparatus of claim 16 wherein said x_k and y_k signal sequences are capable of representing n bits per signal, said y_k signals fall within an alphabet of possible y_k signals that are spaced evenly by an amount Δ

, said predetermined range is controlled by a parameter β

, and S_x is approximately S_o /(1-β

²), and S_y is approximately 2S_o /(1+β

), S_o being approximately the minimum signal power required to represent n bits per symbol with a Δ

-spaced alphabet in accordance with said code.

18. Apparatus for generating a sequence in a given N-dimensional modulation code by generating a sequence of one-dimensional signals, N being a positive number, said modulation code being based on an N-dimensional constellation partitioned into subsets associated with said code, said subsets each containing N-dimensional signal points, the choice of said subset being based on coded bits and uncoded bits of said signal points, said apparatus comprising

means for receiving an input signal and generating the coded bits and the uncoded bits therefrom;

and

an encoder for deriving from said coded and uncoded bits, for each said N-dimensional symbol, a set of N, M-valued one-dimensional coset representatives c_k corresponding to congruence classes of each of the N coordinates (modulo M), M being a positive number, each coset representative designating a subset of one-dimensional values in a one-dimensional constellation of possible coordinate values for each of said N dimensions,

each said one-dimensional signal in said sequence being selected from said possible coordinate values based on uncoded bits.

31. In a decoder for decoding a sequence z_k =y_k +n_k, k=1, 2, . . . , into a decoded sequence y_k, where the sequence of signals y_k is such that

(a) said sequence is from a given modulation code;

(b) the running digital sum x_k =y_k-1 +y_k-2 + . . . has finite variance S_x ;

(c) said signals y_k fall in a predetermined permissible range dependent on x_k'"'"', k'"'"'<

k; and

the sequence n_k represents noise,

a range violation monitor comprising;

a means for reconstructing the estimated running digital sum x_k =y_k +y_k-1 + . . . , and

a means for comparing said decoded sequence y_k with said predetermined permissible range based on said estimated running digital sum x_k'"'"', k'"'"'<

k, and for generating an indication when said y_k is outside said permissible range.

32. A decoder according to claim 31, in which said estimated running digital sum x_k is adjusted based on said indication so that y_k will be inside said permissible range.

33. A decoder according to claim 32, in which said adjustment is by the minimum possible amount such that y_k falls inside said permissible range.

34. A decoder for decoding a sequence x_k =y_k +n_k, k=1, 2, . . . , where sequence n_k represents noise and the sequence of signals y_k is such that

(a) said sequence is from a given modulation code, said code being capable of being generated by an encoder with a finite number Q of states;

(b) y_k =x_k ±

x_k-L, L an integer, where said sequence x_k has finite variance S_x, and the sequence n_k represents noise, comprising

a means for receiving the sequence z_k ; and

a modified maximum likelihood sequence estimator responsive to the receiving means, said estimator being adapted to find MQ partial decoded sequences, up to some time K, where M, Q, and K are positive finite numbers, one such said sequence for each combination of said finite number Q of states and each of a finite number M of integer-spaced values modulo M, such that each said sequence

(a) is in said code up to said time K;

(b) corresponds to said encoder being in a given said state at said time K;

(c) corresponds to a value of x_k at said time K that is congruent to a given one of said values, modulo M.

35. A decoder as in claim 34 wherein M is 2.

36. A decoder as in claim 34 wherein M is 4.