System and method for trellis decoding in a multi-pair transceiver system

• US 6,253,345 B1
• Filed: 08/09/1999
• Issued: 06/26/2001
• Est. Priority Date: 11/13/1998
• Status: Expired due to Term

• Current Assignee: Avago Technologies International Sales Pte Limited (Broadcom, Inc.)
• Original Assignee: Broadcom Corporation (Broadcom, Inc.)
• Inventors: Kruse, David, Hatamian, Mehdi, Agazzi, Oscar E., Abnous, Arthur
• Primary Examiner(s): Decady, Albert
• Assistant Examiner(s): LAMARRE, GUY J
• Application Number:
  US09/370,370
• Time in Patent Office: 687 Days
• Field of Search: 714/752, 714/800, 714/6, 714/763, 714/749, 714/786, 714/792, 714/790, 375/286, 375/261, 375/265, 375/240.01, 375/240.24, 375/340, 375/341, 370/347, 455/509, 341/55, 341/67, 341/79, 710/68
• US Class Current: 714/752
• CPC Class Codes: G01R 31/3004 Current or voltage test
• CPC Class Codes: G01R 31/3008 Quiescent current [IDDQ] test or leakage current test
• CPC Class Codes: G01R 31/3016 Delay or race condition test, e.g. race hazard test
• CPC Class Codes: G01R 31/31715 Testing of input or output circuits; test of circuitry between the I/C pins and the functional core, e.g. testing of input or output driver, receiver, buffer
• CPC Class Codes: G01R 31/318502 Test of Combinational circuits
• CPC Class Codes: G01R 31/318552 Clock circuits details
• CPC Class Codes: G01R 31/318594 Timing aspects clock circuits G01R31/318552
• CPC Class Codes: H04B 3/23 using a replica of transmitted signal in the time domain, e.g. echo cancellers
• CPC Class Codes: H04B 3/32 Reducing cross-talk, e.g. by compensating
• CPC Class Codes: H04L 1/0054 Maximum-likelihood or sequential decoding, e.g. Viterbi, Fano, ZJ algorithms
• CPC Class Codes: H04L 1/0059 Convolutional codes
• CPC Class Codes: H04L 1/242 by comparing a transmitted test signal with a locally generated replica
• CPC Class Codes: H04L 2025/03363 Multilevel H04L2025/03369 takes precedence
• CPC Class Codes: H04L 2025/03369 Partial response
• CPC Class Codes: H04L 2025/03477 not time-recursive
• CPC Class Codes: H04L 2025/0349 as a feedback filter
• CPC Class Codes: H04L 2025/03496 as a prediction filter
• CPC Class Codes: H04L 2025/03503 as a combination of feedback and prediction filters
• CPC Class Codes: H04L 2025/03617 Time recursive algorithms H04L2025/03643 takes precedence
• CPC Class Codes: H04L 2025/03745 Timing of adaptation
• CPC Class Codes: H04L 25/03038 : with a non-recursive structure H04L25/03031 takes precedence
• CPC Class Codes: H04L 25/03057 : with a recursive structure H04L25/03031 takes precedence
• CPC Class Codes: H04L 25/03146 : with a recursive structure H04L25/03127 takes precedence
• CPC Class Codes: H04L 25/03267 : with decision feedback equalisers
• CPC Class Codes: H04L 25/067 : providing soft decisions, i.e. decisions together with an estimate of reliability H04L25/068 and H04L25/069 take precedence; sequence estimation techniques H04L25/03178
• CPC Class Codes: H04L 25/14 : Channel dividing arrangements , i.e. in which a single bit stream is divided between several baseband channels and reassembled at the receiver
• CPC Class Codes: H04L 25/4917 : using multilevel codes
• 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 7/0062 : detection of error based on data decision error, e.g. Mueller type detection
• CPC Class Codes: H04L 7/0334 : Processing of samples having at least three levels, e.g. soft decisions

Abstract

A method and a system for decoding information signals encoded in accordance with a multi-state encoding scheme and transmitted over a multi-dimensional transmission channel by computing a distance of a received word from a codeword. One-dimensional (1D) input signals are processed in a pair of symbol decoders, implemented as look-up tables, to produce a pair of 1D errors, with each representing a distance metric between the input signal and a symbol in one of two disjoint symbol-subsets. The 1D errors are combined based on the multi-state encoding scheme in order to produce a set of multi-dimensional error terms. Each of the multi-dimensional error terms corresponds to a distance between a received word and a nearest codeword.

Claims

1. A method for computing a distance of a received word from a codeword, the codeword being a concatenation of L symbols selected from two disjoint symbol subsets X and Y, the codeword being included in one of a plurality of code-subsets, the received word being represented by L inputs, each of the L inputs uniquely corresponding to one of L dimensions, the method comprising the operations of:

(a) producing a set of one-dimensional errors from the L inputs, each of the one-dimensional errors representing a distance metric between one of the L inputs and a symbol in one of the two disjoint symbol-subsets; and

(b) combining the one-dimensional errors to produce a set of L-dimensional errors such that each of the L-dimensional errors is a distance of the received word from a nearest codeword in one of the code-subsets.

2. The method of claim 1 wherein each of the one-dimensional errors is represented by substantially fewer bits than each of the L inputs.

3. The method of claim 1 wherein operation (a) comprises the operation of slicing each of the L inputs with respect to each of the two disjoint symbol-subsets X and Y to produce a set of X-based errors, a set of Y-based errors and corresponding sets of X-based and Y-based decisions, the sets of X-based and Y-based errors forming the set of one-dimensional errors, the sets of X-based and Y-based decisions forming the set of one-dimensional decisions, each of the X-based and Y-based decisions being a symbol in a corresponding symbol-subset closest in distance to one of the L inputs, each of the one-dimensional errors representing a distance metric between a corresponding one-dimensional decision and one of the L inputs.

4. The method of claim 3 wherein each of the one-dimensional errors is represented by 3 bits.

5. The method of claim 3 wherein the operation of slicing is performed via a look-up table.

6. The method of claim 5 wherein the look-up table is implemented using a read-only-memory storage device.

7. The method of claim 5 wherein the look-up table is implemented using a random-logic device.

8. The method of claim 1 wherein operation (a) comprises the operation of:

(1) slicing each of the L inputs with respect to each of the two disjoint symbol-subsets X and Y to produce a set of X-based decisions and a set of Y-based decisions, the sets of X-based and Y-based decisions forming the set of one-dimensional decisions, each of the X-based and Y-based decisions being a symbol in a corresponding symbol-subset closest in distance to one of the L inputs;

(2) slicing each of the L inputs with respect to a symbol-set comprising all symbols of the two disjoint symbol-subsets to produce a set of hard decisions; and

(3) combining each of the sets of X-based and Y-based decisions with the set of hard decisions to produce the set of one-dimensional errors, each of the one-dimensional errors representing a distance metric between the corresponding one-dimensional decision and one of the L inputs.

9. The method of claim 8 wherein operations (1), (2) and (3) are performed via a look-up table.

10. The method of claim 9 wherein the look-up table is implemented using a read-only-memory storage device.

11. The method of claim 9 wherein the look-up table is implemented using a random-logic device.

12. The method of claim 8 wherein each of the one-dimensional errors is represented by one bit.

13. The method of claim 1 wherein operation (b) comprises the operations of:

combining the one-dimensional errors to produce two-dimensional errors;

combining the two-dimensional errors to produce intermediate L-dimensional errors;

arranging the intermediate L-dimensional errors into pairs of errors such that the pairs of errors correspond one-to-one to the code-subsets; and

determining a minimum for each of the pairs of errors, the minima being the L-dimensional errors.

14. The method of claim 1 wherein L is equal to 4.

15. The method of claim 1 wherein the plurality of code-subsets comprises 2^L-1 code-subsets.

16. The method of claim 15 wherein the set of one-dimensional errors comprises 2L one-dimensional errors.

17. The method of claim 16 wherein the set of L-dimensional errors comprises 2^L-1 L-dimensional errors.

18. The method of claim 17 wherein operation (b) comprises the operations of:

combining the 2L one-dimensional errors to produce 2L two-dimensional errors;

combining the 2L two-dimensional errors to produce the 2^L intermediate L-dimensional errors;

arranging the 2^L intermediate L-dimensional errors into 2^L-1 pairs of errors such that the 2^L-1 pairs of errors correspond one-to-one to the 2^L-1 code-subsets; and

determining a minimum for each of the 2^L-1 pairs of errors, the minima being the 2^L-1 L-dimensional errors.

19. A system for computing a distance of a received word from a codeword, the codeword being a concatenation of L symbols selected from two disjoint symbol-subsets X and Y, the codeword being included in one of a plurality of code-subsets, the received word being represented by L inputs, each of the L inputs uniquely corresponding to one of L dimensions, the system comprising:

(a) a set of slicers for producing a set of one-dimensional errors from the L inputs, each of the one-dimensional errors representing a distance metric between one of the L-inputs and a symbol in one of the two disjoint symbol-subsets; and

(b) a combining module for combining the one-dimensional errors to produce a set of L-dimensional errors such that each of the L-dimensional errors is a distance of the received word from a nearest codeword in one of the code-subsets.

20. The system of claim 19 wherein each of the one-dimensional errors is represented by substantially fewer bits than each of the L inputs.

21. The system of claim 19 wherein the slicers slice the L inputs with respect to each of the two disjoint symbol-subsets X and Y to produce a set of X-based errors, a set of Y-based errors and corresponding sets of X-based and Y-based decisions, the sets of X-based and Y-based errors forming the set of one-dimensional errors, the sets of X-based and Y-based decisions forming the set of one-dimensional decisions, each of the X-based and Y-based decisions being a symbol in a corresponding symbol-subset closest in distance to one of the L inputs, each of the one-dimensional errors representing a distance metric between a corresponding one-dimensional decision and one of the L inputs.

22. The system of claim 21 wherein each of the one-dimensional errors is represented by 3 bits.

23. The system of claim 21 wherein the slicers are implemented using a look-up table.

24. The system of claim 23 wherein the look-up table is implemented using a read-only-memory storage device.

25. The system of claim 23 wherein the look-up table is implemented using a random-logic device.

26. The system of claim 19 wherein the set of slicers comprises:

(1) first slicers for slicing each of the L inputs with respect to each of the two disjoint symbol-subsets X and Y to produce a set of X-based decisions and a set of Y-based decisions, the sets of X-based and Y-based decisions forming the set of one-dimensional decisions, each of the X-based and Y-based decisions being a symbol in a corresponding symbol-subset closest in distance to one of the L inputs;

(2) second slicers for slicing each of the L inputs with respect to a symbol-set comprising all symbols of the two disjoint symbol-subsets to produce a set of hard decisions; and

(3) error-computing modules for combining each of the sets of X-based and Y-based decisions with the set of hard decisions to produce the set of one-dimensional errors, each of the one-dimensional errors representing a distance metric between the corresponding one-dimensional decision and one of the L inputs.

27. The system of claim 26 wherein the first and second slicers and the error computing modules are implemented using a look-up table.

28. The system of claim 27 wherein the look-up table is implemented using a read-only-memory storage device.

29. The system of claim 27 wherein the look-up table is implemented using a random-logic device.

30. The system of claim 26 wherein each of the one-dimensional errors is represented by one bit.

31. The system of claim 19 wherein the combining module comprises:

a first set of adders for combining the one-dimensional errors to produce two-dimensional errors;

a second set of adders for combining the two-dimensional errors to produce intermediate L-dimensional errors, the intermediate L-dimensional errors being arranged into pairs of errors such that the pairs of errors, correspond one-to-one to the code-subsets; and

a minimum-select module for determining a minimum for each of the pairs of errors, the minima being the L-dimensional errors.

32. The system of claim 19 wherein L is equal to 4.

33. The system of claim 19 wherein the plurality of code-subsets comprises 2^L-1 code-subsets.

34. The system of claim 33 wherein the set of one-dimensional errors comprises 2L one-dimensional errors.

35. The system of claim 34 wherein the set of L-dimensional errors comprises 2^L-1 L-dimensional errors.

36. The system of claim 35 wherein the combining module comprises:

a first set of adders for combining the 2L one-dimensional errors to produce 2L two-dimensional errors;

a second set of adders for combining the 2L two-dimensional errors to produce the 2^L intermediate L-dimensional errors, the 2^L intermediate L-dimensional errors being arranged into 2^L-1 pairs of errors such that the 2^L-1 pairs of errors correspond one-to-one to the 2^L-1 code-subsets; and

a minimum-select module for determining a minimum for each of the 2^L-1 pairs of errors, the minima being the 2^L-1 L-dimensional errors.

37. The system of claim 19 wherein the system is included in a communication transceiver configured to transmit and receive information signals encoded in accordance with a multi-level symbolic scheme.

38. A method for computing a distance of a received word from a codeword, the codeword being a concatenation of L symbols selected from two disjoint symbol-subsets, the codeword being included in one of 2^L-1 code-subsets, the received word being represented by 2^L-1 input sets, each of the 2^L-1 input sets having L inputs, each of the L inputs uniquely corresponding to one of L dimensions, each of the 2^L-1 input sets corresponding to one of the 2^L-1 code-subsets, the method comprising the operations of:

(a) slicing each of the L inputs of each of the 2^L-1 input sets with respect to each of the two disjoint symbol-subsets to produce an error set of 2L one-dimensional errors for each of the 2^L-1 code-subsets; and

(b) combining one-dimensional errors within each of the error sets to produce 2^L-2 L-dimensional errors for the corresponding code-subset such that each of the 2^L-2 L-dimensional errors is a distance of the received word from one of codewords.

39. The method of claim 38 wherein L is equal to 4.

40. The method of claim 38 wherein operation (b) comprises the operations of:

combining the 2L one-dimensional errors to produce 2L two-dimensional errors;

combining the 2L two-dimensional errors to produce a set of 2^L intermediate L-dimensional errors;

arranging the 2^L intermediate L-dimensional errors into 2^L-1 pairs of errors such that the 2^L-1 pairs of errors correspond one-to-one to the 2^L-1 code-subsets; and

determining a minimum for each of the 2^L-1 pairs, the minima being the 2^L-1 L-dimensional errors.

41. The method of claim 40 wherein operation (a) comprises the operation of producing a decision set of 2L one-dimensional decisions for each of the 2^L-1 code-subsets.

42. The method of claim 40 wherein operation (b) comprises the operation of combining one-dimensional decisions within each of the decision sets to produce 2^L-2 L-dimensional decisions for the corresponding code-subset such that each of the 2^L-2 L-dimensional decisions is a codeword closest in distance to the received word, the codeword being in one of 2^L-2 code-subsets included in the 2^L-1 code-subsets.

43. The method of claim 38 wherein the method is performed in a communication transceiver configured to transmit and receive information signals encoded in accordance with a multi-level symbolic scheme.