System and method for trellis decoding in a multi-pair transceiver system
First Claim
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.
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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.
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Citations
43 Claims
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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:
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(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. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18)
(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.
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9. The method of claim 8 wherein operations (1), (2) and (3) are performed via a look-up table.
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10. The method of claim 9 wherein the look-up table is implemented using a read-only-memory storage device.
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11. The method of claim 9 wherein the look-up table is implemented using a random-logic device.
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12. The method of claim 8 wherein each of the one-dimensional errors is represented by one bit.
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13. The method of claim 1 wherein operation (b) comprises the operations of:
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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.
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14. The method of claim 1 wherein L is equal to 4.
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15. The method of claim 1 wherein the plurality of code-subsets comprises 2L-1 code-subsets.
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16. The method of claim 15 wherein the set of one-dimensional errors comprises 2L one-dimensional errors.
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17. The method of claim 16 wherein the set of L-dimensional errors comprises 2L-1 L-dimensional errors.
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18. The method of claim 17 wherein operation (b) comprises the operations of:
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combining the 2L one-dimensional errors to produce 2L two-dimensional errors;
combining the 2L two-dimensional errors to produce the 2L intermediate L-dimensional errors;
arranging the 2L intermediate L-dimensional errors into 2L-1 pairs of errors such that the 2L-1 pairs of errors correspond one-to-one to the 2L-1 code-subsets; and
determining a minimum for each of the 2L-1 pairs of errors, the minima being the 2L-1 L-dimensional errors.
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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:
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(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. - View Dependent Claims (20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37)
(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.
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27. The system of claim 26 wherein the first and second slicers and the error computing modules are implemented using a look-up table.
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28. The system of claim 27 wherein the look-up table is implemented using a read-only-memory storage device.
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29. The system of claim 27 wherein the look-up table is implemented using a random-logic device.
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30. The system of claim 26 wherein each of the one-dimensional errors is represented by one bit.
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31. The system of claim 19 wherein the combining module comprises:
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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.
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32. The system of claim 19 wherein L is equal to 4.
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33. The system of claim 19 wherein the plurality of code-subsets comprises 2L-1 code-subsets.
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34. The system of claim 33 wherein the set of one-dimensional errors comprises 2L one-dimensional errors.
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35. The system of claim 34 wherein the set of L-dimensional errors comprises 2L-1 L-dimensional errors.
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36. The system of claim 35 wherein the combining module comprises:
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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 2L intermediate L-dimensional errors, the 2L intermediate L-dimensional errors being arranged into 2L-1 pairs of errors such that the 2L-1 pairs of errors correspond one-to-one to the 2L-1 code-subsets; and
a minimum-select module for determining a minimum for each of the 2L-1 pairs of errors, the minima being the 2L-1 L-dimensional errors.
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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.
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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 2L-1 code-subsets, the received word being represented by 2L-1 input sets, each of the 2L-1 input sets having L inputs, each of the L inputs uniquely corresponding to one of L dimensions, each of the 2L-1 input sets corresponding to one of the 2L-1 code-subsets, the method comprising the operations of:
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(a) slicing each of the L inputs of each of the 2L-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 2L-1 code-subsets; and
(b) combining one-dimensional errors within each of the error sets to produce 2L-2 L-dimensional errors for the corresponding code-subset such that each of the 2L-2 L-dimensional errors is a distance of the received word from one of codewords. - View Dependent Claims (39, 40, 41, 42, 43)
combining the 2L one-dimensional errors to produce 2L two-dimensional errors;
combining the 2L two-dimensional errors to produce a set of 2L intermediate L-dimensional errors;
arranging the 2L intermediate L-dimensional errors into 2L-1 pairs of errors such that the 2L-1 pairs of errors correspond one-to-one to the 2L-1 code-subsets; and
determining a minimum for each of the 2L-1 pairs, the minima being the 2L-1 L-dimensional errors.
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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 2L-1 code-subsets.
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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 2L-2 L-dimensional decisions for the corresponding code-subset such that each of the 2L-2 L-dimensional decisions is a codeword closest in distance to the received word, the codeword being in one of 2L-2 code-subsets included in the 2L-1 code-subsets.
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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.
Specification