Pair-swap independent trellis decoder for a multi-pair gigabit transceiver

A method for correctly computing a distance of a received word represented by L inputs from a codeword in the presence of an incorrect permutation of the L inputs, each of the L inputs uniquely corresponding to one of L dimensions, 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 method comprising the operations of:

• (a) providing pair-select signals indicating an order of the L inputs, the order identifying the incorrect permutation;
• (b) generating a plurality of sets of swap indicators based on the pair-select signals, each of the sets of swap indicators corresponding to one of the code-subsets and having at least one swap indicator corresponding to one of the L inputs;
• (c) generating a set of X-based decisions, a set of Y-based decisions and associated sets of X-based and Y-based errors, the sets of X-based and Y-based errors forming a set of one-dimensional (1D) errors, the sets of X-based and Y-based decisions forming a set of 1D 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 1D errors representing a distance metric between an associated 1D decision and one of the L inputs;
• (d) generating, for each of the code-subsets, corresponding corrected 1D errors and corresponding corrected 1D decisions by interchanging/not interchanging the X-based decisions and associated X-based errors with corresponding ones of the Y-based decisions and associated Y-based errors, respectively, based on the corresponding set of swap indicators;
• (e) combining, for each of the code-subsets, the corresponding corrected 1D errors, and corrected 1D decisions, respectively, to produce an L-dimensional error and an associated L-dimensional decision, respectively, such that the L-dimensional error is a distance of the received word from a nearest codeword in said code-subset and the corresponding L-dimensional decision is the nearest codeword.

A system for correctly computing a distance of a received word represented by L inputs from a codeword in the presence of an incorrect permutation of the L inputs, each of the L inputs uniquely corresponding to one of L dimensions, 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 incorrect permutation being identified by pair-select signals, the system comprising:

• (a) a lookup table for storing a plurality of sets of swap indicators based on the pair-select signals, each of the sets of swap indicators corresponding to one of the code-subsets and having at least one swap indicator corresponding to one of the L inputs;
• (b) a set of slicers for generating a set of X-based decisions, a set of Y-based decisions and associated sets of X-based and Y-based errors, the sets of X-based and Y-based errors forming a set of one-dimensional (1D) errors, the sets of X-based and Y-based decisions forming a set of 1D 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 1D errors representing a distance metric between an associated 1D decision and one of the L inputs;
• (c) a set of multiplexers for generating, for each of the code-subsets, corresponding corrected 1D errors and corresponding corrected 1D decisions by interchanging/not interchanging the X-based decisions and associated X-based errors with corresponding ones of the Y-based decisions and associated Y-based errors, respectively, based on the corresponding set of swap indicators;
• and
• (d) a set of combining modules corresponding to the code-subsets for combining, for each of the code-subsets, the corresponding corrected 1D errors, and corrected 1D decisions, respectively, to produce an L-dimensional error and an associated L-dimensional decision, respectively, such that the L-dimensional error is a distance of the received word from a nearest codeword in said code-subset and the corresponding L-dimensional decision is the nearest codeword.