Vector signaling codes with increased signal to noise characteristics
Vector signaling codes are synergistically combined with multi-level signaling, the increased alphabet size provided by the multi-level signaling enabling a larger codeword space for a given number of symbols, at the cost of reduced receiver detection margin for each of the multiple signal levels. Vector signaling code construction methods are disclosed in which code construction and selection of multi-level signal levels are coordinated with the design of an associated receive comparator network, wherein modified signal levels encoded and emitted by the transmitter result in increased detection margin at the receive comparators.
1. An apparatus comprising:
a multi-wire bus configured to receive a set of symbols of a codeword, the set of symbols representing a weighted sum of sub-channel code vectors, each sub-channel code vector weighted according to a corresponding antipodal weight of a set of antipodal weights, the set of antipodal weights containing at least two unique magnitudes, wherein the sub-channel code vectors are mutually orthogonal, and wherein the sub-channel code vectors form a scaled-orthogonal matrix;
a comparator network, connected to the multi-wire bus, comprising a plurality of sub-channel comparators configured to generate a respective plurality of comparator output values based on the received set of symbols of the codeword, each comparator comprising a set of chi-normalized input weights, wherein each set of chi-normalized input weights is selected according to a respective sub-channel code vector, and
wherein the antipodal weight set is selected such that each subchannel comparator generates antipodal values greater than a predetermined vertical opening threshold, δ.
2. The apparatus of claim 1 , wherein the set of antipodal weights is selected such that each subchannel comparator generates antipodal values of substantially similar magnitudes.
3. The apparatus of claim 1 , wherein each of the antipodal weights in the set of antipodal weights has a magnitude less than 1.
4. The apparatus of claim 1 , wherein the set of antipodal weights is based on a codeword symbol normalization constant, μ.
5. The apparatus of claim 4 , wherein the codeword symbol normalization constant μ normalizes the symbols of the codeword to values having magnitudes less than or equal to 1.
6. The apparatus of claim 1 , wherein a sum of the antipodal weights in the set of antipodal weights is maximized according to the antipodal value corresponding a minimum vertical opening threshold.
7. The apparatus of claim 6 , wherein the sum of the antipodal weights in the set of antipodal weights is also maximized according to the codeword symbol normalization constant μ.
8. A method comprising:
receiving a set of symbols of a codeword on a multi-wire bus, the set of symbols representing a weighted sum of sub-channel code vectors, each sub-channel code vector weighted based on a corresponding antipodal weight of a set of antipodal weights, wherein the sub-channel code vectors are mutually orthogonal, and wherein the sub-channel code vectors form a scaled-orthogonal matrix; and,
generating a plurality of comparator output values based on the received set of symbols of the codeword using a plurality of sub-channel comparators, wherein each sub-channel comparator comprises a set of chi-normalized input weights, each set of chi-normalized input weights selected according to a respective sub-channel code vector, wherein each comparator output value is represented as an antipodal value, and wherein the set of antipodal weights is selected such that each antipodal value is greater than a predetermined vertical opening threshold, δ.
9. The method of claim 8 , wherein the set of antipodal weights comprises at least two antipodal weights having distinct magnitudes.
10. The method of claim 8 , wherein each of the antipodal weights in the set of antipodal weights has a magnitude less than 1.
11. The method of claim 8 , wherein the set of antipodal weights is based on a codeword symbol normalization constant, μ.
12. The method of claim 11 , wherein the codeword symbol normalization constant μ normalizes the symbols of the codeword to values having magnitudes less than or equal to 1.
13. A method comprising:
receiving a vector having a plurality of components, each component having an associated antipodal weight of a set of antipodal weights;
generating a set of symbols of a codeword, the codeword representing a weighted sum of a plurality of sub-channel vectors, wherein a weighting of each sub-channel vector is determined by the associated antipodal weight of a corresponding component of the vector, and wherein the plurality of sub-channel vectors form a scaled-orthogonal matrix, wherein the plurality of sub-channel vectors are weighted to produce codeword symbols that are normalized to have symbol values having magnitudes between 0 and 1, wherein the codeword, when detected by a plurality of sub-channel comparators having chi-normalized input weights, produces a set of antipodal values representing vertical openings of the sub-channel comparators that are greater than a predetermined vertical opening threshold δ; and,
transmitting the set of symbols of the codeword on a multi-wire bus.
14. The method of claim 13 , wherein the scaled-orthogonal matrix is represented as
M
=
(
1
1
1
1
-
1
0
1
1
-
2
)
and the vector corresponding to the set of antipodal weights is represented as (0, ±⅗, +⅖).
15. The method of claim 13 , wherein the scaled-orthogonal matrix is represented as
M
=
(
1
1
1
1
1
1
-
1
0
0
0
0
0
1
-
1
0
1
1
-
1
-
1
0
1
1
1
1
-
4
)
and the vector corresponding to the set of antipodal weights is represented as (0, ± 5/12, ± 5/12, ± 5/12, ±⅙).
16. The method of claim 13 , wherein the scaled-orthogonal matrix is represented as
M
=
(
1
1
1
1
1
1
1
-
1
0
0
0
0
0
0
1
-
1
0
0
0
0
0
0
1
-
1
1
1
-
1
-
1
0
0
1
1
1
1
-
2
-
2
)
and the vector corresponding to the set of antipodal weights is represented as (0, +⅜, ±⅜, ±½, ±⅜, ±¼).
17. The method of claim 13 , wherein the scaled-orthogonal matrix is represented as
M
=
(
1
1
1
1
1
1
1
-
1
0
0
0
0
1
1
-
2
0
0
0
0
0
0
1
-
1
0
0
0
0
1
1
-
2
1
1
1
-
1
-
1
-
1
)
and the vector corresponding to the set of antipodal weights is represented as (0, +⅜, ±¼, ±⅜, ±¼, ±⅜).
18. The method of claim 13 , wherein the scaled-orthogonal matrix is represented as
M
=
(
1
1
1
1
1
1
1
1
1
1
-
1
0
0
0
0
0
0
0
0
0
1
-
1
0
0
0
0
0
0
0
0
0
1
-
1
0
0
0
0
0
0
0
0
0
1
-
1
0
1
1
-
1
-
1
0
0
0
0
0
0
0
0
0
1
1
-
1
-
1
0
1
1
1
1
-
1
-
1
-
1
-
1
0
1
1
1
1
1
1
1
1
-
8
)
and the vector corresponding to the set of antipodal weights is represented as (0,± 3/10,± 3/10,± 3/10,± 3/10,± 3/10,± 3/10,± 3/10,± 1/10).