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. A method comprising:
receiving a set of input bits;
generating a plurality of symbols of a codeword of a vector signaling code, the codeword representing a weighted summation of a plurality of mutually orthogonal sub-channel vectors, the plurality of mutually orthogonal sub-channel vectors weighted by a set of weights determined according to
(i) a set of chi-normalization constants and
(ii) a predetermined minimum vertical opening threshold δ, each mutually orthogonal sub-channel vector of the plurality of mutually orthogonal sub-channel vectors further weighted by a corresponding bit of the set of input bits; and transmitting each symbol of the codeword as a signal over a respective wire of a multi-wire bus.
2. The method of claim 1 , wherein the set of weights comprises pairs of antipodal weights.
3. The method of claim 2 , wherein at least two pairs of antipodal weights of the pairs of antipodal weights have different magnitudes.
4. The method of claim 1 , wherein the symbols of the codeword comprise at least three distinct magnitudes.
5. The method of claim 1 , wherein each chi-normalization constant is associated with a respective sub-channel vector of the plurality of mutually orthogonal sub-channel vectors.
6. The method of claim 1 , wherein each weight of the set of weights is combined with a corresponding bit of the set of input bits to form an optimal initial code set vector.
7. The method of claim 6 , wherein the optimal initial code set vector is represented as [0 ±⅜, ±⅜, ±½, ±⅜, ±¼], and is combined with an encoding matrix M comprising the plurality of mutually orthogonal sub-channel vectors:
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
)
.
8. The method of claim 1 , further comprising:
receiving the set of symbols of the codeword at a plurality of multi-input comparators (MICs); and
generating a plurality of comparator output values, each comparator output value generated by forming a respective weighted combination of two or more symbols of the codeword according to a respective chi-normalized sub-channel vector of a set of chi-normalized sub-channel vectors.
9. The method of claim 8 , wherein each comparator output value is a respective antipodal value greater than or equal to the predetermined minimum vertical opening threshold δ.
10. The method of claim 8 , wherein each comparator output value has an antipodal value equal to the predetermined minimum vertical opening threshold δ.
11. An apparatus comprising:
An encoder configured to
receive a set of input bits, and to responsively
generate a plurality of symbols of a codeword of a vector signaling code, the codeword representing a weighted summation of a plurality of mutually orthogonal sub-channel vectors, the plurality of mutually orthogonal sub-channel vectors weighted by a set of weights determined according to
(i) a set of chi-normalization constants and
(ii) a predetermined minimum vertical opening threshold δ, each mutually orthogonal sub-channel vector further of the plurality of mutually orthogonal sub-channel vectors weighted by a corresponding bit of the set of input bits; and
a plurality of drivers configured to transmit each symbol of the codeword as a signal over a respective wire of a multi-wire bus.
12. The apparatus of claim 11 , wherein the set of weights comprises pairs of antipodal weights.
13. The apparatus of claim 12 , wherein at least two pairs of antipodal weights of the pairs of antipodal weights have different magnitudes.
14. The apparatus of claim 11 , wherein the symbols of the codeword comprise at least three distinct magnitudes.
15. The apparatus of claim 11 , wherein each chi-normalization constant is associated with a respective sub-channel vector of the plurality of mutually orthogonal sub-channel vectors.
16. The apparatus of claim 11 , wherein each weight of the set of weights is combined with a corresponding bit of the set of input bits to form an optimal initial code set vector.
17. The apparatus of claim 16 , wherein the optimal initial code set vector is represented as [0 ±⅜, ±⅜, ±½, ±⅜, ±¼], and is combined with an encoding matrix M comprising the plurality of mutually-orthogonal sub-channel vectors:
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
)
.
18. The apparatus of claim 11 , further comprising a plurality of multi-input comparators (MICs) configured to receive the set of symbols of the codeword, and to generate a plurality of comparator output values, each comparator output value generated by forming a respective weighted combination of two or more symbols of the codeword according to a respective chi-normalized sub-channel vector of a set of chi-normalized sub-channel vectors.
19. The apparatus of claim 18 , wherein each comparator output value is a respective antipodal value greater than or equal to the predetermined minimum vertical opening threshold δ.
20. The apparatus of claim 18 , wherein each comparator output value has an antipodal value equal to the predetermined minimum vertical opening threshold δ.