1. A method for performing in iterative decoding of information coded by an error correction code, the method comprising:
defining a transcendent first function representing a quantity to be evaluated for the decoding method;
defining a quantized second function approximating the first function;
computing first values of the second function obtained based on first arguments; the first values being not null and the first arguments being variable in a limited range having a maximum limit;
computing second values of the second function obtained based on second arguments, the second values being null and the second arguments being external to the range;
generating a look-up table representing the first function and containing the first and second values associated with indexes correlated to said first arguments and to an expected maximum limit; and
retrieving tabled values from said look-up table based on corresponding indexes for computing said quantity.
2. The method according to claim 1, wherein retrieving the values includes:
computing a current index by processing one of the first arguments and the maximum expected limit,
using the look-up table to determine a tabled value.
3. The method according to claim 2, wherein said current index is variable within a second range equal to twice than the maximum expected limit plus one, said look-up table including:
a first group of values constituted by said first values;
a second group of values constituted by the first values ordered in a mirror-like order to the first group;
a third group of values constituted by said second values.
4. The method according to claim 3, wherein computing the current index includes:
summing said first argument, said maximum expected limit and the value one.
5. The method according to claim 1, wherein said method includes computing a log-likelihoods ratio by means of said look-up table.
6. The method according claim 1, wherein said decoding is performed in accordance with a Log-MAP algorithm.
7. The method according to claim 1, wherein said look-up table is used to computing a correcting factor of the Log-MAP algorithm.
8. The method according to claim 7, wherein the decoding includes performing a decoding of a turbo code and the tabled values represent correction factors used to compute metrics.
9. The method according to claim 8, further comprising:
performing a first calculation to obtain forward metrics;
performing a second calculation to obtain backward metrics; and
performing a third calculation to obtain a log-likelihood ratio for every information bit to be decoded.
10. The method according to claim 9, wherein each of said first, second and third calculations includes using said look-up table in accordance with a corresponding Log-MAP decoding algorithm.
11. The method according to claim 9, wherein at least one and no more than two of said calculations are performed by the use of said look-up table for implementing the Log-MAP decoding algorithm and the remaining calculations are performed implementing a Max Log-MAP decoding algorithm.
12. The method according to claim 1, wherein said second function corresponds to a further look-up table LUT(\u0394) which has substantially the following form:
LUT(\u0394)=round(log(1+exp(\u2212\u03942p))2p)
where p is a factor corresponding to a number of bits dedicated to the precision of the value LUT(\u0394) and \u0394 is indicative of the first arguments varying within said range having maximum limit \u0394max.
13. The method according to claim 12, wherein said current index is variable within a second range equal to twice than the maximum expected limit plus one said look-up table including:
a first group of values constituted by said first values:
a second group of values constituted by the first values ordered in a mirror-like order to the first group;
a third group of values constituted by said second values, wherein the first group of tabled values of said look-up table are equal to the values of said further look-up table.
14. The method according to claim 8, wherein implementing the Log-MAP decoding algorithm further includes estimating functions max*(a1,a2) where a1 and a2 are parameters correlated to the one of the following quantities: forward and backward metrics and likelihood ratio.
15. The method according to claim 8, further comprising:
receiving first and second soft values produced by a turbo encoder representing information transmitted on a communication channel, the first soft value corresponding to a transmitted bit to be decoded;
computing the log-likelihood ratio by an iterative processing in a first decoder based on the forward and backward metrics and on the first and a second soft values; and
feeding an interleaver with the calculated log-likelihood ratio to obtain an interleaved log-likelihood ratio.
16. The method according to claim 15, further comprising:
receiving a third soft value produced by a turbo encoder representing further information transmitted on the communication channel;
feeding a second decoder with said interleaved log-likelihood ratio and said third soft value to generate an output first quantity and a second quantity;
feeding a first deinterleaver with the second quantity obtaining a feedback quantity;
supplying said feedback quantity to the first decoder;
supplying to a second interleaver the first quantity to generate an interleaved quantity; and
starting from said interleaved quantity generating a decoded bit corresponding to the transmitted bit.
17. An apparatus, comprising:
a first decoder for performing iterative decoding of information coded by an error correction code, the first decoder including:
a memory storing a look-up table comprising a plurality of tabled values associated with corresponding indexes, said plurality of tabled values comprising:
a first set of non-null values associated with a first set of arguments included in a limited range; and
a second set of null values associated with a second set of arguments external to said limited range; and
a processor module for retrieving said tabled values from the look-up table based on said indexes and evaluating a quantity related to a decoding function.
18. The apparatus according to claim 17, wherein the processor module comprises:
a first computing module for computing a current index by processing a current first argument and a maximum limit; and
a retrieving module for reading the look-up table to determine a tabled value.
19. The apparatus according to claim 17, wherein said indexes are variable within a second range equal to twice maximum limit plus one.
20. The apparatus according to claim 19, wherein the computing module is configured for computing the current index value by summing said argument, said maximum limit and the value one.
21. The apparatus according to claim 18, wherein said processing module is configured to compute a log-likelihoods ratio by means of said look-up table.
22. The apparatus according to claim 18, wherein said processing module is configured in accordance with a Log-MAP algorithm.
23. The apparatus according to claim 18, wherein said processing module is configured to read the look-up table for computing a correcting factor of the Log-MAP algorithm.
24. The apparatus according to claim 18, so a to perform a decoding of a turbo code and the tabled values represent a correcting factor of a max*(a1,a2) function.
25. The apparatus according to claim 18, wherein said decoder further includes a second computing module configured for:
performing a first calculation to obtain forward metric;
performing a second calculation to obtain backward metrics; and
performing a third calculation to obtain a log-likelihood ratio for every information bit to be decoded.
26. The apparatus according to claim 25, said decoder further comprising an input for receiving first and second soft values produced by a turbo encoder representing information transmitted on a communication channel, the first soft value corresponding a transmitted bit to be decoded; the processing module being configured to computing the log-likelihood ratio by an iterative processing based on forward and backward metrics and on said first and a second soft values.
27. The apparatus according to claim 26, further comprising an interleaver for elaborating the calculated log-likelihood ratio to obtain an interleaved log-likelihood ratio.
28. The apparatus according to claim 27, wherein said input is so as to receive a third soft value produced by a turbo encoder representing further information transmitted on the communication channel.
29. The apparatus according to claim 28, further comprising:
a second decoder for elaborating said interleaved log-likelihood ratio and said third soft value to generate a first output quantity and a second quantity; and
a first deinterleaver of the second quantity for obtaining a feedback quantity; said feedback quantity being to be supplied to said first decoder.
30. The apparatus according to claim 29, further comprising:
a second interleaver to be feed with the first output quantity and generate an interleaved quantity; and
a decision module for generating a decoded bit corresponding to the transmitted bit, starting from said interleaved quantity.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
What is claimed is:
1. A method of synthesizing a double metal cyanide (DMC) catalyst, said method comprising the step of:
combining an aqueous solution of a first metal salt of the general formula M(X)n wherein;
M is selected from the group consisting of aluminum, zinc, and the transition metals,
X is an anion selected from the group consisting of halides, hydroxides, sulfates, acetates, carbonates, cyanides, oxalates, thiocyanates, isocyanates, isothiocyanates, carboxylates, and nitrates, and
n is a value from 1 to 3 satisfying the valency state of M;
with an aqueous solution of a second metal salt of the general formula N(Y)n wherein;
N is selected from the group consisting of the transition metals and the lanthanides,
Y is an anion selected from the group consisting of halides, hydroxides, sulfates, carbonates, cyanides, oxalates, thiocyanates, isocyanates, isothiocyanates, carboxylates, and nitrates, and
n is a value from 1 to 3 satisfying the valency state of N; and
with an aqueous solution of an alkali metal cyanide in a single step to form a suspension having a particle phase and a continuous phase wherein the particle phase comprises the DMC catalyst synthesized from the combination of the aqueous solutions of the first metal salt, the second metal salt, and the alkali metal cyanide, and the continuous phase comprises a secondary product.
2. A method as set forth in claim 1 further comprising the step of separating the particle phase from the continuous phase.
3. A method as set forth in claim 2 wherein the step of separating the particle phase from the continuous phase comprises the step of filtering the suspension to collect the particle phase comprising the DMC catalyst as a retentate.
4. A method as set forth in claim 3 further comprising the step of washing the particle phase with a water-soluble, organic activator after the liquid has been decanted.
5. A method as set forth in claim 4 wherein the water-soluble, organic activator comprises at least one of ethanol, isopropyl alcohol, n-butyl alcohol, sec-butyl alcohol, tert-butyl alcohol, isobutyl alcohol, and glyme.
6. A method as set forth in claim 3 wherein the step of separating the particle phase from the continuous phase further comprises the step of drying the retentate.
7. A method as set forth in claim 2 wherein the step of separating the particle phase from the continuous phase comprises the step of holding the suspension until the continuous phase at least partially separates from the particle phase.
8. A method as set forth in claim 7 wherein the step of holding the suspension is further defined as holding the suspension for from 0.5 to 24 hours.
9. A method as set forth in claim 7 wherein the step of separating the particle phase from the continuous phase comprises the step of decanting the continuous phase after the suspension has been held.
10. A method as set forth in claim 9 wherein the step of separating the particle phase from the continuous phase further comprises the step of centrifuging the particle phase to separate liquid from the particle phase after the continuous phase has been decanted.
11. A method as set forth in claim 10 wherein the step of separating the particle phase from the continuous phase further comprises the step of decanting the liquid after the particle phase has been centrifuged.
12. A method as set forth in claim 11 wherein the step of separating the particle phase from the continuous phase further comprises the step of washing the particle phase with a water-soluble, organic activator after the liquid has been decanted.
13. A method as set forth in claim 12 wherein the water-soluble, organic activator comprises at least one of ethanol, isopropyl alcohol, n-butyl alcohol, sec-butyl alcohol, tert-butyl alcohol, isobutyl alcohol, and glyme.
14. A method as set forth in claim 12 wherein the step of separating the particle phase from the continuous phase further comprises the step of drying the particle phase after the particle phase has been washed with the water-soluble, organic activator.
15. A method as set forth in claim 1 wherein at least one of the aqueous solutions of the first metal salt, the second metal salt, and the alkali metal cyanide further comprise a water-soluble, organic activator.
16. A method as set forth in claim 1 wherein the first metal salt is combined in molar excess relative to the second metal salt.
17. A method as set forth in claim 1 wherein the secondary product comprises KCl.
18. A method of synthesizing a double metal cyanide (DMC) catalyst, said method comprising the step of:
combining an aqueous solution of a first metal salt of the general formula M(X)n wherein;
M is selected from the group consisting of aluminum, zinc, and the transition metals,
X is an anion selected from the group consisting of halides, hydroxides, sulfates, acetates, carbonates, cyanides, oxalates, thiocyanates, isocyanates, isothiocyanates, carboxylates, and nitrates, and
n is a value from 1 to 3 satisfying the valency state of M;
with an aqueous solution of a second metal salt of the general formula N(Y)n wherein;
N is selected from the group consisting of the transition metals and the lanthanides,
Y is an anion selected from the group consisting of halides, hydroxides, sulfates, carbonates, cyanides, oxalates, thiocyanates, isocyanates, isothiocyanates, carboxylates, and nitrates, and
n is a value from 1 to 3 satisfying the valency state of N; and
with an aqueous solution of an alkali metal cyanide in a single step to synthesize the DMC catalyst.
19. A method as set forth in claim 17 wherein the first metal salt comprises at least one of zinc acetate and aluminum acetate.
20. A method as set forth in claim 17 wherein the second metal salt comprises neodymium chloride.
21. A method as set forth in claim 17 wherein the first metal salt is combined in molar excess relative to the second metal salt.
22. A method as set forth in claim 20 wherein the molar ratio of the first metal salt to the second metal salt is from 1.1:1 to 6:1.
23. A method of synthesizing a double metal cyanide (DMC) catalyst, said method comprising the step of:
combining an aqueous solution of a first metal salt of the general formula M(X)n wherein;
M is selected from the group consisting of aluminum, zinc, and the transition metals,
X is an anion selected from the group consisting of halides, hydroxides, sulfates, acetates, carbonates, cyanides, oxalates, thiocyanates, isocyanates, isothiocyanates, carboxylates, and nitrates, and
n is a value from 1 to 3 satisfying the valency state of M;
with an aqueous solution of a second metal salt of the general formula N(Y)n wherein;
N is selected from the group consisting of the transition metals and the lanthanides,
Y is an anion selected from the group consisting of halides, hydroxides, sulfates, carbonates, cyanides, oxalates, thiocyanates, isocyanates, isothiocyanates, carboxylates, and nitrates, and
n is a value from 1 to 3 satisfying the valency state of N; and
with an aqueous solution of an alkali metal cyanide in a single step to synthesize the DMC catalyst,
wherein the aqueous solution of the first metal salt and the aqueous solution of the second metal salt are each independently fed into the aqueous solution of the alkali metal cyanide.
24. A method as set forth in claim 23 wherein M is selected from the group consisting of Al(III) and Zn(II).
25. A method as set forth in claim 23 wherein X is selected from the group consisting of halides and acetates.
26. A method as set forth in claim 23 wherein N is selected from the group consisting of Fe(II), Fe(III), Co(II), Co(III), Nd(III).
27. A method as set forth in claim 23 wherein Y is selected from the group consisting of halides.
28. A method as set forth in claim 23 wherein the alkali metal cyanide is selected from the group consisting of LiCN, NaCN, and KCN.
29. A method as set forth in claim 23 wherein the first metal salt is ZnCl2, the second metal salt is CoCl2, and the alkali metal cyanide is KCN.
30. A method as set forth in claim 23 wherein the step of combining the aqueous solutions of the first metal salt, the second metal salt, and the alkali metal cyanide further comprises the step of forming a suspension having a particle phase and a continuous phase wherein the particle phase comprises the DMC catalyst synthesized from the combination of the aqueous solutions of the first metal salt, the second metal salt, and the alkali metal cyanide, and the continuous phase comprises a secondary product.
31. A method as set forth in claim 30 wherein the secondary product comprises KCl.
32. A method as set forth in claim 30 further comprising the step of separating the particle phase from the continuous phase.
33. A method as set forth in claim 32 further comprising the step of washing the particle phase with a water-soluble, organic activator.
34. A method as set forth in claim 33 wherein the step of washing the particle phase with the water-soluble, organic activator occurs after the particle phase has been separated from the continuous phase.
35. A method as set forth in claim 23 wherein at least one of the aqueous solutions of the first metal salt, the second metal salt, and the alkali metal cyanide further comprise a water-soluble, organic activator.
36. A method as set forth in claim 23 wherein the first metal salt is combined in molar excess relative to the second metal salt.
37. A method of synthesizing a double metal cyanide (DMC) catalyst, said method comprising the steps of:
(A) combining an aqueous solution of a metal salt of the general formula N(Y)n wherein;
N is selected from the group consisting of the transition metals and the lanthanides,
Y is an anion selected from the group consisting of halides, hydroxides, sulfates, carbonates, cyanides, oxalates, thiocyanates, isocyanates, isothiocyanates, carboxylates, and nitrates, and
n is a value from 1 to 3 satisfying the valency state of N;
with an aqueous solution of an alkali metal cyanide of the general formula XCN wherein;
X is selected from the group consisting of alkali metals, and
to form an intermediate solution comprising a DMC catalyst precursor and a secondary product of the general formula XnY, wherein n is a value from 1 to 3 satisfying the valency state of Y; and
(B) combining an aqueous solution of a metal salt of the general formula M(X)n wherein;
M is selected from the group consisting of aluminum, zinc, and the transition metals,
X is an anion selected from the group consisting of halides, hydroxides, sulfates, acetates, carbonates, cyanides, oxalates, thiocyanates, isocyanates, isothiocyanates, carboxylates, and nitrates, and
n is a value from 1 to 3 satisfying the valency state of M;
with the intermediate solution such that the DMC catalyst is synthesized upon reaction between the DMC catalyst precursor and the metal salt of the general formula M(X)n.
38. A method as set forth in claim 37 wherein M is selected from the group consisting of Al(III) and Zn(II).
39. A method as set forth in claim 37 wherein X is selected from the group consisting of halides and acetates.
40. A method as set forth in claim 37 wherein N is selected from the group consisting of Fe(II), Fe(III), Co(II), Co(III), Nd(III).
41. A method as set forth in claim 37 wherein Y is selected from the group consisting of halides.
42. A method as set forth in claim 37 wherein the alkali metal cyanide is selected from the group consisting of LiCN, NaCN, and KCN.
43. A method as set forth in claim 37 wherein the metal salt of the general formula N(Y)n is CoCl2, the alkali metal cyanide is KCN, and the metal salt of the general formula M(X)n is ZnCl2.
44. A method as set forth in claim 37 wherein the secondary product comprises KCl.
45. A method as set forth in claim 37 further comprising the step of forming a suspension having a particle phase and a continuous phase after step (B), wherein the particle phase comprises the DMC catalyst synthesized from the combination of the aqueous solution of the metal salt of the general formula M(X)n with the intermediate solution, and the continuous phase comprises a secondary product.
46. A method as set forth in claim 45 further comprising the step of separating the particle phase from the continuous phase.
47. A method as set forth in claim 46 further comprising the step of washing the particle phase with a water-soluble, organic activator.
48. A method as set forth in claim 47 wherein the step of washing the particle phase with the water-soluble, organic activator occurs after the particle phase has been separated from the continuous phase.
49. A method as set forth in claim 37 wherein at least one of the aqueous solutions of the metal salt of the general formula N(Y)n, the alkali metal cyanide, and the metal salt of the general formula M(X)n further comprise a water-soluble, organic activator.
50. A method as set forth in claim 37 wherein the molar ratio of the metal salt of the general formula M(X)n to the metal salt of the general formula N(Y)n is greater than 1.