1. A heat treatment method in which a plurality of substrates to be treated is held by a substrate holder at predetermined vertical intervals, the substrate holder is carried into a heat treating furnace, and a predetermined heat treatment is performed on the substrates, the method comprising the steps of:
forming a multi-plate unit to hold circumferential portions of two substrates under the condition that back surfaces of the two substrates face each other;
holding a plurality of the multi-plate units by means of the substrate holder at a vertical interval larger than a distance between the front surface of one of the two substrates held by the multi-plate unit and the back surface of the other of the two substrates such that a first distance between one of a first pair of substrates that are vertically adjacent each other and have respective front surfaces facing each other and the other of the first pair of substrates is larger than a second distance between one of a second pair of substrates that are vertically adjacent each other and have respective back surfaces facing each other and the other of the second pair of substrates; and
performing the predetermined heat treatment, wherein
each of the multi-plate units has a first support ring and a second support ring, each of the first support rings being adapted to hold the substrate under the condition that the back surface of the substrate faces upward, each of the second support rings being adapted to hold the substrate under the condition that the front surface of the substrate faces upward.
2. The heat treatment method according to claim 1, wherein
each of the first and second support rings has protrusions that protrude from the circumference thereof and are arranged at a predetermined interval, the protrusions of the second support ring of each of the support rings being placed on the protrusions of the first support ring of the support ring, and having respective thicknesses that allow a distance between the substrate held by the first support ring and the substrate held by the second support ring to be maintained to a predetermined value.
3. The heat treatment method according to claim 1, wherein the step of holding the plurality of multi-plate units comprises holding the first pair of substrates so that the front faces thereof face each other directly.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. An apparatus for recovering an error-correction encoded codeword, the apparatus comprising:
an error-correction decoder that performs error-correction decoding to attempt to recover the error-correction-encoded codeword from a set of channel soft-output values; and
a controller that:
determines, if the error-correction decoder converges on an observed trapping set, whether or not the observed trapping set corresponds to any known trapping set stored in a database of known trapping sets; and
selects, if the controller determines that the observed trapping set does not correspond to any known trapping set, one or more known trapping sets from the database, wherein:
the apparatus adjusts the set of channel soft-output values based on the one or more known trapping sets to generate a set of adjusted channel soft-output values for subsequent error-correction decoding.
2. The invention of claim 1, wherein:
for each known trapping set, the database stores (i) a number of unsatisfied check nodes corresponding to the known trapping set and (ii) distances between the unsatisfied check nodes corresponding to the known trapping set; and
the controller determines whether or not the observed trapping set corresponds to a known trapping set by comparing (i) a number of unsatisfied check nodes corresponding to the observed trapping set to the number of unsatisfied check nodes corresponding to the known trapping set and (ii) distances between the unsatisfied check nodes corresponding to the observed trapping set to the distances between the unsatisfied check nodes corresponding to the known trapping set.
3. The invention of claim 1, wherein the controller selects the one or more known trapping sets from the database based on dominance of the known trapping sets in the database.
4. The invention of claim 3, wherein the controller selects the one or more known trapping sets such that the one or more known trapping sets are the most-dominant trapping sets stored in the database.
5. The invention of claim 3, wherein dominance of the one or more known trapping sets is determined based on the effects of a known trapping set on bit-error rate.
6. The invention of claim 1, wherein:
for each known trapping set, the database stores indices of one or more erroneous bit nodes corresponding to the known trapping set; and
the controller selects for adjustment a selected subset of one or more channel soft-output values in the set of channel soft-output values such that the selected subset corresponds to the one or more erroneous bits nodes.
7. The invention of claim 6, wherein:
the controller selects two or more known trapping sets from the database; and
the selected subset of one or more channel soft-output values corresponds to erroneous bit nodes in the two or more known trapping sets.
8. The invention of claim 6, wherein the adjuster adjusts the set of channel soft-output values by flipping hard-decision bits of one or more of the channel soft-output values in the selected subset of one or more channel soft-output values.
9. The invention of claim 8, wherein, for each channel soft-output value in the selected subset, the adjuster increases a confidence value corresponding to the channel soft-output value.
10. The invention of claim 8, wherein, if subsequent error-correction decoding results in convergence on an observed trapping set that does not correspond to a known trapping set, then the apparatus attempts to recover the correct error-correction-encoded codeword by flipping a different arrangement of hard-decision bits in the selected subset.
11. The invention of claim 6, wherein, if subsequent error-correction decoding results in convergence on the error-correction-encoded codeword, then the apparatus stores the unknown trapping set in the trapping set database as a new known trapping set.
12. The invention of claim 1, wherein the error-correction decoder is a low-density parity-check decoder.
13. A method for recovering an error-correction encoded codeword, the method comprising:
(a) performing error-correction decoding to attempt to recover the error-correction-encoded codeword from a set of channel soft-output values;
(b) determining, if the error-correction decoding converges on an observed trapping set, whether or not the observed trapping set corresponds to any known trapping set stored in a database of known trapping sets;
(c) selecting, if the observed trapping set does not correspond to any known trapping set, one or more known trapping sets from the database; and
(d) adjusting the set of channel soft-output values based on the one or more known trapping sets to generate a set of adjusted channel soft-output values for subsequent error-correction decoding.
14. The invention of claim 13, wherein:
for each known trapping set, the database stores (i) a number of unsatisfied check nodes corresponding to the known trapping set and (ii) distances between the unsatisfied check nodes corresponding to the known trapping set; and
step (b) determines whether or not the observed trapping set corresponds to a known trapping set by comparing (i) a number of unsatisfied check nodes corresponding to the observed trapping set to the number of unsatisfied check nodes corresponding to the known trapping set and (ii) distances between the unsatisfied check nodes corresponding to the observed trapping set to the distances between the unsatisfied check nodes corresponding to the known trapping set.
15. The invention of claim 13, wherein step (c) comprises selecting the one or more known trapping sets from the database based on dominance of the known trapping sets in the database.
16. The invention of claim 15, wherein dominance of the one or more known trapping sets is determined based on the effects of a known trapping set on bit-error rate.
17. The invention of claim 13, wherein:
for each known trapping set, the database stores indices of one or more erroneous bit nodes corresponding to the known trapping set;
step (d) comprises selecting for adjustment a selected subset of one or more channel soft-output values in the set of channel soft-output values such that the selected subset corresponds to the one or more erroneous bits nodes.
18. The invention of claim 17, wherein the step (d) further comprises adjusting the set of channel soft-output values by flipping hard-decision bits of one or more of the channel soft-output values in the selected subset of one or more channel soft-output values.
19. The invention of claim 18, wherein step (d) further comprises, for each channel soft-output value in the selected subset, increasing a confidence value corresponding to the channel soft-output value.
20. The invention of claim 18, further comprising:
(e) attempting to recover the correct error-correction-encoded codeword by flipping a different arrangement of hard-decision bits in the selected subset, if subsequent error-correction decoding results in convergence on an observed trapping set that does not correspond to a known trapping set.