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3.2 Estimation of complexity and fast operations of the device of correction of errors in an optical computer memory

The offered device accepts one symbol of a code word (8 bits) for 2 steps. At decoder implementation on modern circuit arrays ASIC

The processor clock rate will make 500 MHz, thus carrying capacity of the device qбудет is equal:

Where nb - number of the bats arriving in the decoder for 1 step; fc ικ - a clock rate on which the device works.

Carrying capacity of the decoder is simple for lifting twice, if procedure Chenja-Forni which is carried out by blocks 1300, 2300..., N300 and 1700, 2700..., N700выполнять with parallelism 2.

For an estimation of apparatus complexity of implementation of the developed device reduction of apparatus complexity of all blocks making the device to equivalent complexity in coincidence gates is used. At calculations the coincidence gate will fathom dvuhvhodovyj an element And or OR without the account of inversions on element entries/exits. Total complexity of the developed device will be defined as the sum of complexities of blocks entering into its composition and elements.

Complexity of base elements of which all blocks entering into the device consist, is resulted in table 5. Thus t - capacity of an element.

Table 5 Complexity of base elements of the device

The element name Number of coincidence gates, Hv
The adder of elements of final field GF (2m) (2 vhodovoj)
The commutator (2-vhodovoj)
The binary counter
The multiplier of elements of final field GF (2m) (2 vhodovoj) 2
The circuit design of a quadrating of elements of a final field

GF (2m)


The multiplier on constant factor in final field GF (2m)
The inverter of elements of final field GF (2m) 4m2
The register-lug-latch working on front 8m
The block of coincidence gates (with 1st operating entry) t
The selector of a zero element of final field GF (2m) 7
The D-trigger 8
The comparison circuit design (on equality) t = 8 31
The shift register 11т

Table 6 contains an estimation of complexity of the block of scaling of syndromes of horizontal code words (drawing 24 see).

Table 6 Complexity of the block of scaling of syndromes of the horizontal code

Words

Element Number of coincidence gates, hv
Multipliers on the constant

Factor 1101

480
Adders of elements of field G alua 240
1102
Registers-lug-latches 1103 640
Total H-syn calculator 1360

Table 7 contains an estimation of complexity of the block of storage and modification of syndromes of horizontal code words (drawing 19 see).

Table 7 Complexity of the block of storage and modification of syndromes of horizontal code words

Element Number of coincidence gates, Hv Number of bats of memory, χπ
The adder of elements of a field

Galua 1201

240
Five-section commutators 1202, 1205 588
Memory blocks with 33280

Direct access

1203, 1206

dvuhvhodovye

Commutators 1204, 1207

480
The binary counter 1208 64
Total H-syn storage 1372 33280

Table 8 contains an estimation of complexity of the block of a finding of locators and values of errors of horizontal code words (drawing 25 see).

Table 8 Complexity of the block of a finding of locators and values of errors of horizontal code words

Element Number of coincidence gates, Hv
The module of discrete transformation

The Fourier 1310

472
The module of discrete transformation

The Fourier 1320

1080
The module of discrete transformation

The Fourier 1330

880
The inverter of elements of field Galua 1301 256
Remultiplier of elements of field Galua

1302

256
The block of coincidence gates 1303 8
The shift register 1304 18018
The D-trigger 1305 8
The selector of a zero element of field Galua

1306

7
Logical units And 1307, 1308 2
The comparator 1309 72
The binary counter on nh 1310 64
Registers-lug-latches 1311, 1312 707
The multiplier on constant factor 1313 64

The register 1314 48
Total H-Chien Forney 21939

Table 9 contains an estimation of complexity of the block of scaling of values of modifications of syndromes of horizontal code words (drawing 21 see).

Table 9 Complexity of the block of scaling of values of modifications of syndromes of horizontal code words

Element Number of coincidence gates, Hv
Remultipliers of elements of field G alua

1401.1 - 1401.9, 1403.1 - 1403.4

3328
Squaring devices 1402.1 - 1402.4 64
Total H - ∆ syn 3392

Table 10 contains an estimation of complexity of the block of scaling of values of modifications of syndromes of vertical code words (drawing 22 see).

Table 10 Complexity of the block of scaling of values of modifications of syndromes of vertical code words

Element Number of coincidence gates, Hv
Remultipliers of elements of field Galua

1501.1 - 1501.15, 1503.1 - 1503.7

5632
Squaring devices 1502.1 - 1502.7 112
Total V - ∆ syn 5744

Table 11 contains an estimation of complexity of the block of scaling and storage of syndromes of vertical code words (drawing 20 see).

Table 11 Complexity of the block of scaling and storage of syndromes of vertical code words

Element Number of coincidence gates, Hv Number of bats of memory, χn
The block of coincidence gates 1601 128
Multipliers on constant factor

1602.1 - 1602. G

768
///-razrjadnye adders 384

Elements of field Galua

1603.1 - 1603. G

Logical unit NOT

1604

0
The binary counter on kh

1605

64
Memory blocks with

Direct access

1606, 1610

44032
dvuhvhodovye

Commutators 1607, 1609,

1611, 1612

96
Two-section commutators 1608, 1613 12
Total V-syn calc./stor. 1516 44032

Table 12 contains an estimation of complexity of the block of a finding of locators and

Values of errors of vertical code words.

Table 12 Complexity of the block of a finding of locators and values of errors

Vertical code words

Element Number of coincidence gates, Hv
The module of discrete transformation

The Fourier 1710

672
The module of discrete transformation

The Fourier 1720

2528
The module of discrete transformation

The Fourier 1730

1480
The inverter of elements of field Galua 1701 256
Remultiplier of elements of field Galua

1702

256
The block of coincidence gates 1703 8
The shift register 1704 20592

The D-trigger 1705 8
The selector of a zero element of field Galua

1706

7
Logical units And 1707, 1708 2
The comparator 1709 72
The binary counter on nh 1710 64
Registers-lug-latches 1711, 1712 1088
The multiplier on constant factor 1713 48
The register 1714 64
Total V-Chien Forney 27145

Table 13 contains an estimation of complexity of the block of storage of values

Errors of vertical code words (drawing 23 see).

Table 13 Complexity of the block of storage of values of errors vertical

Code words

Element Number of coincidence gates, hv Number of bats of memory, χπ
Memory blocks with

Direct access

1801, 1806

572416
dvuhs ektsionnye commutators 1802, 1807 96
Logical units And

1803, 1804, 1811, 1812

4
dvuhvhodovyj the commutator 1805 24
Binary counters on kh

1808, 1809

128
The binary counter on nv

1810

64
Total V-XY storage 316 572416

Table 14 contains an estimation of complexity of the block of storage and modification of syndromes of vertical code words.

Table 14 Complexity of the block of storage and modification of syndromes of vertical code words

Element Number of coincidence gates, hv Number of bats of memory, χπ
The adder of elements of a field

Galua 2601

384
The five-section

Commutators 2602, 2605

876
Memory blocks with

Direct access

2603, 2606

44032
dvuhvhodovye

Commutators 2604, 2607

768
The binary counter 2608 64
Total V-syn storage 2092 44032

Table 15 contains an estimation of complexity of separate blocks of decoders of iterations from which there is a device.

For time storage of the symbols of corrected data units accepted from the channel in the device of correction of errors blocks of a buffer memory 1001, 2001 are added..., Λ7001. The size of each of them is equal to number octad in two data units. For calculation of volume of a buffer memory it is possible to take advantage of the following formula:

χπ = 2 * 172 * 208 * t = 605696 bits.

Table 15 Complexity of the device of correction of errors

Element Number of coincidence gates, Hv Number of bats of memory, χπ
Buffer memory of given 1001 605696
Adders of elements of the final

Fields 1002, 1003

48
The block of scaling of syndromes 1360

Horizontal code words 1100
The block of storage and modification of syndromes of horizontal code words 1200 1372 33280
The block of scaling of polynomials of locators and values of errors of horizontal code words 1004 10792
The block of a finding of locators and values of errors of horizontal code words 1300 31939
The block of scaling of values of modifications of syndromes of horizontal code words 1400 3392
The block of scaling of values of modifications of syndromes of vertical code words 1500 5744
The block of scaling and storage of syndromes of vertical code words 1600 1516 44032
The block of scaling of polynomials of locators and values of errors of vertical code words 1005 17128
The block of a finding of locators and values of errors of vertical code words 1700 27145
The block of storage of values of errors of vertical code words 1800 316 572416
The block of storage and modification of syndromes of vertical code words 2600 2092 44032
Total 1st decoder of iterations 90752 1255424

Total 2nd and subsequent decoders of iterations 89968 1255424

The device of decoding of products of Rs-codes represents synchronous potokovyj the decoder, processing an input information in rate of their receipt. An output information taktirujutsja frequency of an input information, and, hence, is given out with the same speed. The delay of data on each decoder is equal in the device to a time of receipt of two blocks, and a delay of all decoder of a time of receipt 2Nблоков (N - quantity of decoders).

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A source: Krivonos Alexey Vladimirovich. METHODS, ALGORITHM And the DEVICE of CORRECTION of ERRORS In the OPTICAL COMPUTER MEMORY. The DISSERTATION on competition of a scientific degree of a Cand.Tech.Sci. Kursk - 2018. 2018

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