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Operating Segments and Geographic Information - Reconciliation of Total Reportable Segments' Revenues and EBITDA to Consolidated Revenues and Consolidated Income Before Taxes (Details) - USD ($) $ in Thousands | 3 Months Ended | 12 Months Ended
--- | --- | ---
Dec. 31, 2019 | Sep. 29, 2019 | Jun. 30, 2019 | Mar. 31, 2019 | Dec. 31, 2018 | Sep. 30, 2018 | Jul. 01, 2018 | Apr. 01, 2018 | Dec. 31, 2019 | Dec. 31, 2018 | Dec. 31, 2017
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |  |  |  |  |  |  |
Total Segment Revenues | $ 549,688 | $ 533,098 | $ 548,352 | $ 500,140 | $ 552,052 | $ 554,037 | $ 560,898 | $ 498,715 | $ 2,131,278 | $ 2,165,702 | $ 2,087,185
Amortization of intangibles |  |  |  |  |  |  |  |  | (74,609) | (75,140) | (90,188)
Depreciation expense |  |  |  |  |  |  |  |  | (40,400) | (38,300) | (38,600)
Severance, restructuring, and acquisition integration costs | (21,000) | (3,000) | (2,500) | (0) | (2,200) | (4,600) | (4,600) | (11,200) | (26,544) | (22,625) | (41,893)
Gain from patent litigation |  |  |  |  |  |  |  |  | 0 | (62,141) | 0
Operating income | $ 43,400 | $ 57,542 | $ 58,775 | $ 47,490 | $ 71,264 | $ 129,160 | $ 68,706 | $ 44,878 | 207,207 | 314,008 | 233,641
Interest expense, net |  |  |  |  |  |  |  |  | (55,814) | (60,839) | (82,651)
Non-operating pension benefit (cost) |  |  |  |  |  |  |  |  | 1,017 | (99) | (561)
Loss on debt extinguishment |  |  |  |  |  |  |  |  | 0 | (22,990) | (52,441)
Consolidated income from continuing operations before taxes |  |  |  |  |  |  |  |  | 152,410 | 230,080 | 97,988
Reportable Segment |  |  |  |  |  |  |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |  |  |  |  |  |  |
Total Segment Revenues |  |  |  |  |  |  |  |  | 2,131,278 | 2,165,702 | 2,087,185
Deferred revenue adjustments |  |  |  |  |  |  |  |  | 0 | 0 | 0
Total Segment EBITDA |  |  |  |  |  |  |  |  | 351,223 | 394,656 | 405,429
Amortization of intangibles |  |  |  |  |  |  |  |  | (74,609) | (75,140) | (90,188)
Depreciation expense |  |  |  |  |  |  |  |  | (40,409) | (38,309) | (38,624)
Severance, restructuring, and acquisition integration costs |  |  |  |  |  |  |  |  | (26,544) | (22,625) | (41,893)
Purchase accounting effects related to acquisitions |  |  |  |  |  |  |  |  | 592 | 1,690 | 6,133
Amortization of software development intangible assets |  |  |  |  |  |  |  |  | (525) | (79) | 0
Loss on sale of assets (3) |  |  |  |  |  |  |  |  | 0 | 94 | 1,013
Costs related to patent litigation |  |  |  |  |  |  |  |  | 0 | (2,634) | 0
Gain from patent litigation |  |  |  |  |  |  |  |  | 0 | (62,141) | 0
Income from equity method investment |  |  |  |  |  |  |  |  | 0 | 0 | 7,502
Operating income |  |  |  |  |  |  |  |  | 207,207 | 314,008 | 233,641
Interest expense, net |  |  |  |  |  |  |  |  | (55,814) | (60,839) | (82,651)
Eliminations |  |  |  |  |  |  |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |  |  |  |  |  |  |
Operating income |  |  |  |  |  |  |  |  | (1,337) | (2,218) | (1,439)
Enterprise Solutions |  |  |  |  |  |  |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |  |  |  |  |  |  |
Total Segment Revenues |  |  |  |  |  |  |  |  | 1,081,232 | 1,095,900 | 1,054,847
Severance, restructuring, and acquisition integration costs |  |  |  |  |  |  |  |  | (11,050) | (14,862) | (28,146)
Enterprise Solutions | Reportable Segment |  |  |  |  |  |  |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |  |  |  |  |  |  |
Total Segment EBITDA |  |  |  |  |  |  |  |  | 162,276 | 190,910 | 196,554
Amortization of intangibles |  |  |  |  |  |  |  |  | (23,500) | (22,255) | (37,245)
Depreciation expense |  |  |  |  |  |  |  |  | (20,765) | (19,374) | (19,255)
Severance, restructuring, and acquisition integration costs |  |  |  |  |  |  |  |  | (11,050) | (14,863) | (28,146)
Purchase accounting effects related to acquisitions |  |  |  |  |  |  |  |  | 592 | 1,690 | 6,133
Segment revenues | Reportable Segment |  |  |  |  |  |  |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |  |  |  |  |  |  |
Total Segment Revenues |  |  |  |  |  |  |  |  | 2,131,278 | 2,165,702 | 2,087,185
Segment revenues | Enterprise Solutions | Reportable Segment |  |  |  |  |  |  |  |  |  |  |
Segment Reporting, Reconciling Item for Operating Profit (Loss) from Segment to Consolidated [Line Items] |  |  |  |  |  |  |  |  |  |  |
Total Segment Revenues |  |  |  |  |  |  |  |  | $ 1,081,232 | $ 1,095,900 | $ 1,054,847

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