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Szemerédi Theorem on Arithmetic Progressions
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Classroom Contents
Mathematics of Signal Design for Communication Systems and Szemerédi’s and Green-Tao’s Theorems
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- 1 Intro
- 2 Motivation - Orthogonal Transmission Scheme
- 3 Orthogonal Transmission Scheme - Sketch
- 4 Motivation - Dynamics of Orthogonal Transmission Scheme
- 5 Drawback of OFDM - The Effect of Clipping
- 6 Motivation - High Dynamics of Orthogonal Transmission Scheme
- 7 Motivation - Tone Reservation method
- 8 PAPR Reduction Problem - Remarks
- 9 Necessary and Sufficient Conditions - Essential Subspaces
- 10 Necessary Condition - Sketch of Proof
- 11 Outline
- 12 Solvability of PAPR Problem - OFDM
- 13 Szemerédi Theorem on Arithmetic Progressions
- 14 Szemerédi Theorem - Historical Remarks
- 15 Szemerédi Theorem - Asymptotic Case and Probabilistic Case
- 16 Solvability of PAPR reduction problem & Arithmetic Progressions
- 17 Asymptotic Tightenings of Thm. 3.7
- 18 Walsh functions
- 19 Perfect Walsh Sum
- 20 PAPR reduction problem for CDMA Case - PWS
- 21 Asymptotic results for PWS
- 22 Summary and Conclusions
- 23 PAPR Reduction Problem - Formulation
