Network OS Abstraction: Data to Function Store

1. CS434/534: Topics in Networked (Networking) SystemsNetwork OS Abstraction: From Data to Function Store;Wireless Foundation: Frequency-Domain AnalysisYang (Richard) YangComputer Science DepartmentYale University208A WatsonEmail: yry@cs.yale.eduhttp://zoo.cs.yale.edu/classes/cs434/

2. Outline • Admin and recap • High-level datapath programming • Network OS supporting programmable networks • overview • OpenDaylight • distributed network OS (Paxos, Raft) • from data store to function store • Programmable wireless communications and networking • Background

3. Admin • Hardcopies of PS1 can be turned into my mail box (208A) on the first floor • A talk on mobile systems • Time: Tuesday 10:30 am • Location: AKW

4. Recap • Distributed data store using Raft • Programming complexities of data store • Programmers need to manually record data access and register subscriptions • Programmers need to handle cleanup of any changes made in previous execution • Programmers need to make sure that no data-change loops are triggered, to avoid instability • From data store to function store • Function store API • add(func, [meta]), remove(handler) • Data access API • read(xpath), update(xpath, op, val), test(xpath, booleanExpr, ??

5. Recap: From API to Realization Re-exec a function using collected dependency. • Assume exec’d the seq f1-f6. Then a changes. How to recover? Which functions must re-execute? Which do not need re-exec? R: {b, c} f2 f4 R: {h} R: {h} f1 f6 f3 f5 R: {a, b, c} R: {a, f}

6. From API to Realization: Design 1 UpdateAlg1( a ) Fupdate = a.DEPENDENCY_CHANGEFfixed = executed before Fupdate in total order restore2( Ffixed) while ( ! Fupdate.empty() ) { pick f as a root in Fupdate Fupdate -= f; Ffixed += f execute f add functions: not in Ffixed ^ depends on f updates }

7. Question R: {b, c} • Is UpdateAlg1 correct? f2 f4 R: {h} R: {h} f1 f6 f3 f5 R: {a, b, c} R: {a, f}

8. Function Store • There are multiple directions where one can explore: • How to best utilize test()? • How to best utilize past computation to learn dependency (e.g., learning)? • How to utilize multi-cores in recovery? • Can we distribute the functions at multiple servers (e.g., running Raft)? • A good topic as a course project.

9. Roadmap • High-level networking system programming • Networking operating system • overview • OpenDaylight • distributed networking OS (Paxos, Raft) • from data store to function store • Programmable wireless communications and networking • background • software defined wireless networking systems • Network function virtualization

10. Recap: Wireless and Mobile Computing • Driven by infrastructure and device technology • global infrastructures • device miniaturization and capabilities • software development platforms • Challenges: • wireless channel: unreliable, open access • mobility • portability • changing environment • heterogeneity

11. Wireless Networking Systems: Objectives • Avoid a full course on wireless communications, but cover enough to understand the main issues and main emerging techniques.

12. Implementing Wireless Systems: From Hardware to Software

13. sender analog signal bit stream source decoding channel coding channel decoding source coding modulation demodulation Overview of Wireless Communicatinos/Networking receiver bit stream

14. Wireless Example: Wireless: 802.11

15. 1 digital signal 0 t Basic Question: Why Not Send Digital Signal in Wireless Communications?

16. Outline • Admin and recap • Programmable wireless communications and networking • background • Frequency domain analysis (Fourier series)

17. Fourier Series: Decomposing a function into a Collection of Harmonics • A periodic real function g(t) on [-π, π] can be decomposed as a set of harmonics (cos, sin): Time domain 1 1 0 0 t t decomposition periodical signal set bk = 0

18. Fourier Series

19. Fourier Series

20. Fourier Series: Example http://en.wikipedia.org/wiki/File:Periodic_identity_function.gif

21. Fourier Series: An Alternative Representation • A problem of the expression It contains both cos() and sin() functions, and hence is somehow complex to manipulate.

22. Fourier Series: Using Euler’s formula • Applying Euler’s formula • We have

23. Fourier Series: Using Euler’s formula

24. Making Sense of Complex Numbers What is the effect of multiplying c by ejπ/2? What is the effect of multiplying c by j?

25. Making Sense of Complex Numbers

26. Making Sense of Complex Numbers: Conjugate

27. Summary of Progress: Fourier Series of Real Function on [-π, π]

28. Defining Decomposition on a General Interval • A periodic function g(t) with period T on [a, a+T] can be decomposed as:

29. Defining Decomposition on [0, 1]

30. ej2πft Making Sense of ej2πft

31. Making Sense of ej2πft ej2πft G[f]ej2πft ϕ=2πft ϕ=-2πft e-j2πft G[-f]e-j2πft

32. Fourier Transform • For those who are curious, we do not need it formally • Problem: Fourier series for periodic function g(t), what if g(t) is not periodical? • Approach: • Truncate g(t) beyond [-L/2, L/2] (i.e., set = 0) and then repeat to define gL(t)

33. Fourier Transform Define Let L grow to infinity, we derive Fourier Transform:

34. Fourier Series vs Fourier Transform • Fourier series • For periodical functions, e.g., [0, 1] • Fourier transform • For non periodical functions http://www.differencebetween.com/difference-between-fourier-series-and-vs-fourier-transform/

35. Two Domain Representations • Two representations: time domain; frequency domain • Knowing one can recover the other

36. Example: Frequency Seriesof sine and cosine

37. Example: Frequency Seriesof sine and cosine

38. Example: Frequency Domain’s View of Euler’s Formula

39. Example: Frequency Domain’s View of Euler’s Formula

40. Example: Frequency Domain’s View of Euler’s Formula

41. From Integral to Computation

42. Discrete Domain Analysis • FFT: Transforming a sequence of numbers x0, x1, …, xN-1 to another sequence of numbers X0, X1, …, XN-1 • Interpretation: consider x0, x1, …, xN-1 as sampled values of a periodical function defined on [0, 1] • Xk is the coefficient (scaled by N) for k Hz harmonics if the FFT N samples span one sec

43. Discrete Domain Analysis • FFT: • Inverse DFFT