MASSACHVSETTS INSTITVTE OF TECHNOLOGY epartment of Electrical Engineering and Computer Se lence 001--Structure and Interpretation of Computer Programs Spring Semester, 2005 Quiz I- Sample Solutions

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.243j(Fall 2003): DYNAMICS OF NONLINEAR SYSTEMS

The TCP/P Protocol Suite Transmission Control Protocol Internet protocol Developed by darPa to connect Universities and Research Labs Four Layer model Applications Telnet, FTP, email, etc Transport TCP, UDP Network IP ICMP, IGMP Link

Automatic repeat request (ARQ) Break large files into packets FILE PKT PKT PKT Check received packets for errors Use a feedback channel to request retransmissions Retransmit packets containing errors acket Receive ACK

CSMA/CD and Ethernet Two way cable wsws Ws W CSMA with Collision Detection(CD)capability Nodes able to detect collisions Upon detection of a collision nodes stop transmission Reduce the amount of time wasted on collisions Protocol

Cyclic Codes a cyclic code is a linear block code where if c is a codeword, so are all cyclic shifts of c E.g., 1000, 110, 101,011 is a cyclic code Cyclic codes can be dealt with in the very same way as all other lbc s Generator and parity check matrix can be found a cyclic code can be completely described by a generator string G All codewords are multiples of the generator string In practice, cyclic codes are often used for error detection(CRc) Used for packet networks When an error is detected by the received, it requests retransmission

Noise is additional\unwanted \signal that interferes with the transmitted signal Generated by electronic devices The noise is a random process Each\sample \ of n(tis a random variable Typically, the noise process is modeled as\Additive White Gaussian noise”(AWGN) White: Flat frequency spectrur Gaussian noise distribution

The signal suffers an attenuation loss l Received power PR= PT/L Received snr=E,/No, Eb=Pr/Rb Antennas are used to compensate for attenuation loss Capture as much of the signal as possible

Sampling Sampling provides a discrete-time representation of a continuous waveform Sample points are real-valued numbers In order to transmit over a digital system we must first convert into discrete valued numbers

Information content of a random variable Random variable x Outcome of a random experiment Discrete R V takes on values from a finite set of possible outcomes PMF: P(X=y)=Py) How much information is contained in the event X=y? Will the sun rise today Revealing the outcome of this experiment provides no information Will the Celtics win the NBa championship? Since this is unlikely, revealing yes provides more information than revealing Events that are less likely contain more information than likely events