Channel Concepts CS 571 Fall Kenneth L. Calvert

Transcription

1 Channel Concepts CS 571 Fall Kenneth L. Calvert

2 What is a Channel? Channel: a means of transmitting information A means of communication or expression Webster s NCD Aside: What is information...? Information can be defined as removal of uncertainty Unit of information: bit, nat Example: conveying the outcome of a series of coinflipping experiments How much uncertainty ~ how many possibilities/choices Each outcome (assuming fair coins) corresponds to 1 bit

3 Shannon's Definition of Information Modeling a channel as a random variable Finite set of possible symbols {s 0, s 1, s 2,... s n } that can be transmitted through the channel From the receiver's point of view: the next symbol to "emerge" from the channel is a random variable, S That random variable can take on values s 0, s 1, s 2,... s n Entropy of a random variable: Each outcome (symbol) s i occurs with probability p i In other words, over infinite time, the fraction of outcomes (transmitted symbols) that are equal to s i is p i Note that all the p i 's are postulated/assumed known a priori! The entropy of S in bits is defined by: n H(S) = -Σ s i log 2 p i i=0

4 Given: Computing Channel Capacity The rate at which symbols arrive The set (or at least the number) of symbols s i Probability of each symbol, p i Compute: H = -Σ s i log 2 p i The average information per symbol Multiply H by the symbol rate

5 Computing Channel Capacity Example: symbols 0, 1 occur with equal probability (0.5 each) Entropy is (0.5(-1) + 0.5(-1)) = 1 bit/symbol Example: 0 occurs ¾ of the time, 1 occurs ¼ of the time Entropy is -(0.75(log 2 ¾) (log 2 ¼)) = -(0.75(-0.415) (-2)) 0.56 bits/symbol Example: 64 symbols, each occur with equal probability Entropy is -64(1/64)(-log 2 64) = 6 bits/symbol Quadrature-Amplitude Modulation (QAM), used in cable modem systems, achieves better than this!

6 Analog and Digital Channels Information can be transmitted in different forms: Analog signal a signal (e.g. a waveform) that is continuous in time and continuous in value 2 Digital signal a signal that takes on discrete values at discrete points in time (e.g., a sequence of symbols from an alphabet)

7 Analog and Digital Examples Simple analog channels: two cans connected with a piece of string two wires with a voltage modulator (e.g. potentiometer) at one end, and a voltmeter at the other Simple digital channels: Ship flags (symbols = flags) Telegraph (symbols = dots/dashes)

8 Building Digital Channels Low-level electronic channels are typically analog Time-varying voltage across a pair of wires Computer information is digital Represented as 1 s and 0 s in storage Computers can only deal with digital channels Digital channels are built from analog ones by constraining the signal to take on specific values at specific times Example: Morse Code Other examples: Manchester coding, Alternate mark inverted, etc. Note well: this always involves measuring time, i.e. a clock

9 Example: Alternate Mark Inverted (AMI) Each 1 ("mark") is transmitted as a voltage pulse Absence of a pulse is interpreted as 0 ("space") Alternating 1's have different polarity Ensures DC balance Bit rate determines "width" of each symbol +Vmax time -Vmax

10 Example: Alternate Mark Inverted (AMI) Problem: long strings of 0's How many 0's between these two 1's? Center of 1 bit is marked by transition in the signal Locations of 0's determined solely by receiver's clock Clocks drift! Transmitter's clock: 21 0's! +Vmax time -Vmax Receiver's clock: 23 0's

11 Example: Alternate Mark Inverted (AMI) Solution: prohibit long strings of 0's Insert framing bits (1's) periodically in the stream Example: In the T1 voice carrier system, every 193 rd bit is a framing bit 24 voice channels 24 8-bit samples/frame = 192 bits/frame 8000 frames/sec = 1 frame/125 microseconds Clocks must not drift more than ~1/4 bit time (0.16 µsec) in 125 µsec +Vmax bits or 125 µsec 1 time -Vmax

12 Example: Manchester Coding Each bit has two "elements": one high and one low 1: first element low (low-to-high transition) 0: first element high (high-to-low transition)* Advantage: transition marks the middle of each bit, keeps clocks synchronized Disadvantage: crossed wires invert all symbols! +Vmax -Vmax *Authors differ on which coding indicates which bit.

13 Differential Manchester Coding Every bit has a transition in the middle 0's have a transition at the beginning 1's have no transition at the beginning Polarity does not matter! +Vmax -Vmax *Authors differ on which coding indicates which bit.

14 Example: Asynchronous Serial (Start-Stop) Signaling/Framing Ancient (50+ years old?) mechanism combining framing and symbol transmission Used to send characters via modem over telephone lines Originally used with Teletypes Still supported on PCs ("serial interface")

15 Example: Asynchronous Serial (Start-Stop) Signaling/Framing Two voltage levels: high ("mark", 1), low ("space", 0) Idle: line is held high Sender and Receiver agree on # of bits/frame Typically 8 Receiver senses the line at 4 or 8 x the bit rate Begin of frame indicated by a "start bit" = 0 End of frame indicated by one or more "stop bits" = 1 ½ 1 Idle Receiver senses line Start bit Stop bit

16 Building Higher-level Channels By processing the signal before transmitting and after receiving, we can build an enhanced channel This layering process can be iterated to build higherlevel channels Frame channels Reliable frame channels Digital channel Analog channel (wires) D-to-A processing A-to-D processing

17 Concatenating Channels To build a scalable network, we need to be able to connect channels together to make an end-toend channel This is where routing (= selection of the sequence of channels) comes in

18 Channel Characteristics Every channel has certain fundamental characteristics that determine how it can be used: Capacity Rate of carrying information, units: information/time Latency Delay through the channel, units: time Distortion Difference between received and transmitted signals, units vary for analog/digital

19 Channel Capacity Capacity the maximum rate at which information can be transmitted through the channel Analog channel capacity is called bandwidth, and is measured in Hertz (cycles/sec) Digital channel capacity is measured in bits/sec It is often called bandwidth also, but this is technically wrong Information may be sent at a lower rate than the capacity, but it cannot be sent faster!

20 Channel Capacity Shannon showed that the theoretical capacity of a digital channel built upon an underlying analog channel is given by: where: C = B log 2 (1 + S/N) bits/sec B = bandwidth in Hz of the analog channel, S/N = ratio of signal power to noise power

21 Channel Latency Latency the delay between the time a signal is transmitted and the time it is received at the other end Transmit time Receive latency Note that a channel s latency may vary with time

22 Channel Latency All channels have a lower bound on their latency due to the speed of light Speed of light in free space 3 x 10 8 m/s Latency is at least channel length / speed of light For low-level physical channels (wires, optical fiber, etc.) latency is primarily determined by this propagation delay Signals in electronic (wire) channels usually propagate at a lower speed 2 x 10 8 m/s

23 Channel Latency For higher-level channels (e.g. TCP connections) built up from concatenated lower-level channels, latency has several components: Propagation delay Transmission delay = size of message (bits) / rate of transmission (bits/sec) Processing delay = context switching time, time to allocate/free buffers, etc. Queueing delay = time spent waiting for transmission capacity to become available

24 Channel Distortion Sometimes the signal that goes in is not the signal that comes out Analog channels Transmit Receive Is this a pulse? Is this? Digital Channels: 1 goes in, 0 comes out, or vice versa

25 Channel Distortion For digital channels we are usually concerned with the error rate: the fraction of bits (or symbols, or messages) that are received in error Modern optical fiber channels have bit error rates of or even lower However, wireless channels have much higher bit error rates, on the order of 10-5

26 Components: A pipe The Marble Channel: a Model of a Digital Channel An infinite supply of colored marbles that just fit (one at a time) through the pipe How it works: Marbles symbols # of colors # of symbols

27 How Do Marbles Carry Information? What s the uncertainty? Which color marble will emerge next Assume all colors are equally likely, i.e. all transmitted equally often The number of possibilities (=colors) determines the amount of uncertainty It takes log 2 n bits to distinguish between n colors, assuming all colors occur randomly with equal frequency E.g. 2 colors 1 bit/marble 4 colors 2 bits/marble 64 colors? bits/marble

28 Marble Channel Characteristics Let: w = width of a marble in meters (marbles may be lozenge-shaped) p = length of pipe in meters σ = speed of marbles through pipe in m/s N = number of distinct marble colors Latency L (sec) Time from when a marble enters the pipe until it emerges at the other end Either leading-edge to leading-edge or trailing-edge to trailing-edge Latency = p/σ Capacity C (bits/sec) C = σ /w marbles/sec x log 2 N bits/marble Note well that for fixed σ, latency and capacity are independent!

29 Note: speed σ is fixed Marble Channel Examples Low-latency, low capacity short pipe, long marbles, few colors Low-latency, high capacity short pipe, short marbles/many colors High-latency, low capacity long pipe (holds many marbles), long marbles, few colors High-latency, high capacity long pipe, short marbles/many colors

30 Multiplexing When a single channel is used to carry information from many (lower-rate) channels, it is called multiplexing Example: the coaxial cable coming into your house carries analog television signals over one pair of wires Those channels are combined using frequency-division multiplexing Example: an Ethernet carries the information for many TCP connections over one channel Those channels are combined using time-division multiplexing