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Universal product code

The Universal Product Code (UPC), often known as a bar code, labels virtually every sold good. An example of a portion of the code is shown.

Here a sequence of black and white bars, each having width d , presents an 11-digit number (consisting of decimal digits) that uniquely identifies theproduct. In retail stores, laser scanners read this code, and after accessing a database of prices, enter the priceinto the cash register.

  1. How many bars must be used to represent a single digit?
  2. A complication of the laser scanning system is that the bar code must be read either forwards or backwards.Now how many bars are needed to represent each digit?
  3. What is the probability that the 11-digit code is read correctly if the probability of reading a singlebit incorrectly is p e ?
  4. How many error correcting bars would need to be present so that any single bar error occurring in the11-digit code can be corrected?

Error correcting codes

A code maps pairs of information bits into codewords of length 5 as follows.

Data Codeword
00 00000
01 01101
10 10111
11 11010
  1. What is this code's efficiency?
  2. Find the generator matrix G and parity-check matrix H for this code.
  3. Give the decoding table for this code. How many patterns of 1, 2, and 3 errors are correctlydecoded?
  4. What is the block error probability (the probability of any number of errors occurring in the decoded codeword)?

Digital communication

A digital source produces sequences of nine letters with the following probabilities.

letter a b c d e f g h i
probability 1 4 1 8 1 8 1 8 1 8 1 16 1 16 1 16 1 16
  1. Find a Huffman code that compresses this source. How does the resulting code compare with the best possible code?
  2. A clever engineer proposes the following (6,3) code to correct errors after transmission through a digital channel.
    c 1 d 1 c 4 d 1 d 2 d 3
    c 2 d 2 c 5 d 2 d 3
    c 3 d 3 c 6 d 1
    What is the error correction capability of this code?
  3. The channel's bit error probability is 1/8. What kind of code should be used to transmit data over this channel?

Overly designed error correction codes

An Aggie engineer wants not only to have codewords for his data, but also to hide the information from Rice engineers(no fear of the UT engineers). He decides to represent 3-bit data with 6-bit codewords in which none of the databits appear explicitly.

c 1 d 1 d 2 c 4 d 1 d 2 d 3
c 2 d 2 d 3 c 5 d 1 d 2
c 3 d 1 d 3 c 6 d 1 d 2 d 3
  1. Find the generator matrix G and parity-check matrix H for this code.
  2. Find a 3 × 6 matrix that recovers the data bits from the codeword.
  3. What is the error correcting capability of the code?

Error correction?

It is important to realize that when more transmission errors than can be corrected, error correction algorithmsbelieve that a smaller number of errors have occurred and correct accordingly. For example, consider a (7,4) Hammingcode having the generator matrix G 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 This code corrects all single-bit error, but if a double bit error occurs, it corrects using a single-bit error correction approach.

  1. How many double-bit errors can occur in a codeword?
  2. For each double-bit error pattern, what is the result of channel decoding? Express your result as abinary error sequence for the data bits.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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cm
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
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Can you compute that for me. Ty
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2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
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progressive wave
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A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Source:  OpenStax, Fundamentals of electrical engineering i. OpenStax CNX. Aug 06, 2008 Download for free at http://legacy.cnx.org/content/col10040/1.9
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