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Information Theory and Coding Basics

When compressing data, which of the following must use lossless compression rather than lossy compression?

  1. ACompressing a program's executable file for distribution
  2. BShrinking video to match the speed of the connection in a video streaming service
  3. CMaking music files smaller to listen to on a portable player
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Answer: A. Compressing a program's executable file for distribution

Lossless compression restores the original data without a single bit of difference, while lossy compression discards parts that people hardly notice in return for much greater shrinkage. A program does not run correctly if even one bit differs, so lossless compression such as ZIP is used. Small differences in images and sound are hard to see or hear, so lossy compression such as JPEG, MP3 and video coding formats is widely used for them.

  • A. Correct. An executable file does not run correctly unless it is exactly the same as the original.
  • B. Some degradation of video is acceptable, so lossy compression is used. On a slow connection, the picture quality is lowered to shrink it further.
  • C. Lossy compression such as MP3 and AAC is widely used. It shrinks files by discarding components the ear hardly notices.
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More Information Theory and Coding Basics questions

  1. A single even parity bit is added to a bit string of data so that the number of 1s is even, and the receiver checks the number of 1s. Which of the following correctly describes this check?
  2. Four rows of 4-bit data were sent with an even parity bit for each row at its right end and a final row of even parity bits for each column (vertical and horizontal parity). The received bits were row 1: 1011 1, row 2: 0100 0, row 3: 1100 0, row 4: 0101 0 and parity row: 0100 (the rightmost bit of each row is its row parity). If exactly one bit is wrong, which of the following is its position?
  3. Data are added up one byte at a time, and the low 8 bits of the sum are sent along as a check value (checksum). Which of the following errors cannot be detected by this check?
  4. Three CRC check bits for the generator polynomial x³ + x + 1 (bit string 1011) are to be appended to the data 1101. The check bits are the remainder of dividing 1101000, the data followed by three 0s, by 1011, using exclusive OR instead of subtraction in the division. Which of the following are the check bits?
  5. Which of the following correctly describes a CRC whose generator polynomial has degree r (r check bits) and a constant term of 1?