Question

If the AZTEC coded data is given by $[5, 10, -5, 100, 2, 5, -4, 100]$, the compression ratio obtained for following reconstruction is

• A. \( \text{1:2} \)
• B. \( \text{1:4} \)
• C. \( \text{1:8} \)
• D. \( \text{1:16} \)

Hint:

Compression ratio is typically defined as the ratio of the uncompressed data size to the compressed data size ($\frac{\text{Uncompressed}}{\text{Compressed}}$) or vice versa. When given coded data like this, the "uncompressed size" is usually the sum of the run-lengths (or number of samples represented), and the "compressed size" is the number of elements in the coded array. If the calculated ratio doesn't match the options, especially simple integer ratios, it's a strong indication that the question might be simplifying the definition of "original data size" or is testing a very specific, potentially non-standard, interpretation. In such cases, if a correct answer is known, work backward to see what "original size" would yield that ratio given the "compressed size". Here, an original size of 16 samples for 8 coded elements gives a 1:2 compressed-to-original ratio.

Answer 1

The Correct Option is C

To solve this problem, we need to calculate the compression ratio for the given AZTEC coded data.

1. Understanding Compression Ratio:

- Compression Ratio: The compression ratio is defined as the ratio of the original size of the data to the size of the compressed data. It is calculated using the formula:

\[ \text{Compression Ratio} = \frac{\text{Original Size}}{\text{Compressed Size}} \]

The original size refers to the number of elements in the uncompressed data, while the compressed size refers to the number of elements in the compressed data.

2. Analyzing the Data:

The given AZTEC coded data is:

\[ [5, 10, -5, 100, 2, 5, -4, 100] \]

The original size of the data is the number of elements in the array, which is 8 (since there are 8 numbers). Assuming that the compressed data uses 1 bit for each value (which is a common case for compression algorithms like AZTEC), the size of the compressed data would be proportional to the number of distinct values or symbols.

For simplicity, we assume that the compressed data contains fewer bits or elements than the original data, typically achieving a significant reduction in size. The exact size of the compressed data can be calculated based on the algorithm used, but the options suggest a common compression ratio.

3. Final Answer:

The most likely compression ratio for the given data is \( \text{1:8} \), which means that the data was compressed to 1/8th of its original size.