Compute Expected Code Length of 5 Nodes

In summary, the purpose of computing the expected code length of 5 nodes is to determine the efficiency of a coding system and the average number of bits required to represent a symbol in a given data set. This is calculated by multiplying the probability of each symbol with its corresponding code length and summing up the values. Factors such as the probability distribution and number of symbols can affect the expected code length. It is important to compute this in order to evaluate the performance of a coding system, compare different systems, and identify potential improvements. Additionally, the expected code length can be used to determine the compression ratio of a coding system, with a higher compression ratio indicating a more efficient system.
  • #1
david90
312
2
The question ask me to compute the expected code length of

5 nodes A B C D E each of frequency .1 .1 .2 .2 .4 respectively.

I already did the tree and derive the huffman code.

What does it mean by " compute the expected code length ?"
 
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  • #2
i guess it means the avg size of the encoded data in bits per symbol.
 
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  • #3
expected code length is also called the average code length (L)
= [tex]\sum_{i=0}^{n} p_i * l_i[/tex]
where p_i is the probability of the symbol and l_i is the length of the symbol

-- AI
 

What is the purpose of computing the expected code length of 5 nodes?

The expected code length of 5 nodes is calculated in order to determine the efficiency of a coding system. It helps in identifying the average number of bits required to represent a symbol or character in a given set of data.

How is the expected code length of 5 nodes calculated?

The expected code length is calculated by multiplying the probability of each symbol with its corresponding code length and then summing up all the values for all the symbols in the data set. This can be expressed mathematically as: ECL = Σ(p(i) * L(i)), where p(i) is the probability of symbol i and L(i) is the code length of symbol i.

What factors can affect the expected code length of 5 nodes?

The expected code length of 5 nodes can be affected by the probability distribution of the symbols in the data set. A more uniform distribution of symbols will result in a shorter expected code length, while a skewed distribution will result in a longer expected code length. The number of symbols also plays a role, as a larger number of symbols will generally result in a longer expected code length.

Why is it important to compute the expected code length of 5 nodes?

Computing the expected code length of 5 nodes is important because it helps in evaluating the efficiency and performance of a coding system. It allows for comparison between different coding systems and helps in choosing the most optimal one. It also helps in identifying any potential improvements that can be made to the coding system.

Can the expected code length of 5 nodes be used to determine the compression ratio of a coding system?

Yes, the expected code length of 5 nodes can be used to determine the compression ratio of a coding system. The compression ratio is calculated by dividing the original data size by the expected code length. A higher compression ratio indicates a more efficient coding system.

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