Source coding with 2 distinct distributions and entropies

In summary, when dealing with a sequence composed of two distinct distributions, it is important to consider both entropies and use a combination of entropy coding and arithmetic coding to design an efficient coding scheme. Additionally, when asked to provide a coding scheme or design a coding scheme, you will need to provide an algorithm that takes into account the specific characteristics of the sequence and produces a compressed output. There are resources available that discuss these types of problems and provide guidance on how to define the typical set in such cases.
  • #1
wu_weidong
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I'm learning about source coding, and many of the books/resources I've read give examples of the source Xn being defined as a sequence of iid random variables. How about when the sequence is independent but belong to 2 distinct distributions (e.g. Px when Xi is odd, and Px' when Xi is even), with 2 distinct entropies (H(X) and H(X'))?

Where can I find resources that talk about such problems, including how to define the typical set in such cases?

One more question - when I'm asked to "provide a coding scheme" or "design a coding scheme", what exactly am I expected to give?
 
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  • #2
In this case, when the sequence is composed of two distinct distributions, you will need to provide a coding scheme that takes into account the two distinct entropies. This can be done by using a combination of entropy coding and arithmetic coding. Entropy coding is a technique which uses the idea of Huffman coding to achieve higher compression, while arithmetic coding is a more advanced technique that allows for better compression by exploiting the correlations between symbols in a sequence. When you are asked to provide a coding scheme or design a coding scheme, you will usually be expected to provide an algorithm that takes a given input and produces a compressed output. This algorithm should include the details of how the input is encoded and decoded, as well as the data structures used to store the resulting compressed data. It should also take into account the two distinct entropies of the source Xn in order to achieve the highest possible compression.
 

FAQ: Source coding with 2 distinct distributions and entropies

What is source coding with 2 distinct distributions and entropies?

Source coding with 2 distinct distributions and entropies is a type of data compression technique used in information theory. It involves encoding data from two different probability distributions into a binary code in order to reduce the amount of storage space required.

How does source coding with 2 distinct distributions and entropies work?

The process of source coding with 2 distinct distributions and entropies involves calculating the entropy of each distribution and then using this information to determine the optimal code for each distribution. The data is then encoded using these codes, resulting in a compressed file.

What is the difference between source coding with 2 distinct distributions and entropies and other data compression techniques?

Unlike other data compression techniques, source coding with 2 distinct distributions and entropies takes into account the specific probability distributions of the data being encoded. This allows for more efficient compression of the data, as it is tailored to the specific characteristics of the data.

What are the advantages of using source coding with 2 distinct distributions and entropies?

One of the main advantages of using source coding with 2 distinct distributions and entropies is that it can achieve higher compression rates compared to other techniques. This is because it takes into account the specific characteristics of the data being compressed. Additionally, it can also help reduce storage space and transmission time.

What are the applications of source coding with 2 distinct distributions and entropies?

Source coding with 2 distinct distributions and entropies is commonly used in various fields, such as telecommunications, data storage, and image and video compression. It is also utilized in various data compression algorithms, such as Huffman coding and arithmetic coding.

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