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In information theory, there are two concepts that are widely used: source encoding and channel encoding.

I'm afraid I may not be capable of expressing my doubts clearly, but the thing is that I don't understand they interact between each other.

To try to make it clearer, I'll try to give an example of my doubts:

Every codeword for the channel encoding must have the same length. Why is this? If the source from which the channel is reciving its input used a Huffman code, for example, lengths might be different for each symbol. Isn't that a contradiction?

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  • $\begingroup$ To be more precise they are called source coding and channel coding. And they are opposite things, as while the source coding tries to minimize the bitrate to represent a message source (either lossless or lossywise) by utilizing statistical redundancies and perceptual irrelevancies in it, the channel coder tries to find an errorless and reliable transmission of the resulting bits over a given channel which will eventually increase the number of bits to send. Being fixed or variable length depends on the selected strategy and they can be designed jointly or independently. $\endgroup$ – Fat32 Oct 4 '16 at 17:25
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Every codeword for the channel encoding must have the same length.

That is not inherently true, but it's usually handy to consider the information that goes into the channel coder to be of constant length, especially when considering block coders.

Why is this? If the source from which the channel is reciving its input used a Huffman code, for example, lengths might be different for each symbol. Isn't that a contradiction?

No. The point is that channel and source coding are two independent things. You take source data, and the source coder maximizes the average information per bit (by converting input words of constant length into source-coded words of varying length). Then the source-coded words are again simply considered as sequences of bits (or to be more general, sequences of fixed-length units of information) and channel-coded, optimizing robustness.

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  • $\begingroup$ But what happens if, for example, the source-code is 0, 10, 110, 111 (four symbols)? Then the channel would recieve different lengths. I don't understand where the lengths are uniformed. $\endgroup$ – Tendero Oct 4 '16 at 3:34
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    $\begingroup$ no, it won't. you consider 0,10,110,111 as 01011011, and partition that arbitrarily. Nothing forces you to keep your ",". As said, the point is that you just consider the output of the source coder as sequence of bits, not as source coding words. Source and channel coder are independent!!! $\endgroup$ – Marcus Müller Oct 4 '16 at 3:36

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