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The converse can be shown by a sphere packing argument. Given a codeword, there are roughly 2n H(p) typical output sequences. There are 2n total possible outputs, and the input chooses from a codebook of size 2nR. Therefore, the receiver would choose to partition the space into "spheres" with 2n /
373:-- What is the definition of the variable R? How do we deduce it has size 2nR, or is this a hypothesis? What is a codebook? A list of possible encodings of one desired message? That sounds like only one entry, a tiny fraction of the whole codebook.
357:-- What is a codeword in this context? A binary sequence of length n? What does a "typical output sequence" mean? A possible damaged version of the original sequence? Then why not 2^n?
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I've attempted to clarify the (previously incoherent) statement of this theorem to something plausible, but it still has the following defect: δ is not quantified.
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1 − H(p), then the spheres will be packed too tightly asymptotically and the receiver will not be able to identify the correct codeword with vanishing probability.
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365:-- What is the difference between an "output" and an "output sequence"? I suppose they can't be the same since there's a factor of H(p).
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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
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I rewrote the capacity section and used a proof which is as far as a know well known. Further improvements or feedback is welcome.
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333:-- What is intended here? A statement that two things are equal does not have a converse.
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the receiver will not be able to identify the correct codeword with vanishing probability
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If you found an error with any archives or the URLs themselves, you can fix them with
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The capacity of the channel is 1 − H(p), where H(p) is the binary entropy function.
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Given a codeword, there are roughly 2n H(p) typical output sequences.
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for additional information. I made the following changes:
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