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Results tagged with information-theory
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user 24701
3
votes
Accepted
What is the overall capacity of two cascaded BSC channel?
No, this is not correct. Consider the chain of two BSCs with error probabilities $p_1$, $p_2$ as a single BSC with unknown error probability $p$.
Now, we know that in overall no error occurs, when:
…
- 6,238
0
votes
Accepted
How to prove relationship between mutual information and differential entropy?
Your derivation is correct. Your second integral can also be written as
$$
\int_{x,y}f(x,y)\log_2(f(y))dxdy=\int_y\log_2(f(y))\left(\int_xf(x,y)dx\right) dy
$$
where the integral in parenthesis is e …
- 6,238
2
votes
Accepted
Why are some LDPC codes more immune to noise than others?
As you mention, the LDPC code is completely determined by its generator matrix H. Hence, the properties of H define the (theoretic) performance of the code.
Since the LDPC code is a linear code, the …
- 6,238
0
votes
Accepted
How to solve this entropy integral?
The integration over a vector $\mathbf x$ as given by you means something like
$$\int f(\mathbf x) d\mathbf x=\int\dots\int f(x_1,\dots,x_n)dx_1\dots dx_n$$
So, you integrate over each component sep …
- 6,238
1
vote
Shannon's entropy for non-equiprobable symbols
You need to distinguish between the entropy of your underlying distribution and the "entropy" of the realization.
Consider a set $\mathcal{X}\subset \mathbb{N}$. This set defines, which symbols are a …
- 6,238