Timeline for Channel Capacity & Dependency Graph
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 20 at 23:26 | comment | added | Euclid | If we represent this particular dependency by a graph (given in Figures 1, 2, 3 in my original post), my question is: Has channel capacity been studied in connection with the properties of its corresponding graph (called dependency graph in my original post)? | |
| May 20 at 23:26 | comment | added | Euclid | Examples: 1) If $Y_n$ depends only on $X_n$, the channel is indeed memoryless, and we deal with transition probabilities $P_{Y|X}(\cdot|\cdot)$. This case is Fig.1 in my original post. 2) If $Y_n$ depends on $X_n$ and $X_{n-1}$, the channel has memory $1$, and we deal with transition probabilities $P_{Y|X,X'}$ where $X$ represents the current input and $X'$ the previous input. This case is Fig.2. 3) If $Y_n$ depends on $X_n$ and $Y_{n-1}$, we deal with transition probabilities $P_{Y|X,Y'}$ where $X$ represents the current input and $Y'$ the previous output. This case is Fig.3. | |
| May 20 at 23:24 | comment | added | Euclid | Thank you for the answer, but I do not see the connection to the zero-error capacity problem. The problem I tried to describe is the following. Fix (discrete) input and output alphabets $\mathcal X$ and $\mathcal Y$. The channel need not be memoryless; the output at each transmission might have a specific dependency to the past inputs & outputs. I.e., at transmission $n$, the output $Y_n$ will depend on $X_n$ as well as other quantities (e.g. $X_{n-1}$ and/or $Y_{n-1}$). We however assume that the dependency is the same as $n$ varies (other than a few possible first cases in the beginning) | |
| May 18 at 2:02 | history | answered | kodlu | CC BY-SA 4.0 |