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Kelvin Lee
Kelvin Lee
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I'm studying information theory right now and I'm reading about channel capacities.

I know that there are known expressions for computing the capacities for some well known simple channels such as BSC, the Z channel.

Could you show me or point me to the source showing how to derive the channel capacity for a binary asymmetric channel? Say that $X$ is input $Y$ is output. $\Pr(x = 0 | y = 1) = p1$$\Pr(x = 0 | y = 1) = p_1$, $\Pr(x = 1 | y = 0) = p2$$\Pr(x = 1 | y = 0) = p_2$.

Further, I'm wondering is there any known result for computing the capacity of an arbitrary non-symmetric channel? By arbitrary non-symmetric channel, I mean, X and Y are from the alphabet set $\{0, 1, \cdots, q-1\}${${0, 1, \cdots, q-1}$}, and $\Pr(x = i \mid y = j) = p_{i, j}$ for $i, j \in \{0, 1, ..., q-1\}$$i, j \in$ {$0, 1, ..., q-1$}.

I'm studying information theory right now and I'm reading about channel capacities.

I know that there are known expressions for computing the capacities for some well known simple channels such as BSC, the Z channel.

Could you show me or point me to the source showing how to derive the channel capacity for a binary asymmetric channel? Say that $X$ is input $Y$ is output. $\Pr(x = 0 | y = 1) = p1$, $\Pr(x = 1 | y = 0) = p2$.

Further, I'm wondering is there any known result for computing the capacity of an arbitrary non-symmetric channel? By arbitrary non-symmetric channel, I mean, X and Y are from the alphabet set $\{0, 1, \cdots, q-1\}$, and $\Pr(x = i \mid y = j) = p_{i, j}$ for $i, j \in \{0, 1, ..., q-1\}$.

I'm studying information theory right now and I'm reading about channel capacities.

I know that there are known expressions for computing the capacities for some well known simple channels such as BSC, the Z channel.

Could you show me or point me to the source showing how to derive the channel capacity for a binary asymmetric channel? Say that $X$ is input $Y$ is output. $\Pr(x = 0 | y = 1) = p_1$, $\Pr(x = 1 | y = 0) = p_2$.

Further, I'm wondering is there any known result for computing the capacity of an arbitrary non-symmetric channel? By arbitrary non-symmetric channel, I mean, X and Y are from the alphabet set {${0, 1, \cdots, q-1}$}, and $\Pr(x = i \mid y = j) = p_{i, j}$ for $i, j \in$ {$0, 1, ..., q-1$}.

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Kelvin Lee
Kelvin Lee
  • 285
  • 2
  • 8

Computing channel capacities for non-symmetric channels

I'm studying information theory right now and I'm reading about channel capacities.

I know that there are known expressions for computing the capacities for some well known simple channels such as BSC, the Z channel.

Could you show me or point me to the source showing how to derive the channel capacity for a binary asymmetric channel? Say that $X$ is input $Y$ is output. $\Pr(x = 0 | y = 1) = p1$, $\Pr(x = 1 | y = 0) = p2$.

Further, I'm wondering is there any known result for computing the capacity of an arbitrary non-symmetric channel? By arbitrary non-symmetric channel, I mean, X and Y are from the alphabet set $\{0, 1, \cdots, q-1\}$, and $\Pr(x = i \mid y = j) = p_{i, j}$ for $i, j \in \{0, 1, ..., q-1\}$.