The Capacity of the Relay Channel
The Capacity of the Relay Channel
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中继通道容量
DOI：
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
T. Cover
中科院分区：
文献类型：
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作者：
T. Cover
Consider the following seemingly simple discrete memoryless relay channel:
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Here Y 1, Y 2 are conditionally independent and conditionally identically distributed given X, that is, (p(y_1,, y_2, |, x) = p(y_1, |, x) p(y_2, |, x)). Also, the channel from Y 1 to Y 2 does not interfere with Y 2. A (2nR, n) code for this channel is a map (x : 2^{nR}
ightarrow X^n), a relay function (r :Y_1^{n}
ightarrow 2^{nC_{0}}), and a decoding function (g : 2^{nC_{0}} imes Y_2^{n}
ightarrow 2^{nR}). The probability of error is given by
$$ P_e^{(n)} = P {,g(r(y_1),y_2)
e W}$$
, where W is uniformly distributed over 2nR and
$$ p(w, y_1, y_2) = 2^{-nR},, underset {i=1}{overset {n}{Pi}} p(y_{1i}, |, x_i(w)) ,,underset {i=1}{overset {n}{Pi}},, p(y_{2i}, |, x_i(w))$$
Consider the following seemingly simple discrete memoryless relay channel:
Open image in new window
Here Y 1, Y 2 are conditionally independent and conditionally identically distributed given X, that is, (p(y_1,, y_2, |, x) = p(y_1, |, x) p(y_2, |, x)). Also, the channel from Y 1 to Y 2 does not interfere with Y 2. A (2nR, n) code for this channel is a map (x : 2^{nR}
ightarrow X^n), a relay function (r :Y_1^{n}
ightarrow 2^{nC_{0}}), and a decoding function (g : 2^{nC_{0}} imes Y_2^{n}
ightarrow 2^{nR}). The probability of error is given by
$$ P_e^{(n)} = P {,g(r(y_1),y_2)
e W}$$
, where W is uniformly distributed over 2nR and
$$ p(w, y_1, y_2) = 2^{-nR},, underset {i=1}{overset {n}{Pi}} p(y_{1i}, |, x_i(w)) ,,underset {i=1}{overset {n}{Pi}},, p(y_{2i}, |, x_i(w))$$