Abstract
Consider the following seemingly simple discrete memoryless relay channel:
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 \(x : 2^{nR} \rightarrow X^n\), a relay function \(r :Y_1^{n}\rightarrow 2^{nC_{0}}\), and a decoding function \(g : 2^{nC_{0}} \times Y_2^{n} \rightarrow 2^{nR}\). The probability of error is given by
, where W is uniformly distributed over 2nR and
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References
T. Cover and A. El Gamal, “Capacity Theorems for the Relay Channel,” IEEE Trans. Inf. Theory, IT-25, No. 5, pp. 572–584 (Sept. 1979).
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© 1987 Springer-Verlag New York Inc.
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Cover, T.M. (1987). The Capacity of the Relay Channel. In: Cover, T.M., Gopinath, B. (eds) Open Problems in Communication and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4808-8_17
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DOI: https://doi.org/10.1007/978-1-4612-4808-8_17
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