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A New Upper Bound on the Capacity of a Primitive Relay Channel Based on Channel Simulation

机译：基于信道仿真的原始中继信道容量的新上限

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摘要

An upper bound on the capacity of a primitive three-node discrete memoryless relay channel is considered, where a source (X) wants to send information to destination (Y) with the help of a relay (Z) . The signals at each node are also denoted as (X) , (Y) , and (Z) , respectively, with a slight abuse of notation. (Y) and (Z) are independent given (X) , and the link from (Z) to (Y) is lossless with rate (R_0) . A new inequality is introduced to upper-bound the capacity when the encoding rate is beyond the capacities of both individual links (XY) and (XZ) . It is based on generalizing the blowing-up lemma, linking conditional entropy to decoding error, and generalizing channel simulation to the case with side information. The upper bound is strictly better than the well-known cut-set bound in several cases when the latter is (C_{XY}+R_0) , with (C_{XY}) being the channel capacity between (X) and (Y) . One particular case is when the channel is stochastically degraded, i.e., either (Y) is a stochastically degraded version of (Z) with respect to (X) , or (Z) is a stochastically degraded version of (Y) with respect to (X) . Moreover, in this case, the bound is shown to be explicitly computable. The upper bound on the capacity of the binary erasure channel is analyzed in detail and evaluated numerically.
机译：考虑原始三节点离散无记忆中继信道的容量上限，其中源（X）希望借助中继（Z）将信息发送到目的地（Y）。每个节点上的信号也分别表示为（X），（Y）和（Z），略有滥用符号。 （Y）和（Z）是独立给定的（X），并且（Z）到（Y）的链接对于速率（R_0）是无损的。当编码率超出单个链接（XY）和（XZ）的容量时，会引入新的不等式来限制容量。它基于泛化爆炸引理，将条件熵与解码错误相关联，并将信道模拟泛化到带有辅助信息的情况。在某些情况下，上限为（C_ {XY} + R_0），其中（C_ {XY}）为（X）与（Y）之间的通道容量。一种特殊情况是当信道随机降级时，即（Y）是相对于（X）的（Z）的随机降级版本，或者（Z）是相对于（X）的（Y）的随机降级版本。 X） 。此外，在这种情况下，边界显示为可显式计算的。对二进制擦除通道容量的上限进行了详细分析并进行了数值评估。

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