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Precoding for the AWGN Channel With Discrete Interference

机译：具有离散干扰的AWGN信道的预编码

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摘要

For a state-dependent discrete memoryless channel with input alphabet ${cal X}$, state alphabet ${cal S}$, and output alphabet ${cal Y}$ where the independent and identically distributed (i.i.d.) state sequence is known causally at the transmitter, it is shown that by using at most $min {vert{cal X}vert vert{cal S}vert -vert{cal S}vert +1,vert{cal Y}vert }$ out of $vert{cal X}vert^{vert{cal S}vert}$ inputs of the Shannon's derived channel, the capacity is achievable. As an example of state-dependent channels with side information at the transmitter, $M$-ary signal transmission for the additive white Gaussian noise (AWGN) channel with additive $Q$-ary interference where the sequence of i.i.d. interference symbols is known causally at the transmitter is considered. The optimal precoding scheme is derived under the constraint that the channel input given any current interference symbol is uniformly distributed over the channel input alphabet. It is shown that at low signal-to-noise ratio (SNR) not doing precoding is optimal. For the special case where the Gaussian noise power is zero, it is shown that the rate $log_2 M$ is achievable by a one-shot coding scheme if ${cal X}$ is an arithmetic progression.
机译：对于具有输入字母$ {cal X} $，状态字母$ {cal S} $和输出字母$ {cal Y} $的状态相关的离散无内存通道，其中因果已知独立且均匀分布的（iid）状态序列在发射机处，显示出通过使用最多$ min {vert {cal X} vert vert {cal S} vert -vert {cal S} vert + 1，vert {cal Y} vert} $的$ min {香农派生频道的cal X} vert ^ {vert {cal S} vert} $输入，容量是可以实现的。作为具有在发射机处的辅助信息的状态相关信道的示例，具有加性$ Q $ ary干扰的加性高斯白噪声（AWGN）信道的$ M $ ary信号传输，其中i.i.d的序列。考虑在发射机处因果已知干扰符号。最佳预编码方案是在给定任何当前干扰符号的信道输入均匀分布在信道输入字母的约束下得出的。结果表明，在低信噪比（SNR）下，不进行预编码是最佳的。对于高斯噪声功率为零的特殊情况，表明如果$ {cal X} $是算术级数，则速率$ log_2 M $是可以通过单次编码方案实现的。

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