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arXiv 1102.2768cs.ITmath.IT
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量化广播信道与MAC信道的可互换速率域

Achievable Rate Region of Quantized Broadcast and MAC Channels

Suresh Chandrasekaran, Saif K. Mohammed, A. Chockalingam

摘要:

本文研究了高斯多用户信道的可达速率域,其中发送的消息来自有限输入字母表,输出在接收端量化为{ \em}。特别是,我们专注于$i)$高斯广播信道(GBC)和$ii)$高斯多址接入信道(GMAC)的可达速率区域。首先,我们研究了两个用户GBC的可达速率区域时,要发送到两个用户的消息从有限的信号集的值和接收到的信号在两个用户进行量化。我们将该信道称为{ \em量化广播信道(QBC)}。我们观察到,为GBC定义的容量区域不会像这样结转到QBC。我们证明了GBC的最佳解码方案(即,高SNR用户进行连续解码和低SNR用户单独解码其消息)对于QBC不是最优。然后,我们提出了一个可实现的速率区域QBC基于两种不同的计划。我们提出了可实现的速率区域结果的情况下,在接收机的均匀量化。接下来,我们研究了有限输入字母表和量化接收机输出的两用户GMAC的可达速率区域。我们将该信道称为{ \em量化多址信道(QMAC)}。我们推导出表达式的两个用户QMAC的可实现的速率区域。我们表明,有限的输入字母,可实现的速率区域与常用的均匀接收器量化器相比,没有接收器量化的可实现的速率区域有一个显着的损失。我们提出了一个{ \em非均匀量化器},它有一个显着更大的速率区域相比,在QMAC的均匀量化器实现。

英文摘要:

In this paper, we study the achievable rate region of Gaussian multiuser channels with the messages transmitted being from finite input alphabets and the outputs being {\em quantized at the receiver}. In particular, we focus on the achievable rate region of $i)$ Gaussian broadcast channel (GBC) and $ii)$ Gaussian multiple access channel (GMAC). First, we study the achievable rate region of two-user GBC when the messages to be transmitted to both the users take values from finite signal sets and the received signal is quantized at both the users. We refer to this channel as {\em quantized broadcast channel (QBC)}. We observe that the capacity region defined for a GBC does not carry over as such to QBC. We show that the optimal decoding scheme for GBC (i.e., high SNR user doing successive decoding and low SNR user decoding its message alone) is not optimal for QBC. We then propose an achievable rate region for QBC based on two different schemes. We present achievable rate region results for the case of uniform quantization at the receivers. Next, we investigate the achievable rate region of two-user GMAC with finite input alphabet and quantized receiver output. We refer to this channel as {\em quantized multiple access channel (QMAC)}. We derive expressions for the achievable rate region of a two-user QMAC. We show that, with finite input alphabet, the achievable rate region with the commonly used uniform receiver quantizer has a significant loss compared to the achievable rate region without receiver quantization. We propose a {\em non-uniform quantizer} which has a significantly larger rate region compared to what is achieved with a uniform quantizer in QMAC.

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