Exact Moderate Deviation Asymptotics in Streaming Data Transmission
Exact Moderate Deviation Asymptotics in Streaming Data Transmission
复制标题
流数据传输中的精确适度偏差渐近
DOI：
10.1109/tit.2017.2678983
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发表时间：
2016
影响因子：
2.5
通讯作者：
A. Khisti
中科院分区：
文献类型：
--
作者：
Si;V. Tan;A. Khisti
本文考虑了一种流传输设置，其中编码器在每个块的开始处观察到一条新消息，解码器在延迟<inline-formula> < text -math notation="LaTeX">$T$ </ text -math></inline-formula>块后依次解码每个消息。在这种流设置中，研究了编码率、误码率和块长度之间的基本相互作用。对于输出对称通道，对于一定范围的中等偏差缩放，中等偏差常数比块编码或非流设置提高了一个因子<inline-formula> < text -math notation="LaTeX">$T$ </ text -math></inline-formula>。对于反向证明，假设一个更强大的解码器，其中一些额外的信息是前馈的。首先对辅助信道的误差概率进行限定，然后使用新开发的测量变化引理将结果转换回原始信道，其中仔细表征了指数中剩余项的衰减速度。为了证明可实现性，在误差分析中采用了一种已知的编码技术，该技术涉及对新消息和过去消息的联合编码和解码，并进行了一些操作。
In this paper, a streaming transmission setup is considered, where an encoder observes a new message in the beginning of each block and a decoder sequentially decodes each message after a delay of <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> blocks. In this streaming setup, the fundamental interplay between the coding rate, the error probability, and the blocklength in the moderate deviations regime is studied. For output symmetric channels, the moderate deviations constant is shown to improve over the block coding or non-streaming setup by exactly a factor of <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula> for a certain range of moderate deviations scalings. For the converse proof, a more powerful decoder, to which some extra information is fedforward is assumed. The error probability is bounded first for an auxiliary channel and this result is translated back to the original channel by using a newly developed change-of-measure lemma, where the speed of decay of the remainder term in the exponent is carefully characterized. For the achievability proof, a known coding technique that involves a joint encoding and decoding of fresh and past messages is applied with some manipulations in the error analysis.