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Tracking Unstable Autoregressive Sources Over Discrete Memoryless Channels

机译：通过离散的无记忆通道跟踪不稳定的自回归源

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摘要

We consider the problem of tracking, in realtime, an unstable autoregressive (AR) source over a discrete memory-less channel (DMC). We present computable achievable bounds on the optimal tracking error for general DMCs, and we particularize these bounds to the binary erasure, packet erasure, and binary symmetric channels. The achievable bounds in this paper are proved using a partially separate source quantization and channel coding architecture. We do not use complete or strict separation in usual Shannon sense: 1) the quantiser's resolution is optimized against the error-correction capabilities of the channel code and the channel code is optimized against an AR Hamming distortion function matched to the source (a weighted Hamming distortion function that provides unequal error protection to different parts of the AR source). The achievability results for general DMCs are proved by combining the AR Hamming distortion function with new realtime (streaming) versions of the random coding union and dependence testing bounds. When applied to erasure channels, these general bounds combine with simple converses to demonstrate that the channel's cutoff rate plays an important role in realtime tracking.
机译：我们考虑了通过离散的无内存通道（DMC）实时跟踪不稳定的自回归（AR）源的问题。我们提出了通用DMC最佳跟踪误差的可计算可达到范围，并将这些范围具体化为二进制擦除，数据包擦除和二进制对称通道。本文使用部分独立的源量化和信道编码架构证明了可达到的界限。在通常的香农意义上，我们不使用完全或严格的分离：1）针对通道代码的纠错能力优化量化器的分辨率，针对与源匹配的AR Hamming失真函数优化通道代码（加权汉明）失真功能，为AR源的不同部分提供不平等的错误保护）。通用DMC的可实现性结果是通过将AR Hamming失真函数与随机编码并集和相关性测试范围的新实时（流）版本相结合来证明的。当应用于擦除通道时，这些一般界限与简单的反推结合起来证明了通道的截止速率在实时跟踪中起着重要的作用。

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