We study the following semi-deterministic setting of the joint source-channel coding problem: a deterministic source sequence (a.k.a. individual sequence) is transmitted via a memoryless channel, using delay-limited encoder and decoder, which are both implementable by periodically-varying finite-state machines, and the decoder is granted with access to side information, which is a noisy version of the source sequence. We first derive a lower bound on the achievable expected distortion in terms of the empirical statistics of the source sequence, the number of states of the encoder, the number of states of the decoder, their period, and the overall delay. The bound is shown to be asymptotically achievable by universal block codes in the limit of long blocks. We also derive a lower bound to the best achievable excess--distortion probability and discuss situations where it is achievable. Here, of course, source coding and channel coding cannot be completely separated without loss of optimality. Finally, we outline a few extensions of the model considered, such as: (i) incorporating a common reconstruction constraint, (ii) availability of side information at both ends, and (iii) extension to the Shannon channel with causal state information at the encoder. This work both extends and improves on earlier work of the same flavor (Ziv 1980, Merhav 2014), which focused only on the expected distortion, without side information at either end, and without the above mentioned additional ingredients.
翻译:我们研究的是联合源-渠道编码问题的以下半确定性设置:确定源序列(a.k.a.a.a.单序)通过一个没有记忆的渠道传输,使用不拖延的编码器和解码器,这些编码器和解码器都可通过定期翻转的限定的限定的限定的限定的限定的固定用途机器加以执行,而解码器则获得侧边信息,这是源序列的一个噪音版本。我们首先从源序列的经验性统计数字、编码器国家的数目、不扭曲的状态数目、其时期和总体延迟等方面,得出一个较低的限制。这一限制显示,通过在长块限制范围内通用的区块编码是有条件的。我们对于最佳可实现的过度扭曲可能性也有较低的约束,并讨论可以实现的源序列的情况。在这里,源编码和渠道编码无法完全分离,但又不丧失更多的最佳性。最后,我们概述了所考虑的模型的少数扩展,例如:(一) 将共同的重建制约因素纳入上方,不扭曲的扭曲状态,它们的时期,以及整体延迟的时期,通过长期的通用的区块代码,我们从预期的轨道上改进了预期的工作。