用于通过具有反馈的DMC进行流传输的可靠性函数
Reliability function for streaming over a DMC with feedback
摘要：
传统上，后验匹配在信道编码和块编码上下文中被研究--源符号是等概率分布的，并且在传输之前编码器完全知道。在本文中，我们考虑一个流源，其符号到达编码器在一个序列的确定性时间。本文推导了在离散无记忆信道（DMC）上进行流媒体传输的联合信源-信道编码（JSCC）可靠性函数。我们提出了一种新的瞬时编码阶段，操作期间的符号到达期间，并实现了JSCC的可靠性功能流时，其次是一个块编码方案，实现了JSCC的可靠性功能的经典源，其符号是完全可访问的传输之前。在瞬时编码阶段期间，演进的消息字母表被划分成组，并且编码器确定包含到目前为止到达的符号的组的索引，并且应用随机化以将所发送的索引的分布与容量实现索引的分布相匹配。令人惊讶的是，用于流传输的JSCC可靠性函数等于用于完全可访问源的JSCC可靠性函数，这意味着在传输之前对整个符号序列的了解没有提供关于可靠性函数的优势。对于对称的2输入DMC流，我们提出了一个瞬时足够小的差异（SED）的代码，不仅实现了JSCC的可靠性功能，但也可以用来稳定一个不稳定的线性系统在嘈杂的信道。我们设计了低复杂度的算法来实现瞬时编码相位和瞬时SED码。虽然可靠性函数推导出非退化的DMC，退化的DMC，我们设计了一个代码与瞬时编码，实现零错误低于香农的JSCC限制的所有速率。
英文摘要：
Conventionally, posterior matching is investigated in channel coding and block encoding contexts -- the source symbols are equiprobably distributed and are entirely known by the encoder before the transmission. In this paper, we consider a streaming source, whose symbols arrive at the encoder at a sequence of deterministic times. We derive the joint source-channel coding (JSCC) reliability function for streaming over a discrete memoryless channel (DMC) with feedback. We propose a novel instantaneous encoding phase that operates during the symbol arriving period and achieves the JSCC reliability function for streaming when followed by a block encoding scheme that achieves the JSCC reliability function for a classical source whose symbols are fully accessible before the transmission. During the instantaneous encoding phase, the evolving message alphabet is partitioned into groups, and the encoder determines the index of the group that contains the symbols arrived so far and applies randomization to match the distribution of the transmitted index to the capacity-achieving one. Surprisingly, the JSCC reliability function for streaming is equal to that for a fully accessible source, implying that the knowledge of the entire symbol sequence before the transmission offers no advantage regarding the reliability function. For streaming over a symmetric 2-input DMC, we propose an instantaneous small-enough difference (SED) code that not only achieves the JSCC reliability function but also can be used to stabilize an unstable linear system over a noisy channel. We design low complexity algorithms to implement both the instantaneous encoding phase and the instantaneous SED code. While the reliability function is derived for non-degenerate DMCs, for degenerate DMCs we design a code with instantaneous encoding that achieves zero error for all rates below Shannon's JSCC limit.
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