具有不可靠反馈的擦除信道的平衡前向和反馈纠错
Balancing forward and feedback error correction for erasure channels with unreliable feedback
摘要：
研究反馈的传统信息论方法是考虑信道输出到编码器的理想瞬时高速率反馈。这在经典的工作中是可以接受的，因为结果是负面的：香农指出，即使是完美的反馈往往不会提高容量，在对称DMC的背景下，Dobrushin表明，它不会提高固定的块编码错误指数在有趣的高速率制度。然而，它最近被证明，完美的反馈允许很大的改进，在渐近的权衡之间的端到端的延迟和错误的概率，即使在高速率的对称信道。由于增益要求与理想的瞬时反馈，这是自然的想知道是否这些改进仍然如果反馈是不可靠的或以其他方式有限的。这里，分组擦除信道被认为是在前向和反馈链路。首先，反馈信道被认为是一个给定的，并给出了一个策略，以平衡前向和反馈纠错在适当的信息理论限制的长端到端延迟。在足够高的速率下，尽管只有不可靠的反馈，但完美的反馈性能是渐近可达的！其次，结果被解释在零和的情况下的“半双工”节点的带宽或时间的分配给反馈信道来在前向信道的直接费用。事实证明，即使在这里，反馈也是值得的，因为通过适当地平衡前向和反馈误差校正，可以显著降低渐近延迟。结果很容易推广到严格正零未声明错误容量的信道。
英文摘要：
The traditional information theoretic approach to studying feedback is to consider ideal instantaneous high-rate feedback of the channel outputs to the encoder. This was acceptable in classical work because the results were negative: Shannon pointed out that even perfect feedback often does not improve capacity and in the context of symmetric DMCs, Dobrushin showed that it does not improve the fixed block-coding error exponents in the interesting high rate regime. However, it has recently been shown that perfect feedback does allow great improvements in the asymptotic tradeoff between end-to-end delay and probability of error, even for symmetric channels at high rate. Since gains are claimed with ideal instantaneous feedback, it is natural to wonder whether these improvements remain if the feedback is unreliable or otherwise limited. Here, packet-erasure channels are considered on both the forward and feedback links. First, the feedback channel is considered as a given and a strategy is given to balance forward and feedback error correction in the suitable information-theoretic limit of long end-to-end delays. At high enough rates, perfect-feedback performance is asymptotically attainable despite having only unreliable feedback! Second, the results are interpreted in the zero- sum case of "half-duplex" nodes where the allocation of bandwidth or time to the feedback channel comes at the direct expense of the forward channel. It turns out that even here, feedback is worthwhile since dramatically lower asymptotic delays are possible by appropriately balancing forward and feedback error correction. The results easily generalize to channels with strictly positive zero-undeclared-error capacities.
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