We study variable-length codes for point-to-point discrete memoryless channels with noiseless unlimited-rate feedback that occurs in $L$ bursts. We term such codes variable-length bursty-feedback (VLBF) codes. Unlike classical codes with feedback after each transmitted code symbol, bursty feedback fits better with protocols that employ sparse feedback after a packet is sent and also with half-duplex end devices that cannot transmit and listen to the channel at the same time. We present a novel non-asymptotic achievability bound for VLBF codes with $L$ bursts of feedback over any discrete memoryless channel. We numerically evaluate the bound over the binary symmetric channel (BSC). We perform optimization over the time instances at which feedback occurs for both our own bound and Yavas et al.'s non-asymptotic achievability bound for variable-length stop-feedback (VLSF) codes, where only a single bit is sent at each feedback instance. Our results demonstrate the advantages of richer feedback: VLBF codes significantly outperform VLSF codes at short blocklengths, especially as the error probability $\epsilon$ decreases. Remarkably, for BSC(0.11) and error probability $10^{-10}$, our VLBF code with $L=5$ and expected decoding time $N\leq 400$ outperforms the achievability bound given by Polyanskiy et al. for VLSF codes with $L=\infty$, and our VLBF code with $L=3$.

翻译：研究具有无噪声无限速率反馈的点对点离散无记忆信道上的变长码，其中反馈以$L$次突发形式发生。我们将此类码称为突发反馈变长码（VLBF码）。与经典的在每个传输码元后提供反馈的编码不同，突发反馈更适配于在数据包发送后采用稀疏反馈的协议，以及无法同时收发信道的半双工终端设备。针对任意离散无记忆信道，我们为具有$L$次反馈突发的VLBF码提出了一种新颖的非渐近可达性界。通过二进制对称信道（BSC）对该界进行了数值评估。我们对自身界以及Yavas等人提出的变长停止反馈（VLSF）码非渐近可达性界中的反馈发生时间点进行优化（此处VLSF码每次反馈仅发送单个比特）。结果表明，更丰富的反馈具有显著优势：在短码长条件下，VLBF码的性能明显优于VLSF码，且当错误概率$\epsilon$降低时优势更为突出。值得注意的是，对于BSC(0.11)且错误概率$10^{-10}$，当期望译码时间$N\leq 400$时，本文提出的$L=5$的VLBF码甚至优于Polyanskiy等人针对$L=\infty$的VLSF码及$L=3$的VLBF码所给出的可达性界。