This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed code employs $L$ decoding times $n_1, n_2, \dots, n_L$ for the point-to-point and multiple access channels and $KL + 1$ decoding times for the random access channel with at most $K$ active transmitters. In the point-to-point and multiple access channels, the decoder uses the observed channel outputs to decide whether to decode at each of the allowed decoding times $n_1, \dots, n_L$, at each time telling the encoder whether or not to stop transmitting using a single bit of feedback. In the random access scenario, the decoder estimates the number of active transmitters at time $n_0$ and then chooses among decoding times $n_{k, 1}, \dots, n_{k, L}$ if it believes that there are $k$ active transmitters. In all cases, the choice of allowed decoding times is part of the code design; given fixed value $L$, allowed decoding times are chosen to minimize the expected decoding time for a given codebook size and target average error probability. The number $L$ in each scenario is assumed to be constant even when the blocklength is allowed to grow; the resulting code therefore requires only sparse feedback. The central results are asymptotic approximations of achievable rates as a function of the error probability, the expected decoding time, and the number of decoding times. A converse for variable-length stop-feedback codes with uniformly-spaced decoding times is included for the point-to-point channel.

翻译：本文研究了无记忆信道在点对点、多址及随机接入通信场景下的可变长度停止反馈码。所提出的码字在点对点和多址信道中采用$L$个译码时刻$n_1, n_2, \dots, n_L$，而在最多包含$K$个活跃发射机的随机接入信道中则采用$KL + 1$个译码时刻。在点对点和多址信道中，译码器利用观测到的信道输出，在每个允许的译码时刻$n_1, \dots, n_L$决定是否进行译码，并通过单比特反馈告知编码器是否停止传输。在随机接入场景中，译码器在时刻$n_0$估计活跃发射机数量，若认为存在$k$个活跃发射机，则从译码时刻$n_{k, 1}, \dots, n_{k, L}$中选择相应时刻进行译码。所有情况下，允许的译码时刻均属于码字设计的一部分；给定固定值$L$时，为最小化特定码本规模和目标平均错误概率下的预期译码时长，需合理选择允许译码时刻。各场景中的参数$L$假设为常数（即使码长可增长），因此生成的码字仅需稀疏反馈。核心结论是可达速率相对于错误概率、预期译码时长及译码时刻数的渐近近似。针对点对点信道中采用均匀间隔译码时刻的可变长度停止反馈码，本文还给出了一个反命题。