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:本文研究了应用于无记忆信道中的可变长度停止反馈码,包括点对点、多址和随机接入通信情境。所提出的码牌在点对点和多址信道中采用$L$个译码时间$n_1, n_2, \dots ,n_L$,在随机接入信道中采用$KL+1$个译码时间,最多$K$个发射器同时活跃。在点对点和多址信道中,译码器使用观察到的信道输出决定是否在允许的译码时间$n_1, \dots, n_L$之一进行译码,在每个时间向编码器传递一个比特的反馈,以告知其是否停止发送。在随机接入场景中,译码器在时间$n_0$估计活跃的发射器数量,然后在它认为存在$k$个活跃发射器时,从译码时间$n_{k,1}, \dots ,n_{k,L}$中选择。在所有情况下,允许的译码时间的选择是码牌设计的一部分;针对给定的码本大小和目标平均错误概率,给定固定的值$L$,选择的允许译码时间可以最小化预期译码时间。每个情况下的$L$被认为是常数,即使允许块长度增长,所得到的码牌仅需要稀疏反馈。主要结果是实现速率的渐进近似,作为误差概率、预期译码时间和译码时间数量的函数。包括点对点信道下等距译码时间的可变长度停止反馈码的对称性。