We proposed an algorithm for the server in ARQ scheme for broadcast channel. In this study, we consider a model in which the feedback delay is a random variable. Specifically, the feedback delay is different for each packet and receiver. For this model, the algorithm proposed in conventional studies cannot be directly applied. Therefore, we propose an algorithm using windows, which are set for the sequence of packets. It is also found that there is a trade-off between throughput and acceptance time in proposed algorithm.

A decision criterion called LR+Th for decision feedback scheme was proposed by Hashimoto. Though Forney’s decision criterion (FR) is optimal and meets the Neyman-Pearson’s lemma, LR+Th is suboptimal. However, the error exponent of LR+Th is shown to be asymptotically equivalent to that of FR by random coding arguments for block codes. In this paper, applying the technique of DS2 bound, we derive an upper bound for the error probability of LR+Th with the ensemble of linear block codes. It elucidates the relation between the random coding exponents of block codes and those of linear block codes.