In downlink massive random access (DMRA), a base station transmits messages to a typically small subset of active users, selected randomly from a massive number of total users. Explicitly encoding the identities of active users would incur a significant overhead scaling logarithmically with the number of total users. Recently, via a random coding argument, Song, Attiah and Yu have shown that the overhead can be reduced to within some upper bound irrespective of the number of total users. In this remark, recognizing that the code design for DMRA is an instance of covering arrays in combinatorics, we show that there exists deterministic construction of variable-length codes that incur an overhead no greater than $1 + log_2 e$ bits.

翻译：在下行大规模随机接入（DMRA）中，基站向一个通常较小的活跃用户子集传输消息，这些用户是从海量总用户中随机选出的。显式编码活跃用户的身份会产生与总用户数成对数关系增长的可观开销。近期，通过随机编码论证，Song、Attiah 和 Yu 已证明该开销可降至与总用户数无关的某个上界之内。在本注记中，我们认识到 DMRA 的码字设计是组合设计中覆盖阵列的一个实例，并证明了存在一种确定性的变长码构造方法，其开销不超过 $1 + \log_2 e$ 比特。