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，基站向通常由海量总用户中随机选取的少量活跃用户子集发送消息。若显式编码活跃用户的身份信息，将产生随总用户数对数增长的高昂开销。近期，Song、Attiah 和 Yu 通过随机编码论证指出，无论总用户数如何，开销均可降至某个上界以内。本注记指出，DMRA 的码设计本质上是组合数学中覆盖阵列的一个实例，并证明存在确定性构造的变长码，其开销不超过 $1 + log_2 e$ 比特。