RBO Protocol: Broadcasting Huge Databases for Tiny Receivers

We propose a protocol (called RBO) for broadcasting long streams of single-packet messages over radio channel for tiny, battery powered, receivers. The messages are labeled by the keys from some linearly ordered set. The sender repeatedly broadcasts a sequence of many (possibly millions) of messages, while each receiver is interested in reception of a message with a specified key within this sequence. The transmission is arranged so that the receiver can wake up in arbitrary moment and find the nearest transmission of its searched message. Even if it does not know the position of the message in the sequence, it needs only to receive a small number of (the headers of) other messages to locate it properly. Thus it can save energy by keeping the radio switched off most of the time. We show that bit-reversal permutation has "recursive bisection properties" and, as a consequence, RBO can be implemented very efficiently with only constant number of $\log_2 n$-bit variables, where $n$ is the total number of messages in the sequence. The total number of the required receptions is at most $2\log_2 n +2$ in the model with perfect synchronization. The basic procedure of RBO (computation of the time slot for the next required reception) requires only $O(\log^3 n)$ bit-wise operations. We propose implementation mechanisms for realistic model (with imperfect synchronization), for operating systems (such as e.g. TinyOS).