An asymptotically optimal random modem and detector for robust communication

Worst-case error probability of a spread-spectrum system in energy-limited interference

“…While difficult to implement in practice for large , chip-level interleaving leads to a communication system that is more robust to impulsive interference. We also compared the performance of both chiplevel and symbol-level interleaving to that of the modem and detector derived in [8], which asymptotically minimize the worst-case error probability as the code block length becomes large. For , the performance of chiplevel interleaving is nearly optimum; for , however, performance is markedly suboptimum.…”

“…, the conditional probability of error of the receiver in (5) and (7) is given by (8) where is the chip signal-to-noise power ratio. For a particular , the (unconditional) probability of error is then , where denotes expectation with respect to the distribution of .…”

“…In an earlier paper [8] we derived, for a fixed encoder, a random modem and detector that asymptotically minimize the worst-case error probability suffered on the channel (2) as the block length of the encoder becomes large. The feasible class of modems and detectors considered includes the DS system described in this paper.…”

“…A simple upper bound to can be found by applying the union bound [17, p. 264] to (8), which yields where and . It then follows from (10) that (14) Most of this section is devoted to finding bounds for the summands on the right.…”

“…Thus, by comparing the performance of these two systems, we can determine how the performance of the DS system described in Section II compares with the optimally robust random modem and detector. In the absence of thermal noise ( ), the error exponent for the optimal random modem and detector on channel (2) reduces to [8] (45)…”