Asynchronous capacity per unit cost under a receiver sampling constraint

Abstract

In a recently proposed asynchronous communication setup, the receiver observes mostly pure background noise except for a brief and a priori unknown period of time when data is transmitted. Capacity per unit cost and minimum communication delay were characterized and shown to be unaffected by a sparse sampling at the receiver as long as the number of samples represents a constant fraction of the total channel outputs.This paper strengthens this result and shows that it continues to hold even if the sampling rate tends to zero. More specifically, if the sampling rate is ω(1/B), where B denotes the number of transmitted message bits, capacity per unit cost and minimum decoding delay are the same as under full output sampling. Conversely, if the sampling rate decreases as o(1/B), reliable communication is impossible.The main ingredient in the achievability argument is a time series sampling/detection procedure that detects transient changes in distribution. This procedure has the property of simultaneously minimizing detection delay and sampling rate, in the regime of vanishing false-alarm probability.

Second-Order Asymptotics for Communication Under Strong Asynchronism

“…We denote t i as the starting time of the ith block. 5 The decoder operates as follows. It takes samples at the beginning of each block and checks for the presence of a message using a cascade of ℓ binary hypothesis tests, of increasing reliability, each acting as a confirmation test of the previous test.…”

“…The results refer to two seemingly close scenarios: small delay and minimum delay. In the small delay scenario the decoder is required to achieve a delay d n ≤ n(1+o (1)) and in the minimum delay scenario the decoder is required to locate the codeword exactly, that is d n = n. We briefly review our results: 1) Capacity, minimum sampling, minimum delay: Theorem 3 is a strenghtening of [5,Theorem 3] and states that subsampling the channel outputs does not impact capacity even if the decoder is required to exactly locate the sent codeword (as opposed to achieve small delay as in [5,Theorem 3]) whenever the sampling rate satisfies ρ n = ω(1/n). 2) Finite length, full sampling, minimum delay: Theorem 4 generalizes [3, Corollary 9] to any α ≥ 0 and shows that, under full sampling and minimum delay constraint, the second term in the rate expansion is a standard O( √ n) term whose dispersion constant only depends on the level of asynchronism (and the error probability).…”

“…In [4], [5] the above setting is generalized to include an output sampling constraint that imposes the receiver to observe only a fraction ρ ≤ 1 of the channel outputs until it makes a decision. 1 Surprisingly, it turns out that even a vanishing sampling rate ρ n = ω(1/n) suffices to achieve the full sampling capacity C(α) with an almost minimal delay of n(1 + o (1)).…”

“…1 Surprisingly, it turns out that even a vanishing sampling rate ρ n = ω(1/n) suffices to achieve the full sampling capacity C(α) with an almost minimal delay of n(1 + o (1)). Conversely, if ρ n = o(1/n) the error probability is always bounded away from zero for any linear delay scheme (see [5,Theorem 3]).…”

“…the error probability is always bounded away from zero for any linear delay scheme (see [5,Theorem 3]).…”