Statistical ARQ link analysis and planning for dynamic links

In [1] and [2], we discussed automatic Repeat-reQuest (ARQ) link analysis and planning in terms of effective data rate, effective throughput, latency, and frame-error-rate (FER), under the standard assumption that the signal-to-noise ratio (SNR) remains the same throughout the ARQ communication session. In [3], we argued that the concept of constant SNR might not be valid when considering events over a long time horizon, as many link parameters are inherently statistical. This is particularly true for long-haul ARQ links because the channel SNR changes during subsequent retransmissions of un-received or non-decodable frames. As shown in [3], this inaccurate assumption of constant SNR might be non-consequential for static links such as S-band and X-band, but can lead to large discrepancies in the analysis and planning of the more dynamic communication links such as Ka-band and optical communication frequencies. In this paper, using similar techniques developed in [3], we incorporate the effect of changing SNR, or link uncertainty, into the analysis of ARQ links. SNR is no longer considered as a fixed value, but a random variable whose long-term statistics can be characterized with a probability distribution function. We consider two limiting cases: 1. “Fast-varying” SNR: when SNRs in subsequent retransmissions of a code-block can assume different values, and they are independent. One example is the deep space link when the ARQ acknowledgement time is much larger than the coherency time of the channel. For communications between Earth's ground stations and spacecraft at Mars, the round trip light time is 20-40 minutes, and this is much more than the typical atmospheric coherency time of Ka-band. 2. “Slow-varying” SNR: when SNR values in subsequent retransmissions of a code-block remain the same. One example is the proximity link between a low-Mars-orbit orbiter and a surface asset at Mars. In this case, the ARQ acknowledgement time is of the order of milliseconds and we can assume identical channel environment in subsequent re-transmissions. We expect the ARQ behavior of real-world dynamic channels would fall in between the “fast-varying” and “slow-varying” cases, thus providing interesting insights on the ARQ data return performance and latency performance. We illustrate the aforementioned analysis using the NASA (1024, ½) low-density-parity check (LDPC) code.