A Systematic Approach to Incremental Redundancy over Erasure Channels

Abstract

As sensing and instrumentation play an increasingly important role in systems controlled over wired and wireless networks, the need to better understand delay-sensitive communication becomes a prime issue. Along these lines, this article studies the operation of data links that employ incremental redundancy as a practical means to protect information from the effects of unreliable channels. Specifically, this work extends a powerful methodology termed sequential differential optimization to choose near-optimal block sizes for hybrid ARQ over erasure channels. In doing so, an interesting connection between random coding and well-known constants in number theory is established. Furthermore, results show that the impact of the coding strategy adopted and the propensity of the channel to erase symbols naturally decouple when analyzing throughput. Overall, block size selection is motivated by normal approximations on the probability of decoding success at every stage of the incremental transmission process. This novel perspective, which rigorously bridges hybrid ARQ and coding, offers a pragmatic means to select code rates and blocklengths for incremental redundancy.

Variable-Length Stop-Feedback Codes With Finite Optimal Decoding Times for BI-AWGN Channels

“…Later, variations of SDO were developed to improve the Gaussian model accuracy, cf. [11], [12], and SDO was applied to systems that employ incremental redundancy and hybrid automatic repeat request [13] and to the binary erasure channel [14], [15]. However, in this paper, we will show that the Gaussian model is still imprecise for small values of n. Additionally, the existing SDO procedure did not consider the gap constraint of decoding times and is only suitable for VLSF codes with sparse decoding times.…”

Variable-Length Stop-Feedback Codes With Finite Optimal Decoding Times for BI-AWGN Channels

“…Later, variations of SDO were developed to improve the Gaussian model accuracy [13], [14]. The SDO algorithm is used to optimize systems that employ incremental redundancy and hybrid automatic repeat request (ARQ) [15], and to code for the binary erasure channel [16], [17]. However, in this paper, we show that the Gaussian model is still imprecise for small values of n. Additionally, the existing SDO procedure fails to consider the inherent gap constraint that two decoding times must be separated by at least one.…”

Timely Transmissions Using Optimized Variable Length Coding

“…For a specified maximum number of feedback transmissions and a maximum probability that the decoder fails to produce a positive acknowledgement (ACK) even when all possible incremental redundancy has been received, SDO finds the transmission lengths that minimize average blocklength. SDO requires a known probability distribution on the probability of ACK at each cumulative blocklength, but works equally well for the variety of distributions that arise from different variable-length codes operating on different channels [15]- [17]. The original formulation of SDO minimizes the average blocklength for a fixed maximum number of feedback transmissions.…”