A rate-compatible sphere-packing analysis of feedback coding with limited retransmissions

Abstract

Abstract-Recent work by Polyanskiy et al. and Chen et al.has excited new interest in using feedback to approach capacity with low latency. Polyanskiy showed that feedback identifying the first symbol at which decoding is successful allows capacity to be approached with surprisingly low latency. This paper uses Chen's rate-compatible sphere-packing (RCSP) analysis to study what happens when symbols must be transmitted in packets, as with a traditional hybrid ARQ system, and limited to relatively few (six or fewer) incremental transmissions.Numerical optimizations find the series of progressively growing cumulative block lengths that enable RCSP to approach capacity with the minimum possible latency. RCSP analysis shows that five incremental transmissions are sufficient to achieve 92% of capacity with an average block length of fewer than 101 symbols on the AWGN channel with SNR of 2.0 dB.The RCSP analysis provides a decoding error trajectory that specifies the decoding error rate for each cumulative block length. Though RCSP is an idealization, an example tail-biting convolutional code matches the RCSP decoding error trajectory and achieves 91% of capacity with an average block length of 102 symbols on the AWGN channel with SNR of 2.0 dB. We also show how RCSP analysis can be used in cases where packets have deadlines associated with them (leading to an outage probability).

Firing the genie: Two-phase short-blocklength convolutional coding with feedback

“…This is analogous to the protocol of our VLFT implementation in [3]. We note that the concept of m maximum transmissions before repetition also appears in, for example, [10], [11].…”

“…In [3], we presented a VLFT scheme with limited decoding times (corresponding to "packets"), using variable-length codes with finite maximum length formed by the puncturing of tail-biting convolutional codes. We also provided a ratecompatible sphere-packing (RCSP) analysis of the scheme and showed that the RCSP predictions closely matched the performance of simulated tail-biting convolutional codes.…”

“…II we extend the incremental redundancy (IR) scheme of [3] to incorporate the second phase and derive the expected throughput and latency. Rate-compatible spherepacking analysis is used to determine the transmission lengths used in each phase-1 incremental transmission and the length of the confirmation messages used in phase 2.…”

Short-blocklength non-binary LDPC codes with feedback-dependent incremental transmissions

“…The latency improvement is made possible by capitalizing on favorable noise realizations and attempting to decode early, instead of needlessly sending additional symbols [5]. In case of an unfavorable noise realization, additional information is required which effectively lowers the communication rate to match the operational capacity of the channel.…”

“…Chen et al [2] and Williamson et al [5] analyzed a VLFT scheme based on rate-compatible sphere-packing with an ML decoder (RCSP-ML). RCSP is an approximation of the performance of repeated incremental redundancy with noiseless transmitter confirmation (IR-NTC).…”