A Sphere-Packing Analysis of Incremental Redundancy with Feedback

Abstract

Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of memoryless Gaussian channels. Recently, Chen et al. [1] demonstrated that an incremental redundancy scheme can use noiseless feedback to help short convolutional codes deliver the bit-error-rate performance of a long blocklength turbo code, but with much lower latency. Such a latency improvement is suggested by the error-exponent analysis, but there is no theoretical work that estimates how much latency improvement is possible with feedback for practical blocklengths and rates. This paper provides a code-independent analysis that quantifies the latency benefits possible by using modified incremental redundancy with feedback (MIRF). A sphere-packing analysis yields the throughput vs. latency performance of both a baseline ARQ scheme and MIRF. The sphere-packing analysis matches well with simulations using turbo and convolutional codes, showing that the analysis has a practical predictive value.

Feedback systems using non-binary LDPC codes with a limited number of transmissions

“…Polyanskiy et al [2] and Chen et al [3] illustrate that by using feedback, one can approach capacity in a small number of channel uses (i.e. with low latency).…”

Incremental redundancy: A comparison of a sphere-packing analysis and convolutional codes

“…The details of calculating I n (r) can be found in [11]. The error probability of the code conditioned on ∩ i j=1 ζ j is approximated by the error probability of the same code but with a new noise vector…”

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

“…Polyanskiy et al [1] and Chen et al [2] illustrated that by using feedback, one can approach capacity in a small number of channel uses (low latency). Polyanskiy et al [1] introduced variable-length coding with termination (VLFT) which theoretically approaches capacity at low latencies.…”

“…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).…”