A Sphere-Packing Analysis of Incremental Redundancy with Feedback

Theoretical analysis has long indicated that feedback improves the error exponent but not the capacity of memoryless Gaussian channels. Recently, Chen et al. 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 ACK/NACK 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.