1An Efficient Feedback Coding Scheme with Low Error Probability for Discrete Memoryless Channels

Existing feedback communication schemes are either specialized to particular channels (Schalkwijk–Kailath, Horstein), or apply to general channels but have high coding complexity (block feedback schemes) or are difficult to analyze (posterior matching). This paper introduces a feedback coding scheme that combines features from previous schemes in addition to a new randomization technique. We show that our scheme achieves the capacity for all discrete memoryless channels and establish a bound on its error exponent that approaches the sphere packing bound as the rate approaches the capacity. These benefits are attained with only O(n logn) coding complexity. Index Terms Index Terms — Feedback, discrete memoryless channel, error exponent