An efficient feedback coding scheme with low error probability for discrete memoryless channels

Cheuk Ting Li, Abbas El Gamal

Abstract: Existing feedback communication schemes are either specialized to particular channels (Schalkwijk-Kailath, Horstein), 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 achieves the capacity for all discrete memoryless channels with a bound on the error exponent that approaches the sphere packing bound as the rate approaches the capacity and coding complexity of only O(n log n). These benefits are attained by combining features from previous schemes with new randomization technique and decoding rule.