Asymptotic Expansion and Error Exponent of Two-Phase Variable-Length Coding with Feedback for Discrete Memoryless Channels

This paper studies variable-length coding with noiseless feedback for discrete memoryless channels. Yamamoto and Itoh’s two-phase scheme achieves the optimal error-exponent, but due to the block-coding nature it is not optimal in the expansion of the message size logM . Polyanskiy et al. showed that with feedback, the back-off from capacity is logarithmic in the expected latency l. The O(log l) back-off is achieved by using an incremental redundancy (IR) scheme that only utilizes feedback to determine the stopping time. However, the achievable error-exponent of the IR scheme is not optimal. This paper shows that a two-phase coding scheme where each phase uses an IR scheme achieves the optimal error-exponent while maintaining an expansion on the message size that yields the O(log l) back-off.