Deep Variable-Length Feedback Codes

Deep learning has enabled significant advances in feedback-based channel coding, yet existing learned schemes remain fundamentally limited: they employ fixed block lengths, suffer degraded performance at high rates, and cannot fully exploit the adaptive potential of feedback. This paper introduces Deep Variable-Length Feedback (DeepVLF) coding, a flexible coding framework that dynamically adjusts transmission length via learned feedback. We propose two complementary architectures: DeepVLF-R, where termination is receiver-driven, and DeepVLF-T, where the transmitter controls termination. Both architectures leverage bit-group partitioning and transformer-based encoder-decoder networks to enable fine-grained rate adaptation in response to feedback. Evaluations over AWGN and 5G-NR fading channels demonstrate that DeepVLF substantially outperforms state-of-the-art learned feedback codes. It achieves the same block error rate with 20%-55% fewer channel uses and lowers error floors by orders of magnitude, particularly in high-rate regimes. Encoding dynamics analysis further reveals that the models autonomously learn a two-phase strategy analogous to classical Schalkwijk-Kailath coding: an initial information-carrying phase followed by a noise-cancellation refinement phase. This emergent behavior underscores the interpretability and information-theoretic alignment of the learned codes.

💡 Research Summary

This paper introduces Deep Variable‑Length Feedback (DeepVLF) coding, a novel deep‑learning framework that brings variable‑length capabilities to feedback‑based channel coding. Traditional learned feedback codes such as DeepCode, AttentionCode, DEFC, GB‑AF, and LightCode operate with a fixed block length, which limits adaptability and leads to severe performance degradation at high code rates where fewer channel uses are available. DeepVLF overcomes these limitations by allowing the transmission length to be decided dynamically based on real‑time feedback, thereby achieving finer granularity in rate adaptation and better utilization of the feedback link.

Two complementary architectures are proposed: DeepVLF‑R, where the receiver decides when to stop (receiver‑termination), and DeepVLF‑T, where the transmitter makes the termination decision (transmitter‑termination). Both designs share three core innovations. First, the message bits are partitioned into Q equal‑size groups (bit‑groups) of m = K/Q bits, reducing the decoder’s output space from 2^K to 2^m per group while preserving enough information to recover the whole message after a small number of groups. Second, a belief matrix P =