The Receiver-Limited Floor: Rate-Distortion Bounds on Serial Decoding Throughput

This study derives a mechanistic bound on effective information per serial decoding event using the M-ary rate-distortion function RM(ε). Applied to three independently characterized systems—the ribosome (M = 21, ε = 10−4), human phonology (M = 31, ε ~ 0.02), and the chromatic scale (M = 12, ε ~ 0.05)—the framework predicts throughput values of 4.39, 4.71, and 3.12 bits, respectively. Under realistic non-uniform amino acid frequencies, the floor shifts from 4.390 to approximately 4.175 bits—a 0.2-bit reduction set by amino-acid usage bias. The vocabulary-independence prediction was tested across 1,749 models spanning two architectures—32 causal language models and 1,717 encoder-decoder translation models—evaluated on a shared reference corpus. Vocabulary size does not predict bits-per-byte in causal models (β1 = 0.058, p = 0.643) or in language-matched translation models (Spearman p = 0.13). Language-mismatch stratification reveals a quantifiable +1.33-bit information cost when models process unfamiliar languages. These results support the hypothesis that the rate-distortion floor is a universal mechanistic bound for serial decoders and vocabulary size is primarily a redundancy parameter.