Small-State Coset Trellis Coding at IQ2_XXS Size: An Equal-Bytes Study in llama.cpp

Trellis-coded quantization of LLM weights is established (QTIP, EXL3), and ik_llama.cpp's IQ2_KT already provides a trellis type in a llama.cpp fork. We ask how much a small-state code adds at a fixed file size, that of llama.cpp's IQ2_XXS, and which part of the pipeline supplies the gain. We store Ungerboeck's 8-state set-partitioned code over 4-weight symbols in a GGUF file, decoded by an unmerged CUDA patch to llama.cpp, behind a random Hadamard rotation and QuIP's LDLQ rounding, with input-column scales that minimise, under a diagonal Hessian model, QuIP's incoherence bound on LDLQ's error. On Qwen3-4B (post hoc) the file reaches WikiText-2 perplexity 16.64, against 28.61 for IQ2_XXS and 18.15 for the strongest IQ2_KT file of this size we built; it decodes at batch 1 at least as fast as IQ2_XXS but processes prompts at 0.74x. Pre-registered, it beats IQ2_KT on Llama-3.1-8B (8.44 against 9.36 with a BOS at every window; IQ2_KT made from Q8_0) and loses on Qwen3-14B (9.57 against 9.40; tie on C4). At equal bytes, removing the trellis memory costs 0.076 nats per token: about 80% (post hoc) of the margin over a perplexity-tuned IQ2_KT, but 14% of the gain over IQ2_XXS. Code: https://github.com/Genrius-AI/pingala8-llmModels: https://huggingface.co/Genrius-AI/Qwen3-4B-Pingala8-2bit and https://huggingface.co/Genrius-AI/Llama-3.1-8B-Pingala8-2bit