Generalization Bounds for Transformer Channel Decoders

TL;DR

This paper provides the first theoretical generalization guarantees for transformer-based channel decoders, linking estimation errors to bit-error-rate and deriving bounds that depend on code length, model size, and training data.

Contribution

It establishes the first theoretical generalization bounds for transformer channel decoders like ECCT, connecting noise estimation errors to decoding performance.

Findings

Derived a generalization gap bound using bit-wise Rademacher complexity.

Showed that sparsity from parity-check masking tightens the bound.

Applicable to both single-layer and multi-layer ECCTs.

Abstract

Transformer channel decoders, such as the Error Correction Code Transformer (ECCT), have shown strong empirical performance in channel decoding, yet their generalization behavior remains theoretically unclear. This paper studies the generalization performance of ECCT from a learning-theoretic perspective. By establishing a connection between multiplicative noise estimation errors and bit-error-rate (BER), we derive an upper bound on the generalization gap via bit-wise Rademacher complexity. The resulting bound characterizes the dependence on code length, model parameters, and training set size, and applies to both single-layer and multi-layer ECCTs. We further show that parity-check-based masked attention induces sparsity that reduces the covering number, leading to a tighter generalization bound. To the best of our knowledge, this work provides the first theoretical generalization guarantees for this class of decoders.