The paper introduces *pseudorandom error-correcting codes* (PRCs), which are error-correcting codes that remain pseudorandom to any computationally bounded adversary, even when a polynomial number of codewords are observed. These codes are robust to substitution and deletion errors, with pseudorandomness based on standard cryptographic assumptions, such as the hardness of the Learning Parity with Noise (LPN) problem or the planted XOR problem at low density. The authors construct PRCs that are robust to a constant rate of random substitutions and deletions, which are crucial for watermarking and steganography applications. Specifically, they present an undetectable watermarking scheme for language model outputs, which is robust to cropping and a constant rate of random substitutions and deletions. This is the first scheme that can tolerate a constant rate of errors while remaining undetectable. Additionally, the paper introduces a constant-rate stateless steganography scheme that is robust to a constant rate of substitutions. This is the first stateless steganography scheme with provable security and robustness to errors. The main contributions of the paper include: 1. **Pseudorandom Codes**: Construction of PRCs that are robust to substitution and deletion errors, based on cryptographic assumptions. 2. **Watermarking for Language Models**: An undetectable watermarking scheme for language model outputs that is robust to a constant rate of random substitutions and deletions. 3. **Steganography**: A robust, stateless steganography scheme that can hide messages in content with a constant rate of substitutions. The paper also discusses related work and provides a technical overview of the constructions and proofs, including the use of low-density parity-check (LDPC) codes and the planted XOR assumption.The paper introduces *pseudorandom error-correcting codes* (PRCs), which are error-correcting codes that remain pseudorandom to any computationally bounded adversary, even when a polynomial number of codewords are observed. These codes are robust to substitution and deletion errors, with pseudorandomness based on standard cryptographic assumptions, such as the hardness of the Learning Parity with Noise (LPN) problem or the planted XOR problem at low density. The authors construct PRCs that are robust to a constant rate of random substitutions and deletions, which are crucial for watermarking and steganography applications. Specifically, they present an undetectable watermarking scheme for language model outputs, which is robust to cropping and a constant rate of random substitutions and deletions. This is the first scheme that can tolerate a constant rate of errors while remaining undetectable. Additionally, the paper introduces a constant-rate stateless steganography scheme that is robust to a constant rate of substitutions. This is the first stateless steganography scheme with provable security and robustness to errors. The main contributions of the paper include: 1. **Pseudorandom Codes**: Construction of PRCs that are robust to substitution and deletion errors, based on cryptographic assumptions. 2. **Watermarking for Language Models**: An undetectable watermarking scheme for language model outputs that is robust to a constant rate of random substitutions and deletions. 3. **Steganography**: A robust, stateless steganography scheme that can hide messages in content with a constant rate of substitutions. The paper also discusses related work and provides a technical overview of the constructions and proofs, including the use of low-density parity-check (LDPC) codes and the planted XOR assumption.