arXiv subjects

Tyler Kann

Publications and source records attributed to Tyler Kann.

6 recordsLinked to original sources

arXiv2026

An SCL-Aware Design of PAC Codes

We develop design methodologies for the rate profile of polarization-adjusted convolutional (PAC) codes tailored to successive cancellation list (SCL) decoding. The crux of our approach is two-fold: first is the creation of a modified density evolution Gaussian approximation (DEGA), called conditional DEGA (CDEGA), to analyze the decoding process in the presence of errors; second is the creation of a dangerous-path occupancy metric to find the conditional occupancy of bit-errors in a finite list. Our approach not only illuminates the role of rate-one precoding, but also provides insight into why certain information sets are particularly well suited to PAC codes. We demonstrate the usefulness of CDEGA and dangerous-path metrics with algorithms that create new information sets, as well as precoders that are extremely sparse yet competitive. In particular, we design codes of length $N \leq 512$ with various rates and list sizes, all of which offer at least half a dB gain over traditional PAC codes at an FER of $10^{-3}$ and improve upon state-of-the-art results.

cs.IT↗

arXiv2026

Finite-Length Empirical Comparison of Polar, PAC, and Invertible-Extractor Secrecy Codes over the Wiretap BSC

We compare three secrecy-coding schemes for the degraded wiretap binary symmetric channel (BSC) in the finite-blocklength regime: (i) polar wiretap coset codes, (ii) PAC codes used as wiretap coset codes, and (iii) the invertible-extractor (IE) framework of Bellare--Tessaro. Our comparison is empirical and uses a common semantic-secrecy metric (distinguishing advantage). For polar coset codes, we compute Eve's polarized bit-channel capacities (via the Tal--Vardy construction) to obtain explicit finite-length upper bounds on mutual-information leakage, yielding strong secrecy bounds. For PAC coset codes, we prove that Eve's synthesized bit-channels are equivalent to those of polar codes (up to a permutation), so the same leakage bounds apply; we then convert these strong-secrecy bounds into semantic-secrecy guarantees for symmetric wiretap channels. For the IE scheme, we use the closed-form semantic-secrecy bounds already established. Finally, we report finite-length results that jointly characterize (a) semantic-secrecy guarantees against Eve and (b) frame-error-rate performance at Bob. Our simulations indicate that Polar and PAC codes exhibit comparable reliability performance under the considered finite-length settings, while PAC codes retain the same secrecy bounds as Polar codes. More broadly, our results highlight that non-universal designs of wiretap codes provide tighter secrecy guarantees than universal design based on invertible extractors.

cs.IT↗

arXiv2026

Covert Multi-bit LLM Watermarking: An Information Theory and Coding Approach

We study the problem of multi-bit watermarking for non-autoregressive large language models (LLMs). We introduce an information-theoretic model inspired by diffusion language models (DLM), in which the encoder has limited non-causal access to token distributions within each token block. This formulation enables an information-theoretic characterization of the non-causal watermarking capacity, in which knowledge of LLM cover statistics is leveraged to enable a multi-bit covert embedding. We study the information-theoretic limits of the model by combining Gelfand--Pinsker and channel synthesis coding techniques and obtain an exact characterization of the capacity. The embedding strategy is further optimized across blocks using a constrained Markov decision process (CMDP) and we develop an explicit algorithm based on polar codes following the information-theoretic principles. We simulate the error performance on LLaDA, and provide empirical total variation (TV) analysis as a function of key randomness.

cs.IT↗

arXiv2026

Stabilizer-Code Channel Transforms Beyond Repetition Codes for Improved Hashing Bounds

The quantum hashing bound guarantees that rates up to $1-H(p_I, p_X, p_Y, p_Z)$ are achievable for memoryless Pauli channels, but it is not generally tight. A known way to improve achievable rates for certain asymmetric Pauli channels is to apply a small inner stabilizer code to a few channel uses, decode, and treat the resulting logical noise as an induced Pauli channel; reapplying the hashing argument to this induced channel can beat the baseline hashing bound. We generalize this induced-channel viewpoint to arbitrary stabilizer codes used purely as channel transforms. Given any $ [\![ n, k ]\!] $ stabilizer generator set, we construct a full symplectic tableau, compute the induced joint distribution of logical Pauli errors and syndromes under the physical Pauli channel, and obtain an achievable rate via a hashing bound with decoder side information. We perform a structured search over small transforms and report instances that improve the baseline hashing bound for a family of Pauli channels with skewed and independent errors studied in prior work.

cs.IT↗

arXiv2026

Quantum Precoded Polar Codes

We introduce a new family of CSS codes obtained from rate-1 precoded polar codes, which harnesses the precoding benefits obtained for classical short blocklength polar codes. We optimize the rate profile and precoder of these codes with a genetic algorithm, and present codes of dimension $ [\![256, 2 ]\!] $ and $ [\![512, 2]\!] $ that have logical error rates similar to the $ [\![1201, 1, 25 ]\!] $ surface code over the depolarizing channel.

cs.IT↗

arXiv2025

Covert Communication over Physically-Degraded Alarm Two-Way Channels

We study covert communications over binary-input discrete memoryless alarm two-way channels, in which two users interact through a two-way channel and attempt to hide the presence of their communication from an eavesdropping receiver. The alarm two-way channel is one in which simultaneous transmissions by both users trigger an alarm at the eavesdropper, which captures the challenges and opportunities of cooperation beyond interference management. In particular, by characterizing the covert capacity region of two-way channels when using public time sharing, we show how cooperation strictly improves achievable covert communication throughputs. While our analysis falls short of characterizing the two-way covert capacity region for all two-way channels, we provide general achievable and converse bounds that illuminate the cooperation mechanisms that benefit covertness and are tight for a physically-degraded alarm two-way channels. Because of the unique nature of covert communications, our analysis also shows that the coordination required to avoid triggering alarms comes asymptotically "for free". The key technical challenge that we address is how to appropriately design auxiliary random variables in a multi-user covert communication setting subject to the square root law.

cs.IT↗