相关论文: Coding Without Fine Structure

It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions…

We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection…

Space-time codes leverage the availability of multiple antennas to enhance the reliability of communication over wireless channels. While space-time codes have initially been designed with a focus on open-loop systems, recent technological…

Special functions, coding theory and $t$-designs have close connections and interesting interplay. A standard approach to constructing $t$-designs is the use of linear codes with certain regularity. The Assmus-Mattson Theorem and the…

The coding theorem for Kolmogorov complexity states that any string sampled from a computable distribution has a description length close to its information content. A coding theorem for resource-bounded Kolmogorov complexity is the key to…

We show that the capacity region of the broadcast channel with confidential messages does not change when the strong security criterion is adopted instead of the weak security criterion traditionally used. We also show a construction method…

We demonstrate that certain Johnson-type bounds are asymptotically exact for a variety of classes of codes, namely, constant-composition codes, nonbinary constant-weight codes and multiply constant-weight codes. This was achieved via an…

The so-called fast polar decoding schedules are meant to improve the decoding speed of the sequential-natured successive cancellation list decoders. The decoding speedup is achieved by replacing various parts of the serial decoding process…

This paper deals with a universal coding problem for a certain kind of multiterminal source coding network called a generalized complementary delivery network. In this network, messages from multiple correlated sources are jointly encoded,…

We present a general framework for constructing error-correcting codes using distributed graph coloring under the LOCAL model. Building on the correspondence between independent sets in the confusion graph and valid codes, we show that the…

Karush's proof of McMillan's theorem is recast as an argument involving polynomials with non-commuting indeterminates certain evaluations of which yield the Kraft sums of codes, proving a strengthened version of McMillan's theorem.

Linear-programming pseudocodewords play a pivotal role in our understanding of the linear-programming decoding algorithms. These pseudocodewords are known to be equivalent to the graph-cover pseudocodewords. The latter pseudocodewords, when…

Constrained sequence (CS) codes, including fixed-length CS codes and variable-length CS codes, have been widely used in modern wireless communication and data storage systems. Sequences encoded with constrained sequence codes satisfy…

For codes equipped with metrics such as Hamming metric, symbol pair metric or cover metric, the Johnson bound guarantees list-decodability of such codes. That is, the Johnson bound provides a lower bound on the list-decoding radius of a…

A modified successive cancellation list (SCL) decoder is proposed for polar-coded probabilistic shaping. The decoder exploits the deterministic encoding rule for shaping bits to rule out candidate code words that the encoder would not…

In this paper, we investigate the necessity of finite blocklength codes in distributed transmission of independent message sets over channels with feedback. Previously, it was shown that finite effective length codes are necessary in…

Inspired by the context of compressing encrypted sources, this paper considers the general tradeoff between rate, end-to-end delay, and probability of error for lossless source coding with side-information. The notion of end-to-end delay is…

The unit-derived method in coding theory is shown to be a unique optimal scheme for constructing and analysing codes. In many cases efficient and practical decoding methods are produced. Codes with efficient decoding algorithms at maximal…

Large-scale pre-trained multi-modal models (e.g., CLIP) demonstrate strong zero-shot transfer capability in many discriminative tasks. Their adaptation to zero-shot image-conditioned text generation tasks has drawn increasing interest.…

We show that under the proper forcing axiom the class of all Aronszajn lines behave like $\sigma$-scattered orders under the embeddability relation. In particular, we are able to show that the class of better quasi order labeled fragmented…