arXiv subjects

Wittawat Kositwattanarerk

Publications and source records attributed to Wittawat Kositwattanarerk.

6 recordsLinked to original sources

arXiv2025

Pseudocodewords of quantum, quasi-cyclic, and spatially-coupled LDPC codes: a fundamental cone perspective

While low-density parity-check (LDPC) codes are near capacity-achieving when paired with iterative decoders, these decoders may not output a codeword due to the existence of pseudocodewords. Thus, pseudocodewords have been studied to give insight into the performance of modern decoders including iterative and linear programming decoders. These pseudocodewords are found to be dependent on the parity-check matrix of the code and the particular decoding algorithm used. In this paper, we consider LP decoding, which has been linked to graph cover decoding, providing functions which capture these pseudocodewords. In particular, we analyze the underlying structure of pseudocodewords from quantum stabilizer codes that arise from LP decoding, quasi-cyclic LDPC codes, and spatially-coupled LDPC codes.

cs.IT↗

arXiv2025

Dynamic Exponent Market Maker: Personalized Portfolio Manager and One Pool to Trade Them All

Decentralized exchange platforms such as Uniswap and Balancer operate on several pools where each pool contains two or more cryptocurrencies and constitutes direct trading pairs. The drawbacks here are that liquidity providing requires contribution of tokens in a specific proportion, and trading may require hopping between pools, hence increasing transaction fee and gas fee. We propose an automated market maker (AMM) protocol where liquidity providers can deposit any amount of tokens into the pool. The protocol will preserve the proportion of tokens by total value at the time of deposit and can be seen as a personalized self-balancing portfolio manager. In addition, since the invariant function is dynamic, all exchange pairs are executed from a single composite pool. Nevertheless, the scheme is vulnerable to flash loan attacks and must be used in conjunction with preventive measures.

cs.IT↗

arXiv2020

Multidimensional Fibonacci Coding

Fibonacci codes are self-synchronizing variable-length codes that are proven useful for their robustness and compression capability. Asymptotically, these codes provide better compression efficiency as the order of the underlying Fibonacci sequence increases, but at the price of the increased suffix length. We propose a circumvention to this problem by introducing higher-dimensional Fibonacci codes for integer vectors. In the process, we provide extensive theoretical background and generalize the theorem of Zeckendorf to higher order. As thus, our work unify several variations of Zeckendorf's theorem while also providing new grounds for its legitimacy.

cs.IT↗

arXiv2017

Pseudocodeword-Free Criterion for Codes with Cycle-Free Tanner Graph

Iterative decoding and linear programming decoding are guaranteed to converge to the maximum-likelihood codeword when the underlying Tanner graph is cycle-free. Therefore, cycles are usually seen as the culprit of low-density parity-check (LDPC) codes. In this paper, we argue in the context of graph cover pseudocodeword that, for a code that permits a cycle-free Tanner graph, cycles have no effect on error performance as long as they are a part of redundant rows. Specifically, we characterize all parity-check matrices that are pseudocodeword-free for such class of codes.

cs.IT↗

arXiv2014

Construction A of Lattices over Number Fields and Block Fading Wiretap Coding

We propose a lattice construction from totally real and CM fields, which naturally generalizes the Construction A of lattices from $p$-ary codes obtained from the cyclotomic field $\mathbb{Q}(ζ_p)$, $p$ a prime, which in turn contains the so-called Construction A of lattices from binary codes as a particular case. We focus on the maximal totally real subfield $\mathbb{Q}(ζ_{p^r}+ζ_{p}^{-r})$ of the cyclotomic field $\mathbb{Q}(ζ_{p^r})$, $r\geq 1$. Our construction has applications to coset encoding of algebraic lattice codes, and we detail the case of coset encoding of block fading wiretap codes.

cs.IT↗

arXiv2014

Connections Between Construction D and Related Constructions of Lattices

Most practical constructions of lattice codes with high coding gains are multilevel constructions where each level corresponds to an underlying code component. Construction D, Construction D$'$, and Forney's code formula are classical constructions that produce such lattices explicitly from a family of nested binary linear codes. In this paper, we investigate these three closely related constructions along with the recently developed Construction A$'$ of lattices from codes over the polynomial ring $\mathbb{F}_2[u]/u^a$. We show that Construction by Code Formula produces a lattice packing if and only if the nested codes being used are closed under Schur product, thus proving the similarity of Construction D and Construction by Code Formula when applied to Reed-Muller codes. In addition, we relate Construction by Code Formula to Construction A$'$ by finding a correspondence between nested binary codes and codes over $\mathbb{F}_2[u]/u^a$. This proves that any lattice constructible using Construction by Code Formula is also constructible using Construction A$'$. Finally, we show that Construction A$'$ produces a lattice if and only if the corresponding code over $\mathbb{F}_2[u]/u^a$ is closed under shifted Schur product.

cs.IT↗