相关论文: Left ideal LRPC codes and a ROLLO-type cryptosyste…
Reinforcement learning with verifiable rewards (RLVR) has become a standard recipe for improving large language models (LLMs) on reasoning tasks, with Group Relative Policy Optimization (GRPO) widely used in practice. Yet GRPO wastes…
Physical layer approaches for generating secret encryption keys for wireless systems using channel information have attracted increased interest from researchers in recent years. This paper presents a new approach for calculating…
We present here some results of applying the Cayley-Dickson process to certain alternative algebras (notably built upon Galois fields and congruence rings), in a manner which might yield new building blocks for cryptographic systems. We…
In this paper we introduce the notion of right waist and right comparizer ideals for semigroups. In particular, we study the ideal theory of semigroups containing right waists and right comparizer ideals. We also study those properties of…
Recent works showed how low-density parity-check (LDPC) erasure correcting codes, under maximum likelihood (ML) decoding, are capable of tightly approaching the performance of an ideal maximum-distance-separable code on the binary erasure…
Low-density parity-check (LDPC) codes form part of the IRIG-106 standard and have been successfully deployed for the Telemetry Group version of shaped-offset quadrature phase shift keying (SOQPSK-TG) modulation. Recently, LDPC code…
This paper proposes a new method of constructing compact fully-connected Quasi-Cyclic Low Density Parity Check (QC-LDPC) codes with girth g = 8, 10, and 12. The originality of the proposed method is to impose constraints on the exponent…
Quantum error correction is an important building block for reliable quantum information processing. A challenging hurdle in the theory of quantum error correction is that it is significantly more difficult to design error-correcting codes…
A $q$-ary $(n,k,r)$ locally repairable code (LRC) is an $[n,k,d]$ linear code over $\mathbb{F}_q$ such that every code symbol can be recovered by accessing at most $r$ other code symbols. The well-known Singleton-like bound says that $d \le…
"Extended Clifford algebras" are introduced as a means to obtain low ML decoding complexity space-time block codes. Using left regular matrix representations of two specific classes of extended Clifford algebras, two systematic algebraic…
A low-density parity-check (LDPC) code is a linear block code described by a sparse parity-check matrix, which can be efficiently represented by a bipartite Tanner graph. The standard iterative decoding algorithm, known as belief…
Low density parity-check (LDPC) codes are a class of linear block codes that are decoded by running belief propagation (BP) algorithm or log-likelihood ratio belief propagation (LLR-BP) over the factor graph of the code. One of the…
Through this work we introduce an action of the skew polynomial ring $\mathbb{F}_{q}\left[X; \sigma, \delta\right]$ over $\mathbb{F}_{q}$ based on its polynomial valuation and the concept of left skew product of functions. This lead us to…
A joint scheme for the channel coding and spectrum spreading communication system is proposed in this paper. The Bit Error Rate (BER) performance of the joint proposed scheme is evaluated and compared with the case of channel coding scheme…
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…
We determine a new technique which allows the computation of the arithmetical rank of certain monomial ideals.
A class of linear codes that extends classic Goppa codes to a non-commutative context is defined. An efficient decoding algorithm, based on the solution of a non-commutative key equation, is designed. We show how the parameters of these…
We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since…
In this paper we propose right-angled Artin groups as a platform for secret sharing schemes based on the efficiency (linear time) of the word problem. Inspired by previous work of Grigoriev-Shpilrain in the context of graphs, we define two…
In this paper, we show that Quasi-Cyclic LDPC codes can efficiently accommodate the hybrid iterative/ML decoding over the binary erasure channel. We demonstrate that the quasi-cyclic structure of the parity-check matrix can be…