相关论文: Index Codes for Interlinked Cycle Structures with …
This paper analyzes the distribution of cycle lengths in turbo decoding and low-density parity check (LDPC) graphs. The properties of such cycles are of significant interest in the context of iterative decoding algorithms which are based on…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
We define and study a class of codes obtained from scrolls over curves of any genus over finite fields. These codes generalize Goppa codes in a natural way, and the orthogonal complements of these codes belong to the same class. We show how…
Graphs are closely related to quantum error-correcting codes: every stabilizer code is locally equivalent to a graph code, and every codeword stabilized code can be described by a graph and a classical code. For the construction of good…
In this paper, we propose to study and optimize a very general class of LDPC codes whose variable nodes belong to finite sets with different orders. We named this class of codes Hybrid LDPC codes. Although efficient optimization techniques…
In this paper, cyclic codes are established over some finite quaternion integer rings with respect to the quaternion Mannheim distance, and de- coding algorithm for these codes is given.
Subspace codes have received an increasing interest recently due to their application in error-correction for random network coding. In particular, cyclic subspace codes are possible candidates for large codes with efficient encoding and…
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalize the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and A.…
In this paper, we study the information-theoretic converse for the index coding problem. We generalize the definition for the alignment chain, introduced by Maleki et al., to capture more flexible relations among interfering messages at…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
For odd length $n$, the cyclic codes construction over $\Re= \Z_4[v]/ \langle v^2-v \rangle$ is provided. The hulls of cyclic codes over $\Re$ are studied. The average $2$-dimension $E(n)$ of the hulls of cyclic codes over $\Re$ is also…
In this paper, we propose new coupled codes constructed by overlapping circular spatially-coupled low-density parity-check (SC-LDPC) codes, which show better asymptotic and finite-length decoding performance compared to the conventional…
In this monography, it is proposed to consider the concepts of spectra of edge cuts and edge cycles of a graph as a basic mathematical structure for solving the problem of graph isomorphism. An edge cut is defined by an edge and the…
It was shown by Beisegel, Chudnovsky, Gurvich, Milani\v{c}, and Servatius in 2022 that every induced $2$-edge path in a vertex-transitive graph closes to an induced cycle. Similar results were obtained for 3-edge paths closing to cycles in…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
Universal cycles, such as De Bruijn cycles, are cyclic sequences of symbols that represent every combinatorial object from some family exactly once as a consecutive subsequence. Graph universal cycles are a graph analogue of universal…
The use of skew polynomial rings allows to endow linear codes with cyclic structures which are not cyclic in the classical (commutative) sense. Whenever these skew cyclic structures are carefully chosen, some control over the Hamming…
Quasi-cyclic codes form an important class of algebraic codes that includes cyclic codes as a special subclass. This chapter focuses on the algebraic structure of quasi-cyclic codes, first. Based on these structural properties, some…
A long-standing conjecture of Thomassen says that every longest cycle of a $3$-connected graph has a chord. Thomassen (2018) proved that if $G$ is $2$-connected and cubic, then any longest cycle must have a chord. He also showed that if $G$…
While constructing polar codes for successive-cancellation decoding can be implemented efficiently by sorting the bit-channels, finding optimal polar codes for cyclic-redundancy-check-aided successive-cancellation list (CA-SCL) decoding in…