Related papers: On the Number of Errors Correctable with Codes on …
An array low-density parity-check (LDPC) code is a quasi-cyclic LDPC code specified by two integers $q$ and $m$, where $q$ is an odd prime and $m \leq q$. The exact minimum distance, for small $q$ and $m$, has been calculated, and tight…
This paper presents a design technique for obtaining regular time-invariant low-density parity-check convolutional (RTI-LDPCC) codes with low complexity and good performance. We start from previous approaches which unwrap a low-density…
This paper focuses on error-correcting codes that can handle a predefined set of specific error patterns. The need for such codes arises in many settings of practical interest, including wireless communication and flash memory systems. In…
We propose a new type of short to moderate block-length, linear error-correcting codes, called moderate-density parity-check (MDPC) codes. The number of ones of the parity-check matrix of the codes presented is typically higher than the…
The minimum distance graph of a code has the codewords as vertices and edges exactly when the Hamming distance between two codewords equals the minimum distance of the code. A constructive proof for reconstructibility of an extended perfect…
We consider linear network error correction (LNEC) coding when errors may occur on edges of a communication network of which the topology is known. In this paper, we first revisit and explore the framework of LNEC coding, and then unify two…
Error correction is a significant step in postprocessing of continuous-variable quantum key distribution system, which is used to make two distant legitimate parties share identical corrected keys. We propose an experiment demonstration of…
In this paper, an expression for the asymptotic growth rate of the number of small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC) codes is derived. The expression is compact and generalizes existing results for LDPC…
The relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable…
Four different ways of obtaining low-density parity-check codes from expander graphs are considered. For each case, lower bounds on the minimum stopping set size and the minimum pseudocodeword weight of expander (LDPC) codes are derived.…
In this paper, we analyze the finite-length performance of codes on graphs constructed by connecting spatially coupled low-density parity-check (SC-LDPC) code chains. Successive (peeling) decoding is considered for the binary erasure…
Low-density parity-check (LDPC) convolutional codes are capable of achieving excellent performance with low encoding and decoding complexity. In this paper we discuss several graph-cover-based methods for deriving families of time-invariant…
We propose a new low-density parity-check code construction scheme based on 2-lifts. The proposed codes have an advantage of admitting efficient hardware implementations. With the motivation of designing codes with low error floors, we…
A generalized low-density parity-check (GLDPC) code is a class of codes, where single parity check nodes in a conventional low-density parity-check (LDPC) code are replaced by linear codes with higher parity check constraints. In this…
Ensembles of (J,K)-regular low-density parity-check convolutional (LDPCC) codes are known to be asymptotically good, in the sense that the minimum free distance grows linearly with the constraint length. In this paper, we use a…
This paper addresses the issue of design of low-rate sparse-graph codes with linear minimum distance in the blocklength. First, we define a necessary condition which needs to be satisfied when the linear minimum distance is to be ensured.…
We study Low-Density Parity-Check (LDPC) codes with iterative decoding on block-fading (BF) Relay Channels. We consider two users that employ coded cooperation, a variant of decode-and-forward with a smaller outage probability than the…
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…
We investigate the relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms. A lower bound on the number of variable…
Low-density parity check (LDPC) codes are a significant class of classical codes with many applications. Several good LDPC codes have been constructed using random, algebraic, and finite geometries approaches, with containing cycles of…