Related papers: Efficient Decoding of Interleaved Low-Rank Parity-…
Low-density parity-check (LDPC) codes have been used for communication over a two-user Gaussian broadcast channel. It has been shown in the literature that the optimal decoding of such system requires joint decoding of both user messages at…
The performance of iterative decoding techniques for linear block codes correcting erasures depends very much on the sizes of the stopping sets associated with the underlying Tanner graph, or, equivalently, the parity-check matrix…
An important property of high-performance, low complexity codes is the existence of highly efficient algorithms for their decoding. Many of the most efficient, recent graph-based algorithms, e.g. message passing algorithms and decoding…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
Considerable interest has been paid in recent literature to codes combining local and global properties for erasure correction. Applications are in cloud type of implementations, in which fast recovery of a failed storage device is…
For efficient modulation and error control coding, the deliberate flipping approach imposes the run-length-limited(RLL) constraint by bit error before recording. From the read side, a high coding rate limits the correcting capability of RLL…
Irregular low-density parity check (LDPC) codes are particularly well-suited for transmission schemes that require unequal error protection (UEP) of the transmitted data due to the different connection degrees of its variable nodes.…
In this paper we investigate the decoding of parallel turbo codes over the binary erasure channel suited for upper-layer error correction. The proposed algorithm performs on-the-fly decoding, i.e. it starts decoding as soon as the first…
We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a…
In this paper we analyze the performance of several bit-interleaving strategies applied to Non-Binary Low-Density Parity-Check (LDPC) codes over the Rayleigh fading channel. The technique of bit-interleaving used over fading channel…
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…
Belief-propagation (BP) decoding for quantum low-density parity-check (QLDPC) codes is appealing due to its low complexity, yet it often exhibits convergence issues due to quantum degeneracy and short cycles that exist in the Tanner graph.…
In Linear Programming (LP) decoding of a Low-Density-Parity-Check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords \cite{03FWK}. In…
Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. Some of its practical drawbacks are the complexity of decoding and the overhead due to the coding vectors. For computationally weak and battery-driven…
Assuming iterative decoding for binary erasure channels (BECs), a novel tree-based technique for upper bounding the bit error rates (BERs) of arbitrary, finite low-density parity-check (LDPC) codes is provided and the resulting bound can be…
Forward Error Correction (FEC) is used ubiquitously in the communication pipeline. We explore noncooperative decoding where we aim to recover the code rate of a linear block code. We present a metric to characterize the quality of the code…
The paper proposes an iterative Hidden Markov Model (HMM) for decoding a Low Density Parity Check (LDPC) code. It is demonstrated that a first-order HMM provides a natural framework for the decoder. The HMM is time-homogeneous with a fixed…
The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…
In this paper, we introduce the Union-Intersection Union-Find (UIUF) algorithm for decoding depolarizing errors in topological codes, combining the strengths of iterative and standard Union-Find (UF) decoding. While iterative UF improves…
We obtain exact expressions for the asymptotic behaviour of the average probability of the block decoding error for ensembles of regular low density parity check error correcting codes, by employing diagrammatic techniques. Furthermore, we…