Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their potential applications in fault-tolerant quantum computing. However, all families of quantum LDPC codes known to this date suffer from a poor distance scaling limited by the square-root of the code length. This is in a sharp contrast with the classical case where good families of LDPC ...

This letter investigates the combination of the Chase-2 and sum-product (SP) algorithms for low-density parity-check (LDPC) codes. A simple modification of the tanh rule for check node update is given, which incorporates test error patterns (TEPs) used in the Chase algorithm into SP decoding of LDPC codes. Moreover, a simple yet effective approach is proposed to construct TEPs for dealing with ...

Abstract — Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes on memoryless binaryinput/symmetric-output channels. The case of nonsymmetric channels is tackled either by the LDPC coset code ensemble (a channel symmetrizing argument) or by the generalized DE for linear codes on non-symmetric channels. Existing simulations show that the b...

Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes on memoryless binary-input/symmetric-output channels. The case of non-symmetric channels is tackled either by the LDPC coset code ensemble (a channel symmetrizing argument) or by the generalized DE for linear codes on non-symmetric channels. Existing simulations show that the performanc...

Strong rate-compatible codes is important to achieve high throughput in hybrid automatic repeat request with forward error correction (ARQ/FEC) systems in packet data transmission. This paper focuses on the construction of efficient rate-compatible low density parity check (RC-LDPC) codes over a wide rate range. The conventional approach of puncturing is first studied. Analysis on the code ense...

Type II and III low-density parity-check codes (QC-LDPC) codes have been shown to have better minimum distance compared to Type I QC-LDPC codes. This article presents a highly flexible method for constructing high-girth type II and III QC-LDPC codes. The proposed algorithm establishes constraints to be observed in creating a bipartite graph of a given girth. The algorithm is by far more flexibl...

In this paper, a new variant of the McEliece cryptosystem, based on Low-Density Parity-Check (LDPC) codes, is studied. Random-based techniques allow to design large families of LDPC codes with equivalent error correction capability; therefore, in principle, such codes can substitute Goppa codes, originally used by McEliece in his cryptosystem. Furthermore, Quasi-Cyclic (QC) LDPC codes can be ad...

In this paper, we investigate the application of nonbinary low density parity check (LDPC) codes over Galois field GF(q) for both single-input single-output (SISO) and multipleinput multiple-output (MIMO) fading channels using higher order modulations. As opposed to the widely studied binary systems that employ joint detection and channel decoding, we propose a nonbinary system where optimal si...

In this paper the low density party check (LDPC) codes used in the IEEE 802.16 standard physical layer are studied, and two novel techniques to enhance the performance of such codes are introduced. In the first technique, a novel parity check matrix for LDPC codes over GF(4) with the non-zero entries chosen to maximize the entropy is proposed, the parity check matrix is based on the binary pari...

We introduce a wide class of LDPC codes, large enough to include LDPC codes over finite fields, rings or groups as well as some non-linear codes. This class is defined by an extension of the parity-check equations involved in the code’s definition. A belief propagation decoding procedure with the same complexity as for the decoding of LDPC codes over finite fields is presented for theses new pa...