Finding Small Fundamental Instantons of LDPC Codes by Path Extension

Parity-Check Matrix Extension to Lower the Error Floors of Irregular LDPC Codes

Trapping sets have been identified as one of the main factors causing error floors of low-density parity-check (LDPC) codes at high SNR values. By adding several new rows to the original parity-check matrix, a novel method is proposed to eliminate small trapping sets in the LDPC code’s Tanner graph. Based on this parity-check matrix extension, we design new codes with low error floors from the ...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

Finding Small Stopping Sets in the Tanner Graphs of LDPC Codes

The performance of low-density parity-check (LDPC) codes over the binary erasure channel for a low erasure probability is limited by small stopping sets. The frame error rate over the additive white Gaussian noise (AWGN) channel for a high signal-to-noise ratio is limited by small trapping sets and by the minimum distance of the LDPC code, which is equal to the codeword with the minimal Hamming...

FPGA Implementations of LDPC over GF(2m) Decoders

Low Density Parity Check (LDPC) codes over GF(2) are an extension of binary LDPC codes that have not been studied extensively. Performances of GF(2) LDPC codes have been shown to be higher than binary LDPC codes, but the complexity of the encoders/decoders increases. Hence there is a substantial lack of hardware implementations for LDPC over GF(2) codes. This paper presents a FPGA serial implem...

Structured LDPC convolutional codes

LDPC convolutional codes, also known as spatially coupled LDPC codes, have attracted considerable attention due to their promising properties. By coupling the protographs from different positions into a chain and terminating the chain properly, the resulting convolutional-like LDPC code ensemble is able to produce capacityachieving performance in the limit of large parameters. In addition, opti...