Weaknesses of Margulis and Ramanujan-Margulis low-density parity-check cCodes

Constructions of LDPC Codes using Ramanujan Graphs and Ideas from Margulis

When does one redundant parity-check equation matter?

We analyze the effect of redundant parity-check equations on the error-floor performance of low-density paritycheck (LDPC) codes used over the additive white Gaussian noise (AWGN) channel. Our findings show that a large number of iterative decoding errors in the [2640, 1320] Margulis code, confined to point trapping sets in the standard Tanner graph, can be corrected if only one redundant parit...

Lowering Error Floors by Concatenation of Low-Density Parity-Check and Array Code

Low-density parity-check (LDPC) codes have been shown to deliver capacity approaching performance; however, problematic graphical structures (e.g. trapping sets) in the Tanner graph of some LDPC codes can cause high error floors in bit-errorratio (BER) performance under conventional sum-product algorithm (SPA). This paper presents a serial concatenation scheme to avoid the trapping sets and to ...

Two Methods for Reducing the Error-Floor of LDPC Codes

We investigate two techniques for reducing the error-floor of low-density parity-check codes under iterative decoding. Both techniques are developed based on comprehensive analytical and simulation studies of combinatorial properties of trapping sets in codes on graphs. The first technique represents an algorithmic modification of beliefpropagation based on data fusion principles and specialize...

A Survey on Trapping Sets and Stopping Sets

LDPC codes are used in many applications, however, their error correcting capabilities are limited by the presence of stopping sets and trappins sets. Trappins sets and stopping sets occur when specific low-wiehgt error patterns cause a decoder to fail. Trapping sets were first discovered with investigation of the error floor of the Margulis code. Possible solutions are constructions which avoi...