Quasi-cyclic generalized ldpc codes with low error floors

Abstract

Abstract-In this paper, a novel methodology for designing structured generalized LDPC (G-LDPC) codes is presented. The proposed design results in quasi-cyclic G-LDPC codes for which efficient encoding is feasible through shift-register-based circuits. The structure imposed on the bipartite graphs, together with the choice of simple component codes, leads to a class of codes suitable for fast iterative decoding. A pragmatic approach to the construction of G-LDPC codes is proposed. The approach is based on the substitution of check nodes in the protograph of a low-density parity-check code with stronger nodes based, for instance, on Hamming codes. Such a design approach, which we call LDPC code doping, leads to low-rate quasi-cyclic G-LDPC codes with excellent performance in both the error floor and waterfall regions on the additive white Gaussian noise channel.

Short low-rate non-binary turbo codes

“…Iteratively-decodable codes able to approach the Shannon limit at low coding rates have been introduced in the past [6]- [8]. However, most of them suffer either from high error floors [6], [7] or from visible losses compared with the sphere packing bound (SPB) [9] when the code dimension k is within few hundreds of bits [8].…”

“…However, most of them suffer either from high error floors [6], [7] or from visible losses compared with the sphere packing bound (SPB) [9] when the code dimension k is within few hundreds of bits [8]. Very low-rate low-density paritycheck (LDPC) codes over moderate order fields F q (e.g., with q = 2 m , 6 ≤ m ≤ 8) possessing decoding thresholds close to channel capacity have been recently proposed in [10].…”

Design of Finite-Length Generalized LDPC Codes

“…LDPC codes can be further extended to generalized LDPC (GLDPC) codes [31][32][33][34][35][36][37][38][39][40][41]. GLDPC codes usually have good minimum distance properties [32,33], compared with LDPC codes, and they generally have faster convergence speed, and have better error floor behavior.…”

“…The brute-force encoding method has the complexity O(N 2 ), where N is the code length, whereas some carefullydesigned codes enjoy linear or even sub-linear encoding complexity. There are a few papers on constructing EE-GLDPC codes with specific structures [37][38][39], however, the systematic design of EE-GLDPC codes and EE-DGLDPC codes are still open issues.…”

“…In this work, we call a GLDPC code "strict-sense" if all the CNs use the same linear code as their component codes, denoted by "sGLDPC code" [32][33][34][35][36][37], otherwise it is called a hybrid GLDPC code, denoted by "hGLDPC code" [40,41].…”