Generalized Low-Density Parity-Check Codes Based on Hadamard Constraints

Low-complexity LDPC coded BICM-ID with orthogonal modulations

“…The mapping strategy is based on two properties: one is the equivalence of OMs and Hadamard codes and the other is an inherent single parity check (SPC) relation of Hadamard codes. It can be shown that, with the proposed mapping strategy, our scheme is equivalent to generalised LDPC (GLDPC) codes with Hadamard constraints [4]. Thus, the demodulation process can be merged into iterative GLDPC decoding, which greatly simplifies the receiver structure.…”

“…0 and -1 ! 1, which results in a matrix C M , and taking the columns c i s of C M as codewords [4]. In fact, column h i of H M can also be viewed as the BPSK modulated version of Hadamard codeword c i with BPSK modulation defined by 0 !…”

“…1 shows that with a simple linear transformation each check node is equivalent to a Hadamard codeword and then the LDPC coded orthogonal modulation scheme is equivalent to a GLDPC code with Hadamard constraints [4]. Thus, orthogonal demodulation can be merged into the iterative decoding of GLDPC with Hadamard constraints, which can be efficiently done by using FHT and APP-FHT [4,5]. Simulation results: We use a special class of LDPC codes, namely concatenated zigzag (CZ) code [6], as the channel code for its simple encoding and decoding structures.…”

Exact split information function for SPC

“…Later, the principle of EXIT charts has been successfully applied to study other iteratively-decoded codes such as parallel concatenated codes (PCCs) [9], serially concatenated codes (SCC) [10], convolutional codes [11], LDPC codes [9], [12], repeat-accumulate codes [13], generalized LDPC codes and DGLDPC codes [7], [14], [15]. In [16], it has been shown that codes with capacityapproaching performance over the binary erasure channel (BEC) can be designed by matching exactly the EXIT curves of the component codes.…”

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.…”