An Improved Throughput for Non-Binary Low-Density-Parity-Check Decoder

Low-Density-Parity-Check (LDPC) based error control decoders find wide range of application in both storage and communication systems, because of the merits they possess which include high appropriateness towards parallelization and excellent performance in error correction. Field-Programmable Gate Array (FPGA) has provided a robust platform in terms of parallelism, resource allocation and excellent performing speed for implementing non-binary LDPC decoder architectures. This paper proposes, a high throughput LDPC decoder through the implementation of fully parallel architecture and a reduction in the maximum iteration limit, needed for complete error correction. A Galois field of eight was utilized alongside a non-uniform quantization scheme, resulting in fewer bits per Log Likelihood Ratio (LLR) for the implementation. Verilog Hardware Description Language (HDL) was used in the description of the non-binary error control decoder. The propose decoder attained a throughput of 10Gbps at 400-MHz clock frequency when synthesized on a ZYNQ 7000 Series FPGA

Ultra-Sparse Non-Binary LDPC Codes for Probabilistic Amplitude Shaping

This work shows how non-binary low-density parity-check codes over GF($2^p$) can be combined with probabilistic amplitude shaping (PAS) (B\"ocherer, et al., 2015), which combines forward-error correction with non-uniform signaling for power-efficient communication. Ultra-sparse low-density parity-check codes over GF(64) and GF(256) gain 0.6 dB in power efficiency over state-of-the-art binary LDPC codes at a spectral efficiency of 1.5 bits per channel use and a blocklength of 576 bits. The simulation results are compared to finite length coding bounds and complemented by density evolution analysis.Comment: Accepted for Globecom 201

Low-Density Arrays of Circulant Matrices: Rank and Row-Redundancy Analysis, and Quasi-Cyclic LDPC Codes

This paper is concerned with general analysis on the rank and row-redundancy of an array of circulants whose null space defines a QC-LDPC code. Based on the Fourier transform and the properties of conjugacy classes and Hadamard products of matrices, we derive tight upper bounds on rank and row-redundancy for general array of circulants, which make it possible to consider row-redundancy in constructions of QC-LDPC codes to achieve better performance. We further investigate the rank of two types of construction of QC-LDPC codes: constructions based on Vandermonde Matrices and Latin Squares and give combinatorial expression of the exact rank in some specific cases, which demonstrates the tightness of the bound we derive. Moreover, several types of new construction of QC-LDPC codes with large row-redundancy are presented and analyzed.Comment: arXiv admin note: text overlap with arXiv:1004.118

Quantum Error Correction beyond the Bounded Distance Decoding Limit

In this paper, we consider quantum error correction over depolarizing channels with non-binary low-density parity-check codes defined over Galois field of size $2^p$ . The proposed quantum error correcting codes are based on the binary quasi-cyclic CSS (Calderbank, Shor and Steane) codes. The resulting quantum codes outperform the best known quantum codes and surpass the performance limit of the bounded distance decoder. By increasing the size of the underlying Galois field, i.e., $2^p$, the error floors are considerably improved.Comment: To appear in IEEE Transactions on Information Theor

Doubly-Irregular Repeat-Accumulate Codes over Integer Rings for Multi-user Communications

Structured codes based on lattices were shown to provide enlarged capacity for multi-user communication networks. In this paper, we study capacity-approaching irregular repeat accumulate (IRA) codes over integer rings $\mathbb{Z}_{2^{m}}$ for $2^m$-PAM signaling, $m=1,2,\cdots$. Such codes feature the property that the integer sum of $K$ codewords belongs to the extended codebook (or lattice) w.r.t. the base code. With it, \emph{% structured binning} can be utilized and the gains promised in lattice based network information theory can be materialized in practice. In designing IRA ring codes, we first analyze the effect of zero-divisors of integer ring on the iterative belief-propagation (BP) decoding, and show the invalidity of symmetric Gaussian approximation. Then we propose a doubly IRA (D-IRA) ring code structure, consisting of \emph{irregular multiplier distribution} and \emph{irregular node-degree distribution}, that can restore the symmetry and optimize the BP decoding threshold. For point-to-point AWGN channel with $$-PAM inputs, D-IRA ring codes perform as low as 0.29 dB to the capacity limits, outperforming existing bit-interleaved coded-modulation (BICM) and IRA modulation codes over GF($2^m$). We then proceed to design D-IRA ring codes for two important multi-user communication setups, namely compute-forward (CF) and dirty paper coding (DPC), with $2^m$-PAM signaling. With it, a physical-layer network coding scheme yields a gap to the CF limit by 0.24 dB, and a simple linear DPC scheme exhibits a gap to the capacity by 0.91 dB.Comment: 30 pages, 13 figures, submitted to IEEE Trans. Signal Processin