Binary message passing decoders for low-density parity-check codes are studied by using extrinsic information transfer charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the log-likelihood ratio (L-value) domain. A hard decision results in the Gallager B algorithm and examples show that increasing the channel output alphabet to two bits gains more than 1.0 dB in signal to noise ratio when using optimized codes. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.

Precoding has emerged as a prominent technique to mitigate interbeam interference (IBI) in the forward link of a multibeam high throughput satellite system. In this paper, we consider zero-forcing (ZF) precoding to mitigate IBI. To reduce the channel state information (CSI) feedback from the user terminals, which consequently reduces the latency and signaling overheads, we design a ZF precoder with matrix and vector normalizations using partial CSI and analyze its ergodic SR performance. We consider a practical scenario where the links between the satellite and user terminals are affected by rain fading attenuation and derive an analytical expression, upper and lower bounds, and asymptotic (in terms of transmit power) approximations for the ergodic SR achieved by this ZF precoder. Many important insights are obtained from these results. Also, the robustness of this ZF precoder to CSI estimation errors is numerically analyzed.

In this paper, we present unified performance analysis framework of distributed transmit beamforming (DTB) with residual phase errors which arise from various sources such as imperfect synchronization and channel feedback quantization. More specifically, we derive statistics of the receive signal-to-noise ratio of DTB in Rayleigh and Rician fading channels in the presence of residual phase errors. In the case of residual phase errors caused by channel feedback quantization, we show that the distribution of residual phase errors can be modeled by uniform distribution in Rayleigh fading channels and Gaussian distribution in Rician fading channels. Also, our results reveal that a small number of bits are sufficient for quantized feedback to achieve comparable performance to DTB with perfect channel feedback. Finally, capitalizing on the derived statistics, we present closed-form expressions for the outage probability and the ergodic capacity of DTB with quantized channel feedback.

This paper considers density evolution for low-density parity-check (LDPC) and multi-edge type LDPC (MET-LDPC) codes over the binary input additive white Gaussian noise channel. We first analyze three single-parameter Gaussian approximations for density evolution and discuss their accuracy under several conditions, namely, at low rates, with punctured and degree-one variable nodes. We observe that the assumption of symmetric Gaussian distribution for the density-evolution messages is not accurate in the early decoding iterations, particularly at low rates and with punctured variable nodes. Thus, single-parameter Gaussian approximation methods produce very poor results in these cases. Based on these observations, we then introduce a new density evolution approximation algorithm for LDPC and MET-LDPC codes. Our method is a combination of full density evolution and a single-parameter Gaussian approximation, where we assume a symmetric Gaussian distribution only after density-evolution messages closely follow a symmetric Gaussian distribution. Our method significantly improves the accuracy of the code threshold estimation. Additionally, the proposed method significantly reduces the computational time of evaluating the code threshold compared with full density evolution thereby making it more suitable for code design.

The degree distribution of low-density parity-check (LDPC) codes is optimized for systems that iterate over the receiver frontend, e.g., soft detector, demodulator, equalizer, etc., and the LDPC decoder. The overall extrinsic information transfer (EXIT) function of an iterative LDPC decoder is computed, based on the code's own EXIT chart, under the Gaussian assumption. While the optimization of the variable node distribution is a nonlinear problem, the optimization of the check node distribution is shown to be a linear problem. This fact is exploited to design codes where both the variable and the check node distributions are optimized, resulting in more robust constructions. The technique presented requires only knowledge of the measured EXIT function of the receiver frontend

We consider the design of bilayer-expurgated low density parity-check (BE-LDPC) codes as part of a decode and-forward protocol for use over the full-duplex relay channel. A new ensemble of codes, termed multi-edge-type bilayer expurgated LDPC (MET-BE-LDPC) codes, is introduced where the BE-LDPC code design problem is transformed into the problem of optimizing the multinomials of a multi-edge-type LDPC code. We propose two design strategies for optimizing MET-BE-LDPC codes; the bilayer approach is preferred when the difference in SNR between the source-to-relay and the source to-destination channels is small, while the bilayer approach with intermediate rates is preferred when this difference is large. In both proposed design strategies multi-edge-type density evolution is used for code optimization. The resulting MET-BE-LDPC codes exhibit improved threshold and bit-error-rate performance as compared to previously reported bilayer LDPC codes.