We investigate the end-to-end outage probability over a multi-source multi-relay network assuming that all the wireless links are suffering from independent block fading variations. The overall transmission is divided into two tandem hops. The first hop represents the transmission between sources and relays, while the relays transmit to the destinations in the second hop. We consider specifically a two-source two-relay single-destination network. Based on the decoding process at the relays, the data recovery at the relays can be classified into three cases based on achievable bounded rate regions. The first case where both relays cannot recover both users' data can be characterized as chief executive officer problem at the second hop. For the second case, the relays recover the data of both users, and the outage probability of the second hop can be computed by exploiting maximum ratio transmission. Finally, for the third case, only one of the users' data is recovered by one of the relays, and the outage probability of the second hop can be calculated by using the theorem of source coding with helper. Numerical results closely follow the theoretical analysis and confirm the improved performance of the multiple-antenna relaying over the single-antenna relaying.

We design rateless codes for correlated multi-source relay networks over packet erasure channels. In particular, we optimize relay combining process of distributed Luby transform (DLT) codes for a multi-source single-relay network where information data is correlated among the sources. Density evolution is used to characterize the asymptotic performance in terms of unrecovered information symbols termed as erasure rate. By exploiting the decoding graph, we derive the closed form expressions for asymptotic performance of DLT codes in a network where correlated sources transmit to a single destination via a relay. Consequently, a design framework is developed to optimize the degree distributions in terms of overhead. It is shown that the proposed DLT codes significantly outperform existing DLT coding schemes in terms of erasure and success rates. Numerical examples are provided to verify the asymptotic analysis. Numerical results also confirm the performance gain of the proposed DLT code as compared to its uncorrelated counterparts in the finite-length regime.

We investigate the erasure floor performance of distributed Luby transform (DLT) codes for transmission within a multi-source, single-relay, and single-destination erasure-link network. In general, Luby transform (LT) codes exhibit a high erasure floor due to poor minimum-distance properties, which can be improved by maximizing the minimum variable-node degree. The same behavior is observed for DLT codes, and therefore a new combining scheme at the relay is proposed to maximize the minimum variable-node degree in the decoding graph. Furthermore, the encoding process at the sources and the combining scheme at the relay are coordinated to improve the transmission overhead. To characterize the asymptotic performance of the proposed DLT codes, we derive closed-form density-evolution expressions, considering both lossless and lossy source-relay channels, respectively. To support the asymptotic analysis, we evaluate the performance of the proposed DLT codes by numerical examples and demonstrate that the numerical results correspond closely to the analysis. Significant improvements in both the erasure floor and transmission overhead are obtained for the proposed DLT codes, as compared to conventional DLT codes.

Luby transform (LT) codes are a class of rateless codes that automatically adapt their rate to the quality of the communication channel. In the original LT codes, fixed check-node degree distributions are used to combine variable nodes uniformly at random to extend the code graph and produce code bits. Here we propose a different approach: we design a sequence of rate-compatible degree distributions, and develop an algorithm that produces code bits in a manner such that the resulting degree distributions follow the designed sequence. Using this new design framework, we develop low-complexity LT codes suitable for time-varying noisy channels. Performance and complexity of the proposed LT codes are measured in terms of bit error rate and average number of edges per information and coded bit, respectively. Numerical examples illustrate the resulting trade-off between performance and complexity of the designed LT codes.

We focus on the design of distributed Luby transform (DLT) codes for erasure networks with multiple sources and multiple relays, communicating to a single destination. The erasure floor performance of DLT codes improves with the maximum degree of the relay-degree distribution. However, for conventional DLT codes, the maximum degree is upper bounded by the number of sources. An additional constraint is that the sources are required to have the same information block length. We introduce a D-bit buffer for each source-relay link, which allows the relay to select multiple encoded bits from the same source for the relay-encoding process; thus, the number of sources no longer limits the maximum degree at the relay. Furthermore, the introduction of buffers facilitates the use of different information block sizes across sources. Based on density evolution, we develop an asymptotic analytical framework for optimization of the relay-degree distribution. We further integrate techniques for unequal erasure protection into the optimization framework. The proposed codes are considered for both lossless and lossy source-relay links. Numerical examples show that there is no loss in erasure rate performance for transmission over lossy source-relay links, as compared with lossless links. Additional delays, however, may occur. The design framework and our contributions are demonstrated by a number of illustrative examples, showing the improvements obtained by the proposed buffer-based DLT codes.

We propose an adaptive decoding scheme for Luby Transform (LT) codes over noisy channels which exhibits lower complexity as compared to the conventional LT decoder. The corresponding modified degree distributions have been derived for the low-complexity LT decoder. The complexity and performance comparison demonstrate that the decoding complexity can be reduced with negligible degradation in bit error rate performance.

We investigate the design and performance of spatially-coupled rateless codes. A modified encoding process is introduced for spatially-coupled Luby Transform (SCLT) codes which leads to an almost regular variable-node degree distribution at the encoding graph. The proposed SCLT codes outperform its counterparts significantly over binary erasure channels, particularly in the erasure floor region. To further improve the erasure floor performance, the approach of spatial coupling is then extended to Raptor codes by concatenating a high-rate pre-coder to the SCLT codes. It is shown that the spatial coupling improves the convergence threshold of Raptor codes. Different ensembles of spatially-coupled Raptor codes are constructed depending on whether pre-coders and/or LT codes are spatially-coupled. The performance of different ensembles of spatially-coupled Raptor codes is then evaluated and compared based on density evolution, leading to an improved spatially-coupled Raptor code in terms of convergence threshold and lower complexity.

We investigate the error floor performance of Luby Transform (LT) codes over the additive white Gaussian noise channel. We first derive a lower bound on the bit error rate for an LT code, which we subsequently use to show that the corresponding error floor is predominantly caused by low-degree variable nodes. Based on this observation, we propose a modified encoding scheme for LT codes that provides a lower error floor with no increase in encoding and decoding complexities. The convergence behavior of the proposed scheme is analyzed using extrinsic information transfer charts, and shown to be similar to the original LT code. Numerical examples demonstrate the improvements of the modified LT code as a stand-alone code and as a component code of a Raptor code.

We consider serial concatenation of a Luby Transform (LT) code with a differential quadrature phase-shift-keying (DQPSK) modulator for transmission over an additive white Gaussian noise (AWGN) Channel. Assuming a target average rate for the operation of the rateless LT DQPSK scheme, the degree distribution of the LT code is optimized in terms of convergence threshold using extrinsic information transfer (EXIT) charts. From the EXIT chart analysis, we show that the proposed LT DQPSK scheme has a similar convergence performance, but lower complexity, as compared to a Raptor code with differential modulation, and a LDPC code optimized for DQPSK. The EXIT chart analysis framework is also applied to evaluate the throughput performance for the three schemes in terms of the average code rate as a function of the signal-to-noise ratio. The comparison demonstrates that the proposed structure is well-suited for adaptive-rate transmission over a wide range of rates.