Systematic Luby Transform Research Articles

Towards systematic Luby transform codes: optimisation design over binary erasure channel

In this Letter, the authors introduce optimisation design technique of systematic Luby transform (SLT) codes over binary erasure channel (BEC). SLT codes are more efficient than Luby transform (LT) codes since the former ones can recover source symbols more quickly. There was some work about designing degree distribution in LT codes and it was shown that erasure probability barely impact performances of LT codes. Using degree distributions designed for LT codes directly in SLT codes does not provide satisfied performances. For the first time, they introduce erasure probability as a parameter to establish a linear programming model in SLT codes. By applying And–or Tree analysis, they propose the asymptotic analysis formulae of SLT codes over BEC. To achieve the goal of recovering source symbols as soon as possible, the authors' objective of optimisation is to minimise overhead. Simulations are offered to validate the performance of their optimisation result. Besides, their degree distribution outperforms other distributions with respect to bit error ratio.

Optimisation design of systematic LT codes over AWGN multiple access channel

Systematic Luby transform (SLT) codes over the additive white Gaussian noise (AWGN) multiple access channels (MACs) are analysed in this study. The authors introduce a novel optimisation model extending from the point-to-point AWGN channels to design the degree distributions over the AWGN MACs, which dramatically improve the bit-error-rate (BER) performance of SLT codes. First, they extend the Gaussian approximation analysis of SLT codes to the AWGN MACs to analyse the asymptotic BER performance where the symmetric condition of log-likelihood ratio message can no longer be assumed. Second, based on the asymptotic BER analysis over the AWGN MACs, they extend the existing optimisation model from the point-to-point AWGN channels to the AWGN MACs. Simulation results show that the degree distributions obtained in this study outperform other common degree distributions (optimised for single-user AWGN channels) over the two-user AWGN MACs.

Systematic Luby transform codes with modified grey‐mapped QAM constellation

Systematic Luby transform (LT) codes with grey-mapped QAM constellations over additive white Gaussian noise (AWGN) channels are investigated. For high-order modulations, it can be learnt that the traditional Gaussian approximation method developed for binary PSK (BPSK) is not accurate any more. To improve BER performance of systematic LT codes with grey-mapped QAM, therefore, presents a novel coded modulation scheme, which only extracts Gaussian alike log-likelihood ratios for decoding, based on the modified QAM constellation. More importantly, the proposed scheme allows to optimise degree distributions for QAM-modulated systematic LT codes as easily as for BPSK. Simulation results show that the degree distribution related to the proposed coded modulation scheme can provide outstanding BER performance for systematic LT codes over the AWGN channel.

Amplify-forward and decode-forward cooperation relying on systematic Luby transform coded Hybrid Automatic-Repeat-reQuest

Systematic Luby transform (SLT) codes constitute rateless codes, which are capable of adaptively adjusting their code rate depending on the channel quality without any explicit channel state information (CSI) at the transmitters. SLTs are also suitable for space time collaboration-aided relay networks. In this study, an iterative decoding-aided SLT scheme is combined with 16 quadrature amplitude modulation (QAM) transmission in a wireless relay-aided network. The bit error ratio (BER) results and extrinsic information transfer (EXIT) charts are provided to evaluate the performance of the proposed scheme. The simulation results show that the proposed scheme using amplify-and-forward (AF) relaying achieves a 2.5 dB gain at a BER of 1025, while the attainable improvement is nearly 6 dB for decode-and-forward (DF) relaying, compared to the non-iterative detection scheme operating without the relay’s assistance. Moreover, the AF relaying-aided SLT coded 16-QAM scheme is more beneficial, when the relay station is close to the source. By contrast, the DF relaying performs best near the mid-point between the source and the destination. Additionally, a modified Hybrid Automatic-Repeat-reQuest (HARQ) protocol using incremental redundancy is applied along with the SLT-coded 16-QAM scheme in order to enhance the achievable throughput and energy efficiency of cooperative networks. This arrangement reduces the total transmit power by about 5%, compared to the classic HARQ scheme.