In this paper, we study systematic Luby Transform (SLT) codes over binary input additive white Gaussian noise (BIAWGN) channels. To improve the bit-error-rate (BER) performance of SLT codes in the BIAWGN channel, this paper presents a novel optimization design of degree distributions. First, we apply the Gaussian approximation (GA) to analyze the asymptotic BER performance of SLT codes and calculate overhead thresholds for successful decoding. Second, we derive an approximate closed-form expression for lower bound on BER by applying the GA and further simplify the expression in low and high signal-to-noise ratio regimes respectively. Third, we adopt the conventional linear programming (CLP) constrained by the GA to optimize the degree distribution of SLT codes. The objective of CLP is to minimize the average degree of the degree distribution that may result in bad error floor. To improve the error floor caused by CLP, we put forth a novel optimization model constrained by the lower bound on BER, and using the model we can design the degree distribution more flexibly with any desired BER. Simulation results show that the proposed degree distribution can provide better BER performance of SLT codes over the BIAWGN channel.
Two-way relay networks in additive white Gaussian noise channels are studied. A novel scheme based on the product relay is proposed and the whole block diagram is obtained. Furthermore, the presented analysis shows that the proposed scheme outperforms the traditional amplifyand-forward relay. Two-way relay networks based on the product relay provide a better bit error ratio performance in high signal-tonoise ratio regions, which is consistent with the simulation result.Introduction: To overcome signal fading problems in wireless channels, the relay technique was introduced. It can not only increase efficient communication ranges but also can provide better reliability. A one-way relay system [1] that works in half-duplex mode brings about loss of spectral efficiency. However, the full-duplex relay system [2], which can make up the loss, still causes self-interference. To obtain a trade-off, Rankov proposed a two-way relay scheme in [3,4]. Relaying cooperation includes amplify-and-forward (AF), detect-and-forward (DF) and so on. The AF scheme is easily accomplished and has low complexities because there is no decoding at the relay. However, the noise is also amplified, which might cause severe error expansion. On the contrary, signals are decoded first at the relay in the DF scheme, but which obviously needs more complex operations.
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