Optimum Design And Analysis Of Fountain Codes

In wireless communication,due to the propagation of electromagnetic waves in free space and the uncertainty of transmission path,it is more easily affected by noise and interference for information.So,it is very important to use error control technology to ensure the reliable transmission of information.Fountain codes as a class of new forward error correction coding scheme,have unique advantages such as rateless,adaptive channel state changes and no need of feedback,which provide a new solution for many application scenarios.To satisfy the requirements of high reliability and low delay in 5th-Generation,fountain codes are adopted as a kind of forward error correction coding scheme.It is important for achieving more reliable information transmission and improving system performance by designing fountain coding scheme with perfect performance for small message length and studying the fountain codes performance for SNR mismatch over wireless channel.The main contributions of this paper are as follows:1.Short block codes have low decoding latency compared with long block codes,which is important in some application scenarios for low latency.Raptor codes are a class of fountain codes which can get capacity achieving performance over various channels.Traditional Raptor codes can obtain perfect performance for large message length.However,small message length can cause significant performance deterioration.In order to improve the performance of Raptor codes for small message length,we modify the design of traditional Raptor codes.The proposed Raptor codes are obtained by pre-coding the information symbols by low rate low-density parity-check(LDPC)codes and utilizing a low constant average degree distribution with high intermediate symbol recovery rate(ISRR).Simulation results demonstrate that,although traditional Raptor codes can get good asymptotical performance,our proposed Raptor codes not only outperform traditional Raptor codes for small message length over binary erasure channels(BECs)and binary input additive white Gaussian noise(BI-AWGN)channels,but also have lower complexities.2.In a binary input additive white Gaussian noise(BIAWGN)channel,belief propagation(BP)decoding for fountain codes requires the knowledge of the signalto-noise ratio(SNR)at the receiver to achieve its optimal performance.However,it is difficult to accurately estimate the channel state information in practice.An erroneous estimation of the SNR at the decoder is referred to as SNR mismatch.SNR mismatch can significantly degrade the BP decoding performance of LT codes.When SNR mismatch appeared,traditional Gaussian approximation and extrinsic information transfer chart are no longer applied.Proposed semi-Gaussian approximation method to predict and compare the asymptotic performance of LT codes under SNR mismatch.Asymptotic analysis and simulation results show that LT codes are more sensitive to SNR over-estimation and underestimation for small and large SNR offset,respectively.Underestimation will lead to serious performance deterioration for large SNR offset.