面向不等差错保护的低误码平台LT编码算法

doi:10.11959/j.issn.1000-436x.2022123

Abstract

Abstract:

Objectives:Rateless LT code is designed to provide an ideal transport protocol for large-scale data distribution and reliable broadcasting.The rateless LT code has three excellent characteristics,namely link adaptation,the code rate can be switched seamlessly, and the feedback method is relatively simple. There is an important application scenario in wireless data transmission, namely unequal error protection (UEP) data transmission. As the first achievable rateless code,the rateless LT code can be conveniently used in conjunction with the UEP algorithm to realize adaptive data transmission.However,the conventional UEP-LT code algorithm has problems such as high error floor and poor convergence performance in the additive white Gaussian noise(AWGN)channel.Therefore,an improved systematic UEP-LT coding scheme is designed in this paper.

Methods: This paper considers designing independent systematic UEP-LT codes for AWGN channels.A design method of check distribution matching this scheme is given,and a coding scheme characterized by segmentation is proposed.In this scheme,systematic nodes connected with information nodes one by one are designed to provide non-zero log-likelihood ratio (LLR) information from the channel.After that, there is a fixed number of check nodes,that is,the fixed segment.The check node of this segment is only connected to the important bit(MIB),and its purpose is to make the MIB the closest to the successful decoding state.The final part of the coding scheme is the rateless coding segment. The check nodes in this segment will select MIB or least important bit (LIB) as neighbor nodes,and the proportion of check nodes connected to MIB and LIB can be flexibly adjusted,so that the MIB is always successfully decoded before the LIB.This paper also proposes a degree distribution design model adapted to the above coding scheme.This design model aims to provide a sufficiently wide extrinsic information decoding tunnel for the MIB,and an open and not too narrow decoding tunnel for the LIB.When only the fixed segment is transmitted, the degree distribution to be designed should bring the MIB closest to the successful decoding state.When starting to transmit the rateless segment,the degree distribution to be designed should ensure that the MIB is recovered correctly as soon as possible,and the decoding tunnel of the MIB is wide enough when the LIB is in a critical decoding state. Under the above constraints, the designed check degree distribution can provide the MIB with better convergence performance than the LIB.

Results:Taking the code length K equal to 6000 as an example to simulate,and the results are as follows.(i)When the signal-to-noise ratio(SNR) is low,the MIB in this scheme has the lowest error floor.For example, when the reciprocal code rate ^-1=2.05, compared with the reference scheme, the bit error rate (BER) of the MIB proposed in this paper is reduced by nearly an order of magnitude,and the lowest value can reach the order of 10^-7. In addition,the scheme in this paper also has the optimal convergence performance,that is,it can enter the BER waterfall region with a small coding overhead. Taking 10^-6as the BER standard, the overhead saved by the proposed scheme is at least 10% of the code length K,which reflects the advantages of the proposed scheme.(ii) When the SNR is high,whether it is the MIB or the LIB,the BER performance of the proposed scheme is optimal. For the MIB,the BER of the proposed scheme is always more than an order of magnitude lower than the reference scheme. If 10^-6is considered as the BER standard, the overhead saved by this scheme is about 7% of the code length K.However,if 10^-7is further considered as the BER standard,the overhead saved by this scheme is about 15% of the code length K.This means that when the SNR increases,the performance improvement of the proposed scheme is higher than that of the reference scheme.

Conclusions: In this paper, a systematic unequal error protection LT coding scheme is designed, and a check degree distribution design model suitable for this scheme is constructed to solve the problem of high error floor existing in the conventional UEP-LT algorithm in the AWGN channel.The main idea of this scheme is to design fixed coding segments,rateless coding segments and systematic node segments and transmit them in sequence.The advantage of this scheme is that it can provide non-zero LLR information as early as possible for information nodes, and make the MIB and the LIB obtain different and flexibly adjustable average degrees.In addition,based on the extrinsic information transfer(EXIT)chart,the check degree distribution is designed for the fixed segment and the rateless segment,so that the MIB can obtain the optimal protection performance,and the convergence performance of the LIB can be improved as much as possible. In the follow-up work, it can be considered to design a check degree distribution model that can more closely approximate the channel capacity, so as to further improve the coding efficiency of the scheme when the BER standard is given.

Key words: channel coding, rateless code, unequal error protection, convergence, bit error rate

CLC Number:

TN911.22

Xin SONG, Shuyan NI, Zhe ZHANG, Yurong LIAO, Tuofeng LEI. Low error floor LT coding algorithm for unequal error protection[J]. Journal on Communications, 2022, 43(6): 85-97.

Figures/Tables 13

信噪比/dB	$σ_{n}$	$C_{σ_{n}}$
-2.82	0.978 3	0.500 0
-1.53	0.843 3	0.600 5
-0.27	0.729 4	0.700 4
1.07	0.625 2	0.799 4
2.73	0.516 4	0.900 0

期望参数	UEP参数	固定段和无速率段的校验度分布	度分布模型目标函数值
$\begin{array}{l} σ_{n} = 0.843 3 ， \\ α_{G} = 7.3 ， \\ α_{F} = 13.5 \end{array}$	Γ_M =0.25,Γ_L=0.75	$\begin{array}{l} Ω_{G} (x) = 0.238 8 x^{7} + 0.707 2 x^{8} + 0.054 0 x^{66} \\ Ω_{F} (x) = 0.850 8 x^{7} + 0.035 4 x^{14} + 0.019 2 x^{15} + 0.094 6 x^{66} \end{array}$	η=0.020 19
	Γ _M =0.3,Γ_L=0.7	$\begin{array}{l} Ω_{G} (x) = 0.238 8 x^{7} + 0.707 2 x^{8} + 0.054 0 x^{66} \\ Ω_{F} (x) = 0.010 1 x^{6} + 0.846 1 x^{7} + 0.032 0 x^{13} + 0.028 9 x^{14} + 0.082 9 x^{66} \end{array}$	η=0.021 43
	Γ_M =0.35,Γ_L=0.65	$\begin{array}{l} Ω_{G} (x) = 0.238 8 x^{7} + 0.707 2 x^{8} + 0.054 0 x^{66} \\ Ω_{F} (x) = 0.854 2 x^{7} + 0.026 0 x^{8} + 0.049 1 x^{14} + 0.070 7 x^{66} \end{array}$	η=0.022 47
$\begin{array}{l} σ_{n} = 0.729 4 ， \\ α_{G} = 5.3, \\ α_{F} = 12.5 \end{array}$	Γ_M =0.25,Γ_L=0.75	$\begin{array}{l} Ω_{G} (x) = 0.736 8 x^{10} + 0.225 7 x^{11} + 0.037 5 x^{66} \\ Ω_{F} (x) = 0.376 7 x^{9} + 0.485 1 x^{10} + 0.138 2 x^{66} \end{array}$	η=0.027 17
	Γ _M =0.3,Γ_L=0.7	$\begin{array}{l} Ω_{G} (x) = 0.736 8 x^{10} + 0.225 7 x^{11} + 0.037 5 x^{66} \\ Ω_{F} (x) = 0.034 9 x^{8} + 0.837 6 x^{9} + 0.127 5 x^{66} \end{array}$	η=0.028 71
	Γ_M =0.35,Γ_L=0.65	$\begin{array}{l} Ω_{G} (x) = 0.736 8 x^{10} + 0.225 7 x^{11} + 0.037 5 x^{66} \\ Ω_{F} (x) = 0.708 2 x^{9} + 0.182 2 x^{10} + 0.109 6 x^{66} \end{array}$	η=0.030 85
$\begin{array}{l} σ_{n} = 0.625 2 ， \\ α_{G} = 4.3, \\ α_{F} = 11.5 \end{array}$	Γ_M =0.25,Γ_L=0.75	$\begin{array}{l} Ω_{G} (x) = 0.704 1 x^{16} + 0.277 4 x^{17} + 0.018 5 x^{66} \\ Ω_{F} (x) = 0.213 2 x^{12} + 0.566 4 x^{13} + 0.220 4 x^{66} \end{array}$	η=0.034 87
	Γ _M =0.3,Γ_L=0.7	$\begin{array}{l} Ω_{G} (x) = 0.704 1 x^{16} + 0.277 4 x^{17} + 0.018 5 x^{66} \\ Ω_{F} (x) = 0.537 4 x^{13} + 0.270 2 x^{14} + 0.192 4 x^{66} \end{array}$	η=0.036 17
	Γ_M =0.35,Γ_L=0.65	$\begin{array}{l} Ω_{G} (x) = 0.704 1 x^{16} + 0.277 4 x^{17} + 0.018 5 x^{66} \\ Ω_{F} (x) = 0.194 8 x^{12} + 0.629 6 x^{13} + 0.175 7 x^{66} \end{array}$	η=0.039 90

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