Low error floor LT coding algorithm for unequal error protection

Xin SONG; Shuyan NI; Zhe ZHANG; Yurong LIAO; Tuofeng LEI

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

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Low error floor LT coding algorithm for unequal error protection

Papers | 更新时间：2024-06-06

- Low error floor LT coding algorithm for unequal error protection
- Journal on Communications Vol. 43, Issue 6, Pages: 85-97(2022)
- 作者机构：
  
  1. 航天工程大学研究生院，北京 101416
  2. 航天工程大学电子与光学工程系，北京 101416
  3. 北京遥感信息研究所，北京 100192
- 作者简介：
- 基金信息：
  
  The National Natural Science Foundation of China(61805283);The National High Technology Research and Development Program of China(7026085)
- DOI：10.11959/j.issn.1000-436x.2022123
  CLC： TN911.22
- Online First：2022-06，
  
  Published：25 June 2022
- 稿件说明：
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Xin SONG, Shuyan NI, Zhe ZHANG, et al. Low error floor LT coding algorithm for unequal error protection[J]. Journal on Communications, 2022, 43(6): 85-97.
DOI：

Xin SONG, Shuyan NI, Zhe ZHANG, et al. Low error floor LT coding algorithm for unequal error protection[J]. Journal on Communications, 2022, 43(6): 85-97. DOI： 10.11959/j.issn.1000-436x.2022123.

摘要

目的：无速率LT码旨在为大规模数据分发和可靠广播提供一种理想的传输协议。无速率LT码具有三个优良的特点：（1）链路自适应；（2）码率值可无隙切换；（3）反馈方式较为简单。在无线数据传输中有一类重要的应用场景，即不等差错保护（UEP）数据传输。作为第一种可实现的无速率码，无速率LT码可以便捷地与UEP算法联合设计以实现自适应数据传输。但是，传统的UEP-LT码算法在加性白高斯噪声（AWGN）信道中存在的高误码平台、收敛速度慢等问题。为此，本文设计了一种改进的系统UEP-LT编码方案。

方法：本文考虑面向AWGN信道设计独立的系统UEP-LT码，给出了与该方案相匹配的校验度分布设计方法，并提出了一种具有分段特点的编码方案。该方案中设计了与消息节点一一相连的系统节点，用以提供来自信道的非零对数似然比（LLR）信息。之后是固定长度的校验节点，即固定段，该段校验节点只连接到重要比特（MIB），其目的是使MIB最接近译码成功状态。最后是无速率编码段，该段中的校验节点会选取MIB或者次要比特（LIB）作为邻居节点，并且连接至MIB和LIB的校验节点占比可以灵活调整，从而使MIB始终优先于LIB被成功译码。本文还提出了与上述编码方案相适配的度分布设计模型。该设计模型旨在为MIB提供足够宽的外信息译码通道，为LIB提供一个开放且不太窄的译码通道。在只传输固定段时，待设计的度分布应使得MIB最接近于成功译码状态。在开始传输无速率段时，待设计的度分布应确保MIB尽快地被正确恢复，且在LIB处于临界译码状态时，MIB的译码通道足够宽。在上述约束条件下，所设计的校验度分布可以为MIB提供优于LIB的收敛性能。

结果：以码长K等于6000时为例进行仿真，结果显示：（1）信噪比较低时，本文方案的MIB具有最低的误码平台。例如，当码率倒数R

-1

=2.05时，与参考方案相比，本文方案MIB的误比特率（BER）降低了近一个数量级，最低可达10

-7

量级。此外，本文方案还具有最优的收敛性能，即能够以较小的编码开销进入BER瀑布区。以10

-7

作为BER衡量标准，则本文方案可节省的开销至少为码长K的10%，这体现了本文方案的优势。（2）信噪比较高时，无论是MIB还是LIB，本文方案的BER性能是最优的。对于MIB而言，本文方案的BER始终低于参考方案一个数量级以上。若考虑以10

-6

为BER标准，本文方案可节省的开销约为码长K的7%；不过，此时的信噪比较高，若进一步考虑以10

-7

为BER标准，则本文方案可节省的开销约为码长K的15%。这意味着当信噪比增加时，

本文方案的性能提升幅度要高于参考方案。

结论：本文设计了一种系统不等差错保护LT编码方案，并构建了适用于该方案的校验度分布设计模型，以解决传统UEP-LT算法在AWGN信道中存在的高误码平台的问题。该模型的主要思想是设计固定编码段、无速率编码段以及系统节点段，并将它们按顺序传输，优势在于可为消息节点尽可能早地提供非零的LLR信息，并使MIB和LIB获得不同的且可灵活调整的平均节点度数值。此外，基于外信息传递（EXIT）图法为固定段和无速率段设计了校验度分布，使MIB获得最优的保护性能，同时尽可能地提高LIB的收敛性能。在后续工作中，可以考虑设计能够更加逼近信道容量的校验度分布模型，从而在给定BER标准时实现进一步提升方案编码效率的效果。

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

-6

as 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

-6

is considered as the BER standard

the overhead saved by this scheme is about 7% of the code length K.However

if 10

-7

is 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.

关键词

Keywords

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