Unequal Error Protection Using Partially Regular LDPC Codes

In this paper, we propose a scheme to construct low-density parity-check (LDPC) codes that are suitable for unequal error protection (UEP). We derive density evolution (DE) formulas for the proposed unequal error protecting LDPC ensembles over the binary erasure channel (BEC). Using the DE formulas, we optimize the codes. For the finite-length cases, we compare our codes with some other LDPC codes, the time-sharing method, and a previous work on UEP using LDPC codes. Simulation results indicate the superiority of the proposed design methodology for UEP     

Rateless Codes With Unequal Error Protection Property

In this correspondence, a generalization of rateless codes is proposed. The proposed codes provide unequal error protection (UEP). The asymptotic properties of these codes under the iterative decoding are investigated. Moreover, upper and lower bounds on maximum-likelihood (ML) decoding error probabilities of finite-length LT and Raptor codes for both equal and unequal error protection schemes are derived. Further, our work is verified with simulations. Simulation results indicate that the proposed codes provide desirable UEP. We also note that the UEP property does not impose a considerable drawback on the overall performance of the codes. Moreover, we discuss that the proposed codes can provide unequal recovery time (URT). This means that given a target bit error rate, different parts of information bits can be decoded after receiving different amounts of encoded bits. This implies that the information bits can be recovered in a progressive manner. This URT property may be used for sequential data recovery in video/audio streaming     

Design of Systematic Unequal Error Protection Raptor Codes Over Binary Erasure Channels

The third generation partnership project (3GPP) and digital video broadcasting-handheld standards recommend systematic Raptor codes as application-layer forward error correction for reliable transmission of multimedia data. In all previous studies on systematic Raptor codes, equal error protection for all data was considered. However, in many applications, multimedia data requires unequal error protection (UEP) that provides different levels of protection to different parts of multimedia data. In this paper, we propose a new design method for Raptor codes that provide both UEP and systematic properties over binary erasure channels. Numerical results show that the proposed UEP design is effective for reliable multi-level protection.     

On block-coded modulation using unequal error protection codes overRayleigh-fading channels

This paper considers block-coded 8-phase-shift-keying (PSK) modulations for the unequal error protection (UEP) of information transmitted over Rayleigh-fading channels. Both conventional linear block codes and linear UEP (LUEP) codes are combined with a naturally labeled 8-PSK signal set, using the multilevel construction of Imai and Hirakawa (1977). Computer simulation results are presented showing that, over Rayleigh-fading channels, it is possible to improve the coding gain for the most significant bits with the use of binary LUEP codes as constituent codes, in comparison with using conventional binary linear codes alone     

Modified Plotkin bound for unequal error protection codes

The modified Plotkin bound for unequal error protection (UEP) codes is derived. Based on the separation vector of UEP codes, the authors adopt the average separation of all information digits of a given UEP code, and replacing it with minimum distance in the normal Plotkin bound leads to the new bound, which is valid for both linear and nonlinear UEP codes     

Source-optimized irregular repeat accumulate codes with inherent unequal error protection capabilities and their application to scalable image transmission.

The common practice for achieving unequal error protection (UEP) in scalable multimedia communication systems is to design rate-compatible punctured channel codes before computing the UEP rate assignments. This paper proposes a new approach to designing powerful irregular repeat accumulate (IRA) codes that are optimized for the multimedia source and to exploiting the inherent irregularity in IRA codes for UEP. Using the end-to-end distortion due to the first error bit in channel decoding as the cost function, which is readily given by the operational distortion-rate function of embedded source codes, we incorporate this cost function into the channel code design process via density evolution and obtain IRA codes that minimize the average cost function instead of the usual probability of error. Because the resulting IRA codes have inherent UEP capabilities due to irregularity, the new IRA code design effectively integrates channel code optimization and UEP rate assignments, resulting in source-optimized channel coding or joint source-channel coding. We simulate our source-optimized IRA codes for transporting SPIHT-coded images over a binary symmetric channel with crossover probability p. When p = 0.03 and the channel code length is long (e.g., with one codeword for the whole 512 x 512 image), we are able to operate at only 9.38% away from the channel capacity with code length 132380 bits, achieving the best published results in terms of average peak signal-to-noise ratio (PSNR). Compared to conventional IRA code design (that minimizes the probability of error) with the same code rate, the performance gain in average PSNR from using our proposed source-optimized IRA code design is 0.8759 dB when p = 0.1 and the code length is 12800 bits. As predicted by Shannon's separation principle, we observe that this performance gain diminishes as the code length increases.     

New Table-Switching and Data-Multiplexing Schemes of Rate-Compatible Punctured Convolutional Codes for Unequal Error Protection

In this letter, rate-compatible punctured convolutional (RCPC) codes are further investigated for the application to unequal error protection (UEP). Besides the rate-compatible restriction, we show that puncturing tables should be switched in a special way called soft-switching to guarantee the designed UEP performance. A new data-multiplexing scheme is also proposed for RCPC codes which can achieve similar UEP performance as the conventional scheme but requires no extra zero-padding for frame termination to improve the system throughput.     

One-step completely orthogonalisable UEP codes and their softdecision decoding

The concept of one-step complete orthogonality is extended to linear UEP (unequal error protection) codes and then, two soft-decision decoding algorithms for the one-step completely orthogonalisable UEP codes are presented     

On unequal error protection LDPC codes based on plotkin-type constructions

We introduce a new family of unequal error protection (UEP) codes, based on low-density parity-check (LDPC) component codes and Plotkin-type constructions. The codes are decoded iteratively in multiple stages, and the order of decoding determines the level of error protection. The level of UEP among the code bits is also influenced by the choice of the LDPC component codes and by some new reliability features incorporated into the decoding process. The proposed scheme offers a very good tradeoff between code performance on one side and encoding/decoding and storage complexity on the other side. The novel approach to UEP also allows for finding simple approximations for the achievable degrees of UEP, which can be used to govern practical code design implementations.     

LDPC码的不等误差保护性能研究

非规则LDPC(low-density parity-check)码具有不等误差保护性能,但是随机编码过程却使这一特性很难实现.现将PEG(Progressive Edge-Growth)算法与信道编码的UEP(Unequal Error Protection)性能相结合,用于构造具有不等误差保护性能的校验矩阵H.AWGN和Rayleigh信道的仿真结果表明,采用PEG算法构造的具有UEP性能的非规则LDPC码能够有效提高系统性能.     

On Unequal Error Protection of Convolutional Codes From an Algebraic Perspective

In this paper, convolutional codes are studied for unequal error protection (UEP) from an algebraic theoretical viewpoint. We first show that for every convolutional code there exists at least one optimal generator matrix with respect to UEP. The UEP optimality of convolutional encoders is then combined with several algebraic properties, e.g., systematic, basic, canonical, and minimal, to establish the fundamentals of convolutional codes for UEP. In addition, a generic lower bound on the length of a UEP convolutional code is proposed. Good UEP codes with their lengths equal to the derived lower bound are obtained by computer search.     

移动信道下采用Punctured卷积码实现不等错误保护的研究

本文以移动信道的四状态Markov模型为基础,将Punctured卷积码(Punctured Convolutional Codes;PCC)用于快衰落移动信道下的图像传输系统中, 提出了通过对码率、母码约束长度和交织度这三种不同自由度的调整,实现图像传输的不等错误保护(Unequal Error Protection;UEP)方案.计算机模拟结果表明,所提出的方案具有明显的不等错误保护能力,可以满足在具有不等错误保护要求的移动环境下对传输图像质量的要求.     

On primitive BCH codes with unequal error protection capabilities

Presents a class of binary primitive BCH codes that have unequal-error-protection (UEP) capabilities. The authors use a previous result on the span of their minimum weight vectors to show that binary primitive BCH codes, containing second-order punctured Reed-Muller (RM) codes of the same minimum distance, are binary-cyclic UEP codes. The values of the error correction levels for this class of binary LUEP codes are estimated     

关于等重码不可检错误概率的界

本文研究了二元等重码不可检错误概率(UEP)的界.首先,我们通过研究二元等重码的对偶距离分布及其性质,给出二元等重码UEP的一个新的下界,该下界改进了Fu-Kl  ve-Wei的最新结果;然后,我们指出2003年Fu-Kl  ve-Wei关于二元等重码UEP上界的某些结果有错误,我们随后给出更正后的结果,即二元等重码UEP的平均值和一个上界.     

Expanding window fountain codes for unequal error protection

A novel approach to provide unequal error protection (UEP) using rateless codes over erasure channels, named Expanding Window Fountain (EWF) codes, is developed and discussed. EWF codes use a windowing technique rather than a weighted (non-uniform) selection of input symbols to achieve UEP property. The windowing approach introduces additional parameters in the UEP rateless code design, making it more general and flexible than the weighted approach. Furthermore, the windowing approach provides better performance of UEP scheme, which is confirmed both theoretically and experimentally.     

Serial unequal error-protection codes based on trellis-codedmodulation

Unequal error-protection (UEP) codes that are designed using trellis-coded modulation (TCM) are proposed for use with a single data stream consisting of information with two levels of importance. To achieve UEP, the proposed scheme encodes the data according to the importance of the information by switching between two codes which use different signal constellations. Using simple trellis codes, it is shown that the error rate of the important information is lower than the error rate for an equivalent equal error-protection scheme     

Cyclic unequal error protection codes constructed from cyclic codesof composite length

The unequal error correction capabilities of binary cyclic codes of composite length are investigated. Under certain conditions, direct sums of concatenated codes have unequal error correction capabilities. By a modified Hartmann and Tzeng (1973) algorithm, it is shown that a binary cyclic code of composite length is equivalent to the direct sum of concatenated codes. With this, some binary cyclic unequal error protection (UEP) codes are constructed. Finally, the authors present a class of two-level UEP cyclic direct-sum codes which provide error correction capabilities higher than those guaranteed by the Blokh-Zyablov (1974) constructions     

New results on self-orthogonal unequal error protection codes

A lower bound on the length of binary self-orthogonal unequal error protection (UEP) codes is derived, and two design procedures for constructing optimal self-orthogonal UEP codes are proposed. With this lower bound, known self-orthogonal UEP codes can be evaluated. It is pointed out that, for given values of minimum distance and code rate, the self-orthogonal codes must be relatively long, so optimal self-orthogonal codes are not optimal in general. But self-orthogonal codes can be implemented simply, and they have error-correcting capabilities beyond those guaranteed by their minimum distance. These properties can be viewed as a partial compensation for using self-orthogonal codes     

On decoding unequal error protection product codes

The decoding of unequal error protection product codes, which are a combination of linear unequal error protection (UEP) codes and product codes, is addressed. A nonconstructive proof of the existence of a good error-erasure-decoding algorithm is presented; however, obtaining the decoding procedure is still an open research problem. A particular subclass of UEP product codes is considered, including a decoding algorithm that is an extension of the Blokh-Zyablov decoding algorithm for product codes. For this particular subclass the decoding problem is solved     

Two topics on linear unequal error protection codes: Bounds on their length and cyclic code classes

It is possible for a linear block code to provide more protection for selected positions in the input message words than is guaranteed by the minimum distance of the code. Linear codes having this property are called linear unequal error protection (LUEP) codes. Bounds on the length of a LUEP code that ensures a given unequal error protection are derived. A majority decoding method for certain classes of cyclic binary UEP codes is treated. A list of short (i.e., of length less than 16) binary LUEP codes of optimal (i.e., minimal) length and a list of all cyclic binary UEP codes of length less than 40 are included.