Path-compatible pruned convolutional (PCPC) codes

Path pruning, a new coding concept to achieve free distance enlargement for convolutional codes, is proposed. Through path pruning, every convolutional code can be used for unequal error protection (UEP), no matter whether it is originally a UEP code. To avoid undesired path discontinuity and reduce possible path distance loss, a cascaded implementation together with a path-compatible criterion is proposed, under which path-compatible pruned convolutional (PCPC) codes are constructed. Necessary and sufficient conditions are also derived for a subclass of PCPC codes whose decoding can be done by a single decoder for the parent code. Finally, some PCPC codes with good UEP capabilities found by computer search are given     

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     

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     

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.     

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.     

QPSK block-modulation codes for unequal error protection

Unequal error protection (UEP) codes find applications in broadcast channels, as well as in other digital communication systems, where messages have different degrees of importance. Binary linear UEP (LUEP) codes combined with a Gray mapped QPSK signal set are used to obtain new efficient QPSK block-modulation codes for unequal error protection. Several examples of QPSK modulation codes that have the same minimum squared Euclidean distance as the best QPSK modulation codes, of the same rate and length, are given. In the new constructions of QPSK block-modulation codes, even-length binary LUEP codes are used. Good even-length binary LUEP codes are obtained when shorter binary linear codes are combined using either the well-known |u¯|u¯+v¯|-construction or the so-called construction X. Both constructions have the advantage of resulting in optimal or near-optimal binary LUEP codes of short to moderate lengths, using very simple linear codes, and may be used as constituent codes in the new constructions. LUEP codes lend themselves quite naturally to multistage decoding up to their minimum distance, using the decoding of component subcodes. A new suboptimal two-stage soft-decision decoding of LUEP codes is presented and its application to QPSK block-modulation codes for UEP illustrated     

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     

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.     

非均匀纠错Turbo码在图像无线传输中的应用

本文根据信源泉编码流中信息比特重要性不均匀特点，采用变码率信道编码、分集发送、分集接收、非均匀迭代译码策略，对传统的Turbo码编译码器结构做了改进，给出了实验结果。通过比较发现，改进算法降低了时延，提高了Turbo码译码算法的纠错性能，特别适合于多媒体非实时无线传输业务。     

Turbo codes-based image transmission for channels with multiple types of distortion

Product codes are generally used for progressive image transmission when random errors and packet loss (or burst errors) co-exist. However, the optimal rate allocation considering both component codes gives rise to high-optimization complexity. In addition, the decoding performance may be degraded quickly when the channel varies beyond the design point. In this paper, we propose a new unequal error protection (UEP) scheme for progressive image transmission by using rate-compatible punctured Turbo codes (RCPT) and cyclic redundancy check (CRC) codes only. By sophisticatedly interleaving each coded frame, the packet loss can be converted into randomly punctured bits in a Turbo code. Therefore, error control in noisy channels with different types of errors is equivalent to dealing with random bit errors only, with reduced turbo code rates. A genetic algorithm-based method is presented to further reduce the optimization complexity. This proposed method not only gives a better performance than product codes in given channel conditions but is also more robust to the channel variation. Finally, to break down the error floor of turbo decoding, we further extend the above RCPT/CRC protection to a product code scheme by adding a Reed-Solomon (RS) code across the frames. The associated rate allocation is discussed and further improvement is demonstrated.     

Performance Bounds for Unequal Error Protecting Turbo Codes

In many communications systems, data can be divided into different importance levels. For these systems, unequal error protection (UEP) techniques are used to guarantee lower BER for the more important classes. In particular, if the precise characteristics of the channel are not known, UEP can be used to recover the more important classes even in poor receiving conditions. In this paper, we derive bounds on the performance of unequal error protecting turbo codes. These bounds serve as an important tool in predicting the performance of these codes. In order to derive the bounds, we introduce the notion of UEPuniform interleaver which is a random interleaver that does not change the order of classes in the turbo code frame. We also present a method to derive the weight enumerating function for UEP turbo codes.     

Multilevel coded modulation for unequal error protection andmultistage decoding. II. Asymmetric constellations

In this paper, multilevel coded asymmetric modulation with multistage decoding and unequal error protection (UEP) is discussed. These results further emphasize the fact that unconventional signal set partitionings are more promising than traditional (Ungerboeck-type) partitionings, to achieve UEP capabilities with multilevel coding and multistage decoding. Three types of unconventional partitionings are analyzed for asymmetric 8-PSK and 16-QAM constellations over the additive white Gaussian noise channel to introduce design guidelines. Generalizations to other PSK and QAM type constellations follow the same lines. Upper bounds on the bit-error probability based on union bound arguments are first derived. In some cases, these bounds become loose due to the large overlappings of decision regions associated with asymmetric constellations and unconventional partitionings. To overcome this problem, simpler and tighter approximated bounds are derived. Based on these bounds, it is shown that additional refinements can be achieved in the construction of multilevel UEP codes, by introducing asymmetries in PSK and QAM signal constellations     

Multilevel coded modulation for unequal error protection andmultistage decoding .I. Symmetric constellations

In this paper, theoretical upper bounds and computer simulation results on the error performance of multilevel block coded modulations for unequal error protection (UEP) and multistage decoding are presented. It is shown that nonstandard signal set partitionings and multistage decoding provide excellent UEP capabilities beyond those achievable with conventional coded modulation. The coding scheme is designed in such a way that the most important information bits have a lower error rate than other information bits. The large effective error coefficients, normally associated with standard mapping by set partitioning, are reduced by considering nonstandard partitionings of the underlying signal set. The bits-to-signal mappings induced by these partitionings allow the use of soft-decision decoding of binary block codes. Moreover, parallel operation of some of the staged decoders is possible, to achieve high data rate transmission, so that there is no error propagation between these decoders. Hybrid partitionings are also considered that trade off increased intraset distances in the last partition levels with larger effective error coefficients in the middle partition levels. The error performance of specific examples of multilevel codes over 8-PSK and 64-QAM signal sets are simulated and compared with theoretical upper bounds on the error performance     

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     

非规则准循环OOC-LDPC码在图像传输中的应用

介绍了非规则准循环OOC-LDPC码的构造,并将其应用到图像传输中,根据SPIHT压缩图像编码后的码流具有渐进性的特点,进行不等差错保护。在AWGN信道下仿真结果表明,非规则准循环OOC-LDPC码具有很好的纠错能力和不等差错保护特性。     

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     

New results on unequal error protection using LDPC codes

In this letter, we propose a new scheme to construct low-density parity-check (LDPC) codes that are suitable for unequal error protection (UEP). We derive UEP density evolution (UDE) formulas for the proposed ensemble over the binary erasure channel (BEC). Using the UDE formulas, high performance UEP codes can be found. Simulation results depict an improvement in the bit error rate of more important bits in comparison with previous results on UEP-LDPC codes.     

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.     

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.     

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.