Finite-length rate-compatible LDPC codes: a novel puncturing scheme - [transactions letters]

In this paper, we study rate-compatible puncturing of finite-length low-density parity-check (LDPC) codes. We present a novel rate-compatible puncturing scheme that is easy to implement. Our scheme uses the idea that the degradation in performance is reduced by selecting a puncturing pattern wherein the punctured bits are far apart from each other in the Tanner graph of the code. Although the puncturing scheme presented is tailored to regular codes, it is also directly applicable to irregular parent ensembles. By simulations, the proposed rate-compatible puncturing scheme is shown to be superior to the existing puncturing methods for both regular and irregular LDPC codes over the binary erasure channel (BEC) and the additive white Gaussian noise (AWGN) Channel.     

Construction of non-binary quasi-cyclic LDPC codes by arrays and array dispersions - [transactions papers]

This paper presents two algebraic methods for constructing high performance and efficiently encodable nonbinary quasi-cyclic LDPC codes based on arrays of special circulant permutation matrices and multi-fold array dispersions. Codes constructed based on these methods perform well over the AWGN and other types of channels with iterative decoding based on belief-propagation. Experimental results show that over the AWGN channel, these non-binary quasi-cyclic LDPC codes significantly outperform Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision Berlekamp-Massey algorithm or algebraic soft-decision K?tter- Vardy algorithm. Also presented in this paper is a class of asymptotically optimal LDPC codes for correcting bursts of erasures. Codes constructed also perform well over flat fading channels. Non-binary quasi-cyclic LDPC codes have a great potential to replace Reed-Solomon codes in some applications in communication environments and storage systems for combating mixed types of noises and interferences.     

Polynomial based analog source-channel codes - [transactions papers]

In many communication applications one is interested in transmitting a time-discrete analog-valued (i.e. continuous alphabet) source over a time-discrete analog channel. We study this problem in the case of bandwidth expansion, in the sense that one source sample, X, is transmitted over N-orthogonal channels. An analog source-channel code based on orthogonal polynomials is proposed and analyzed. The code can be generated using a Gram-Schmidt procedure, to fit virtually any source distribution.     

基于EXIT Chart的码率兼容LDPC码的构造

提出了一种码率兼容LDPC(Rate-Compatible LDPC,以下简称RC-LDPC)码的构造方法.通过该方法构造所得到的一个高码率LDPC码的校验矩阵(H矩阵)中所包含的其它低码率LDPC码的度分布对都是通过码率兼容约束EXIT Chart优化得到.仿真结果表明这样优化得到的各个码率的LDPC码性能与采用普通的最优约束EXIT Chart优化所得到的LDPC码的性能接近.     

比特级码率兼容多元LDPC码打孔算法

多元低密度奇偶校验(Non-binary Low-density Parity-check,NB-LDPC)码在中短码情况下性能优于传统二元LDPC码,更接近香农限.针对多元LDPC码码率兼容(Rate-compatible)的问题,提出了一种基于比特级的新型多元打孔算法.首先采用二进制镜像矩阵概念对多元校验矩阵进行映...     

Design of rate-compatible structured LDPC codes for hybrid ARQ applications

In this paper, families of rate-compatible protograph-based LDPC codes that are suitable for incrementalredundancy hybrid ARQ applications are constructed. A systematic technique to construct low-rate base codes from a higher rate code is presented. The base codes are designed to be robust against erasures while having a good performance on error channels. A progressive node puncturing algorithm is devised to construct a family of higher rate codes from the base code. The performance of this puncturing algorithm is compared to other puncturing schemes. Using the techniques in this paper, one can construct a rate-compatible family of codes with rates ranging from 0.1 to 0.9 that are within 1 dB from the channel capacity and have good error floors.     

Near-capacity turbo trellis coded modulation design based on EXIT charts and union bounds - [transactions papers]

Bandwidth efficient parallel-concatenated Turbo Trellis Coded Modulation (TTCM) schemes were designed for communicating over uncorrelated Rayleigh fading channels. A symbol-based union bound was derived for analysing the error floor of the proposed TTCM schemes. A pair of In-phase (I) and Quadrature-phase (Q) interleavers were employed for interleaving the I and Q components of the TTCMcoded symbols, in order to attain an increased diversity gain. The decoding convergence of the IQ-TTCM schemes was analysed using symbol-based EXtrinsic Information Transfer (EXIT) charts. The best TTCM component codes were selected with the aid of both the symbolbased union bound and non-binary EXIT charts, for designing capacity-approaching IQ-TTCM schemes in the context of 8PSK, 16QAM, 32QAM and 64QAM modulation schemes.     

Progressive transmission of images over fading channels using rate-compatible LDPC codes.

In this paper, we propose a combined source/channel coding scheme for transmission of images over fading channels. The proposed scheme employs rate-compatible low-density parity-check codes along with embedded image coders such as JPEG2000 and set partitioning in hierarchical trees (SPIHT). The assignment of channel coding rates to source packets is performed by a fast trellis-based algorithm. We examine the performance of the proposed scheme over correlated and uncorrelated Rayleigh flat-fading channels with and without side information. Simulation results for the expected peak signal-to-noise ratio of reconstructed images, which are within 1 dB of the capacity upper bound over a wide range of channel signal-to-noise ratios, show considerable improvement compared to existing results under similar conditions. We also study the sensitivity of the proposed scheme in the presence of channel estimation error at the transmitter and demonstrate that under most conditions our scheme is more robust compared to existing schemes.     

Transactions papers evaluation and design of irregular LDPC codes using ACE spectrum

The construction of finite-length irregular LDPC codes with low error floors is currently an attractive research problem. In particular, for the binary erasure channel (BEC), the problem is to find the elements of selected irregular LDPC code ensembles with the size of their minimum stopping set being maximized. Due to the lack of analytical solutions to this problem, a simple but powerful heuristic design algorithm, the approximate cycle extrinsic message degree (ACE) constrained design algorithm, has recently been proposed. Building upon the ACE metric associated with a cycle in a code graph, we introduce the ACE spectrum of LDPC codes as a useful tool for evaluation of codes from selected irregular LDPC code ensembles. Using the ACE spectrum, we generalize the ACE constrained design algorithm, making it more flexible and efficient. We justify the ACE spectrum approach through examples and simulation results.     

Non-sequential decoding algorithm for hard iterative turbo product codes - [transactions letters]

In this letter, we propose a new decoding algorithm to improve the bit error rate performance of the hard-input hard-output (HIHO) turbo product codes (TPC) with hard iterative decoding. The proposed algorithm iteratively, but not sequentially, decodes the received TPC blocks based on the reliability of the constituent codes. Simulation results confirm a noticeable coding gain improvement using the proposed decoding process with respect to standard HIHO TPC decoding. An efficient implementation of the new technique offers a negligible additional complexity when the channel-bit error probability is less than 10^?2.     

Further results on noncoherent block-coded MPSK [transactions papers]

A novel noncoherent block coding scheme, called noncoherent block-coded MPSK (NBC-MPSK), was proposed recently. In this paper, we present further research results on NBC-MPSK. We first focus on the rotational invariance (RI) of NBC-MPSK. Based on the RI property of NBC-MPSK with multistage decoding, a noncoherent near-optimal linear complexity multistage decoder for NBC-MPSK is proposed. Then we investigate a tree-search ML decoding algorithm for NBCMPSK. The derived algorithm is shown to have low complexity and excellent error performance. In this paper, we also utilize the idea of the NBC-MPSK to design noncoherent space-time block codes, called noncoherent space-time block-coded MPSK (NSTBC-MPSK). For two transmit antennas, we propose a signal set with set partitioning and derive the minimum noncohent distance of NSTBC-MPSK with this signal set. For the decoding of NSTBC-MPSK, we modify the ML decoding algorithm of NBC-MPSK and propose an iterative hard-decision decoding algorithm. Compared with training codes and unitary space-time modulation, NBC-MPSK and NSTBC-MPSK have larger minimum noncoherent distance and thus better error performance for the noncoherent ML decoder.     

Control of wireless networks with rechargeable batteries [transactions papers]

We consider the problem of cross-layer resource allocation for wireless networks operating with rechargeable batteries under general arrival, channel state and recharge processes. The objective is to maximize total system utility, defined as a function of the long-term rate achieved per link, while satisfying energy and power constraints. A policy with decoupled admission control and power allocation decisions is proposed that achieves asymptotic optimality for sufficiently large battery capacity to maximum transmission power ratio (explicit bounds are provided). We present first a downlink resource allocation scenario; the analysis is then extended to multihop networks. The policy is evaluated via simulations and is seen to perform very well even in the non-asymptotic regime. This policy is particularly suitable for sensor networks, which typically satisfy the asymptotic conditions required by our methodology.     

基于分组排序的码率兼容打孔LDPC码BP译码算法

由于在一定码率范围均能获得良好的误码性能,码率兼容打孔LDPC(rate-compatible punctured LDPC,RCP-LDPC)码成为时变信道下优选编码方案。然而,与非打孔码相比,RCP-LDPC码的BP译码收敛速度太慢。为了提高译码收敛速度,提出一种基于打孔变量点分组优化和串行调度的BP译码算法。根据BP译码消息的可靠度对打孔变量点进行排序和分组,使其在译码时,按可靠度由高到低的次序依次更新各组变量点消息。仿真结果表明,当最大译码迭代次数较低时,本文方法的误码性能优于BP算法和随机分组洗牌BP算法。特别是当打孔比特较多时,性能改善越明显。     

Surrogate-channel design of universal LDPC codes

A universal code is a code that may be used across a number of different channel types or conditions with little degradation relative to a good single-channel code. The explicit design of universal codes, which simultaneously seeks to solve a multitude of optimization problems, is a daunting task. This letter shows that a single channel may be used as a surrogate for an entire set of channels to produce good universal LDPC codes. This result suggests that sometimes a channel for which LDPC code design is simple may be used as a surrogate for a channel for which LDPC code design is complex. We explore here the universality of LDPC codes over the BEC, AWGN, and flat Rayleigh fading channels in terms of decoding threshold performance. Using excess mutual information as a performance metric, we present design results which support the contention that an LDPC code designed for a single channel can be universally good across the three channels.     

Multilevel LDPC codes design for semi-BICM

In this letter, we joined the multilevel coding (MLC) and bit-interleaved coded modulation (BICM) together by using Gray mapping, which is called semi-BICM. To perform well at signal-to-noise ratio (SNR) close to the capacity of the additive white Gaussian noise (AWGN) channel, regular low density parity check (LDPC) codes are discussed with parallel independent decoding (PID). The numerical results show that the proposed structure could achieve both power and bandwidth efficiency.     

Improving the distance properties of turbo codes using a third component code: 3D turbo codes - [transactions letters]

Thanks to the probabilistic message passing performed between its component decoders, a turbo decoder is able to provide strong error correction close to the theoretical limit. However, the minimum Hamming distance (d_min) of a turbo code may not be sufficiently large to ensure large asymptotic gains at very low error rates (the so-called flattening effect). Increasing the d_min of a turbo code may involve using component encoders with a large number of states, devising more sophisticated internal permutations, or increasing the number of component encoders. This paper addresses the latter option and proposes a modified turbo code in which a fraction of the parity bits are encoded by a rate-1, third encoder. The result is a noticeably increased d_min, which improves turbo decoder performance at low error rates. Performance comparisons with turbo codes and serially concatenated convolutional codes are given.     

Some notes on rate-compatible punctured turbo codes (RCPTC) design

In this letter, we propose and compare some design criteria for the search of good rate-compatible systematic turbo codes (RCPTC) families. The considerations presented by Benedetto et al. to find "best" component encoders for turbo-code construction are extended to find good rate-compatible puncturing patterns leading to codes with promising performances.     

Distributed source coding using short to moderate length rate-compatible LDPC codes: the entire Slepian-Wolf rate region

In this paper, we propose a scheme for distributed source coding of correlated sources using a single systematic LDPC code. In particular, since we are interested in wireless sensor network applications, we consider LDPC codes with short to moderate lengths that achieve every arbitrary coding rate on the Slepian-Wolf rate region. We simplify the distributed source coding problem to the rate-compatible LDPC code design with an unequal error protection property. The decoders communicate to each other to exchange information bits prior to decoding. However, thereafter, each performs the decoding independently. Therefore, errors in one decoder do not affect the other one. The simulation results confirm that the gap from the theoretical limit remains almost the same for different rates on the Slepian-Wolf rate region. First, we consider two correlated sources. We show that our proposed scheme improves the performance of distributed source coding of two sources considerably. This benefit is more stressed for application with short to moderate length sequences. Then, we study distributed source coding of three sources. As a special case, we investigate three sources that are pairwise correlated with the same correlation probability. We show that the gap from the theoretical limit is smaller than that of previous work. We also investigate the distributed source coding of correlated sources when there is no prior knowledge of the correlation parameter at the time of code design. We note that although the proposed distributed source coding is well suited for sensor networks (where sequences with less than 10000 bits are used), the method can be generalized to other distributed source coding applications.     

半双工中继信道下联合LDPC码设计

为了提高解码前传半双工中继通信系统的编码增益,提出了一种联合LDPC码编码结构及其度分布优化方法。该结构视信源和中继子码为联合LDPC码的一部分,目的端根据从信源和中继接收的消息进行联合译码,同时获得信源和中继的信息。为了分析联合LDPC码的渐进性能,推导了AWGN信道下联合LDPC码的高斯近似密度进化算法。结合译码收敛条件和度分布约束关系,提出联合LDPC码的度分布优化问题。仿真结果表明：联合LDPC码的渐进性能及误码性能优于BE-LDPC码和独立处理（SP）码。