We propose a quasi-linear trellis-coded modulation (TCM) using nonbinary convolutional codes for quadrature amplitude modulation (QAM). First, we study a matched mapping which is able to reduce the computational complexity of the Euclidean distances between signal points of MQAM. As an example, we search for rate R=1/2 convolutional codes for coded 64QAM by this method. The symbol error rates of the proposed codes are estimated by the distance properties theoretically and they are verified by simulation. In addition, we compare the minimum free Euclidean distances of these new codes with their upper bounds. Finally, the bit error probabilitiy of the proposed coded modulation is compared with uncoded signal constellations and a conventional TCM code proposed by Ungerboeck. The result shows the proposed scheme outperform them on the AWGN channels.

In this short correspondence, (1+uv)-constacyclic codes over the finite non-chain ring R[v]/(v2+v) are investigated, where R=F2+uF2 with u2=0. Some structural properties of this class of constacyclic codes are studied. Further, some optimal binary linear codes are obtained from these constacyclic codes.

In this paper, we propose an efficient method for computing the weight spectrum of LDPC convolutional codes based on circulant matrices of quasi-cyclic codes. In the proposed method, we reduce the memory size of their parity-check matrices with the same distance profile as the original codes, and apply a forward and backward tree search algorithm to the parity-check matrices of reduced memory. We show numerical results of computing the free distance and the low-part weight spectrum of LDPC convolutional codes of memory about 130.

This paper investigates power allocation and outage performance for the MIMO full duplex relaying (MFDR) based on orthogonal space-time block Codes (OSTBC) in cognitive radio systems. OSTBC transmission is used as a simple way to obtain multi-antenna diversity gain. Cognitive MFDR systems offer the advantage not only of increasing spectral efficiency by spectrum sharing but also of extending the coverage through the use of relays. In cognitive MFDR systems, the primary user experiences interference from the secondary source and relay simultaneously due to the full duplexing. What is therefore needed is a way to optimize the transmission powers at the secondary source and relay. Therefore, we propose an optimal power allocation (OPA) scheme based on minimizing the outage probability in cognitive MFDR systems. We then analyze the outage probability of the secondary user in the noise-limited and interference-limited environments under Nakagami-m fading channels. Simulation results show that the proposed schemes achieve performance improvement in terms of outage probability.

The relay channel is the common approach to cooperative communication. Quasi-cyclic low-density parity-check (QC-LDPC) code design for the relay channel is important to cooperative communication. This paper proposes a bilayer QC-LDPC code design scheme for the relay channel. Combined with the bilayer graphical code structure, an improved Chinese remainder theorem (CRT) method, the Biff-CRT method is presented. For the proposed method we introduce a finite field approach. The good performance of the finite field based QC-LDPC code can improve the performance of its corresponding objective QC-LDPC code in the proposed scheme. We construct the FF code and the FA code by the Biff-CRT method. The FF code and the FA code are both named as their two component codes. For the FF code, the two component code are both finite field based QC-LDPC codes. For the FA code, one of the component codes is the finite field based QC-LDPC code and the other is the array code. For the existing CRT method, the shortened array code and the array code are usually used as the component codes to construct the SA code. The exponent matrices of FF code, FA code and SA code are given both for the overall graph and the lower graph. Bit error rate (BER) simulation results indicate that the proposed FF code and FA code are superior to the SA code both at the relay node and the destination node. In addition, the theoretical limit and the BER of the bilayer irregular LDPC code are also given to compare with the BER of the proposed QC-LDPC codes. Moreover, the proposed Biff-CRT method is flexible, easy to implement and effective for constructing the QC-LDPC codes for the relay channel, and it is attractive for being used in the future cooperative communication systems.

In this paper, we propose a new encoding method applicable to any linear codes over arbitrary finite field whose computational complexity is O(δ*n) where δ* and n denote the maximum column weight of a parity check matrix of a code and the code length, respectively. This means that if a code has a parity check matrix with the constant maximum column weight, such as LDPC codes, it can be encoded with O(n) computation. We also clarify the relation between the proposed method and conventional methods, and compare the computational complexity of those methods. Then we show that the proposed encoding method is much more efficient than the conventional ones.

In this paper, we consider decouple-and-forward (DCF) relaying, where the relay encodes and amplifies decoupled data using orthogonal space-time block codes (OSTBCs), to achieve the maximum diversity gain of multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying. Since the channel status of all antennas is generally unknown and time-varying for cooperation in multi-antenna multiple-relay systems, we investigate an opportunistic relaying scheme for DCF relaying to harness distributed antennas and minimize the cooperation overheads by not using the global channel state information (CSI). In addition, for realistic wireless channels which have spatial fading correlation due to closely-spaced antenna configurations and poor scattering environments, we analyze the exact and lower bound on the symbol error probability (SEP) of the opportunistic DCF relaying over spatially correlated MIMO Rayleigh fading channels. Numerical results show that, even in the presence of spatial fading correlation, the proposed opportunistic relaying scheme is efficient and achieves additional performance gain with low overhead.

Majority-logic algorithms are devised for decoding non-binary LDPC codes in order to reduce computational complexity. However, compared with conventional belief propagation algorithms, majority-logic algorithms suffer from severe bit error performance degradation. This paper presents a low-complexity reliability-based algorithm aiming at improving error correcting ability of majority-logic algorithms. Reliability measures for check nodes are novelly introduced to realize mutual update between variable message and check message, and hence more efficient reliability propagation can be achieved, similar to belief-propagation algorithm. Simulation results on NB-LDPC codes with different characteristics demonstrate that our algorithm can reduce the bit error ratio by more than one order of magnitude and the coding gain enhancement over ISRB-MLGD can reach 0.2-2.0dB, compared with both the ISRB-MLGD and IISRB-MLGD algorithms. Moreover, simulations on typical LDPC codes show that the computational complexity of the proposed algorithm is closely equivalent to ISRB-MLGD algorithm, and is less than 10% of Min-max algorithm. As a result, the proposed algorithm achieves a more efficient trade-off between decoding computational complexity and error performance.

In this letter, we present a new scheme to find small fundamental instantons (SFIs) of regular low-density parity-check (LDPC) codes for the linear programming (LP) decoding over the binary symmetric channel (BSC). Based on the fact that each instanton-induced graph (IIG) contains at least one short cycle, we determine potential instantons by constructing possible IIGs which contain short cycles and additional paths connected to the cycles. Then we identify actual instantons from potential ones under the LP decoding. Simulation results on some typical LDPC codes show that our scheme is effective, and more instantons can be obtained by the proposed scheme when compared with the existing instanton search method.

Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring $mathbb{F}_{q}+umathbb{F}_{q}$, where u2=0, q=pn, n a positive integer and p a prime number, are investigated. By the Chinese Remainder Theorem, structural properties and the decomposition of GQC codes are given. For 1-generator GQC codes, minimum generating sets and lower bounds on the minimum distance are given.

In this paper, we clarify the relationship between an initial (final) state in a tail-biting error-trellis and the obtained syndromes. We show that a final state is dependent on the first M syndromes as well, where M is the memory length of the parity-check matrix. Next, we calculate the probability of an initial (final) state conditioned by the syndromes. We also apply this method to concrete examples. It is shown that the initial (final) state in a tail-biting error-trellis is well estimated using these conditional probabilities.

We propose a 2 × 2 space-time block code based on a trace criterion for 64-quadrature amplitude modulation (QAM). We introduce a method to easily calculate the trace norm of a space-time code for 64-QAM, and propose a new space-time code searched by this method. The error rate performance of the proposed code is compared with that of the Alamouti code. By comparison of the theoretical upper bounds, the proposed space-time code is better than the Alamouti code, when the number of receiving antennas is more than one. Moreover, bit error rate performance of the proposed code is compared with maximum likelihood decoding on perfect channel state information Rayleigh fading channels by computer simulations. These results show the proposed code almost outperforms the Alamouti code when the number of receive antennas is more than one, and the increased number of receiving antennas with our code is a decided advantage.

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms compared with the linear block codes. The objective of this letter is to present a new family of ternary cyclic codes with parameters [3m-1,3m-1-2m,4], where m is an odd integer. The proposed cyclic codes are optimal in the sense that their parameters meet the Sphere Packing bound.

Recently, non-binary low-density parity-check (NB-LDPC) codes starts to show their superiority in achieving significant coding gains when moderate codeword lengths are adopted. However, the overwhelming decoding complexity keeps NB-LDPC codes from being widely employed in modern communication devices. This paper proposes a hybrid message-passing decoding algorithm which consumes very low computational complexity. It achieves competitive error performance compared with conventional Min-max algorithm. Simulation result on a (255,174) cyclic code shows that this algorithm obtains at least 0.5dB coding gain over other state-of-the-art low-complexity NB-LDPC decoding algorithms. A partial-parallel NB-LDPC decoder architecture for cyclic NB-LDPC codes is also developed based on this algorithm. Optimization schemes are employed to cut off hard decision symbols in RAMs and also to store only part of the reliability messages. In addition, the variable node units are redesigned especially for the proposed algorithm. Synthesis results demonstrate that about 24.3% gates and 12% memories can be saved over previous works.

Spatially coupled (SC) low-density parity-check (LDPC) codes are defined by bipartite graphs that are obtained by assembling prototype graphs. The combination and connection of prototype graphs are designated by specifying some parameters, and Kudekar et al. showed that BP threshold of the ensemble of SC LDPC codes agrees with MAP threshold of the ensemble of regular LDPC codes when those parameters are grown up so that the code length tends to infinity. When we design SC LDPC codes with practical code length, however, it is not clear how to set those parameters to enhance the performance of SC LDPC codes. In this paper, we provide the result of numerical experiments that suggest the dependence of error performance of SC LDPC codes over BEC on their design parameters.

In this paper, we propose a synthesizable LDPC decoder IP core for the WiMAX system with high parallelism and enhanced error-correcting performance. By taking the advantages of both layered scheduling and fully-parallel architecture, the decoder can fully support multi-mode decoding specified in WiMAX with the parallelism much higher than commonly used partial-parallel layered LDPC decoder architecture. 6-bit quantized messages are split into bit-serial style and 2bit-width serial processing lines work concurrently so that only 3 cycles are required to decode one layer. As a result, 12∼24 cycles are enough to process one iteration for all the code-rates specified in WiMAX. Compared to our previous bit-serial decoder, it doubles the parallelism and solves the message saturation problem of the bit-serial arithmetic, with minor gate count increase. Power synthesis result shows that the proposed decoder achieves 5.83pJ/bit/iteration energy efficiency which is 46.8% improvement compared to state-of-the-art work. Furthermore, an advanced dynamic quantization (ADQ) technique is proposed to enhance the error-correcting performance in layered decoder architecture. With about 2% area overhead, 6-bit ADQ can achieve the error-correcting performance close to 7-bit fixed quantization with improved error floor performance.

LT codes are the first practical rateless codes whose reception overhead totally depends on the degree distribution adopted. The capability of LT codes with a particular degree distribution named robust soliton has been theoretically analyzed; it asymptotically approaches the optimum when the message length approaches infinity. However, real applications making use of LT codes have finite number of input symbols. It is quite important to refine degree distributions because there are distributions whose performance can exceed that of the robust soliton distribution for short message length. In this work, a practical framework that employs evolutionary algorithms is proposed to search for better degree distributions. Our experiments empirically prove that the proposed framework is robust and can customize degree distributions for LT codes with different message length. The decoding error probabilities of the distributions found in the experiments compare well with those of robust soliton distributions. The significant improvement of LT codes with the optimized degree distributions is demonstrated in the paper.

In this paper, we propose the construction of quasi-cyclic (QC) LDPC codes based on the modified progressive edge-growth (PEG) algorithm to achieve the maximum local girth. Although the previously designed QC-LDPC codes based on the PEG algorithm has more flexible code rates than the conventional QC-LDPC code, in the design process, multiple choices of the edges may be chosen. In the proposed algorithm, we aim to maximize the girth property by choosing the suitable edges and thus improve the error correcting performance. Simulation results show that the QC-LDPC codes constructed from the proposed method give higher proportion of high local girths than other methods, particularly, at high code rates. In addition, the proposed codes offer superior bit error rate and block error rate performances to the previous PEG-QC codes over the additive white Gaussian noise (AWGN) channel.

Variable-rate linear network codes are investigated in this paper, which are referred to as linear network codes that can support a demanded range of transmission rates on a common netowrk. A new kind of linear network code, called as strict linear broadcast, is defined. Compared with general linear broadcast, it imposes more rigid constraints on the global encoding kernels, but does not require larger finite field size for construction. Then, an efficient scheme is proposed to construct variable-rate linear broadcasts based on the strict linear broadcast. Instead of construcing a fix-rate linear broadcast for each demanded transmission rate, this scheme implements variable-rate linear broadcasts with a single-rate strict linear broadcast. Every node in the network, including the source node, needs to store only one local encoding kernel. When transmission rate varies, the coding operations performed on every network node remain unchanged. Thus, small storage space and no kernel-swithching operations are required on any network code. Furthermore, by combining the strict linear broadcast with a special source-data packetization strategy, a hierarchical broadcast scheme is proposed. With this scheme, multi-rate service can be provided by a single-rate strict linear broadcast to heterogeneous receivers, even at variable transmission rate. Thus, the variable-rate linear broadcasts constructed in this paper are also applicable to the network with heterogeneous receivers.

NAND Flash memories are widely used as data storages today. The memories are not intrinsically error free because they are affected by several physical disturbances. Technology scaling and introduction of multi-level cell (MLC) has improved data density, but it has made error effect more significant. Error control codes (ECC) are essential to improve reliability of NAND Flash memories. Efficiency of codes depends on error characteristic of systems, and codes are required to be designed to reflect this characteristic. In MLC Flash memories, errors tend to direct values to neighborhood. These errors are a class of M-ary asymmetric symbol error. Some codes which reflect the asymmetric property were proposed. They are designed to correct only 1 level shift errors because almost all of the errors in the memories are in such errors. But technology scaling, increase of program/erase (P/E) cycles, and MLC storing the large number of bits can cause multiple-level shift. This paper proposes single error control codes which can correct an error of more than 1 levels shift. Because the number of levels to be corrected is selectable, we can fit it into noise magnitude. Furthermore, it is possible to add error detecting function for error of the larger shift. Proposed codes are equivalent to a conventional integer codes, which can correct 1 level shift, on a certain parameter. Therefore, the codes are said to be generalization of conventional integer codes. Evaluation results show information lengths to respective check symbol lengths are larger than nonbinary Hamming codes and other M-ary asymmetric symbol error correcting codes.