Irregular Vector Turbo Codes with Low Complexity

The term Block Turbo Code typically refers to the iterative decoding of a serially concatenated two-dimensional systematic block code. This paper introduces a Vector Turbo Code that is irregular but with code rates comparable to those of a Block Turbo Code (BTC) when the Bahl Cocke Jelinek Raviv (BCJR) algorithm is used. In Block Turbo Codes, the horizontal (or vertical) blocks are encoded first and the vertical (or horizontal) blocks second. The irregular Vector Turbo Code (iVTC) uses information bits that participate in varying numbers of trellis sections, which are organized into blocks that are encoded horizontally (or vertical) without vertical (or horizontal) encoding. The decoding requires only one soft-input soft-output (SISO) decoder. In general, a reduction in complexity, in comparison to a Block Turbo Code was achieved for the same very low probability of bit error (10−5 ). Performance in the AWGN channel shows that iVTC is capable of achieving a significant coding gain of 1.28 dB for a 64QAM modulation scheme, at a bit error rate (BER) of 10−5over its corresponding Block Turbo Code. Simulation results also show that some of these codes perform within 0.49 dB of capacity for binary transmission over an AWGN channel.

Design of Nonbinary LDPC Cycle Codes with Large Girth from Circulants and Finite Fields

In this paper, we study a class of nonbinary LDPC (NBLDPC) codes whose parity-check matrices have column weight 2, called NBLDPC cycle codes. We propose a design framework of 2 , ρ -regular binary quasi-cyclic (QC) LDPC codes and then construct NBLDPC cycle codes of large girth based on circulants and finite fields by randomly choosing the nonzero field elements in their parity-check matrices. For enlarging the girth values, our approach is twofold. First, we give an exhaustive search of circulants with column/row weight ρ and design a masking matrix with good cycle distribution based on the edge-node relation in undirected graphs. Second, according to the designed masking matrix, we construct the exponent matrix based on finite fields. The iterative decoding performances of the constructed codes on the additive white Gaussian noise (AWGN) channel are finally provided.

OFDM impairment mitigation techniques

In this thesis, we propose novel techniques to improve the performance of OFDM systems. We present a simple adaptive modulation technique to mitigate the nonlinear distortion effects of OFDM signals. Based on an estimation of the nonlinearity of the HPA/channel, for each OFDM symbol, a calculation is done at the transmitter side which identifies the subcarries with high distortion and correpsondingly reduces the modulation level on those subcarriers. This procedure is repeated until the nonlinear distortion is below a predetermined threshold. This technique is shown to improve the BER performance considerably while the reduction in data rate is small. The data rate is reduced by 4% for a system with 64 subcarriers and 16 QAM as primary and 4 QAM as secondary modulation levels. The tone reservation technique used in conventional PAPR reduction is suitably modified to provide a simple solution to reduce the average power requirement in intenstiy modulated optical OFDM systems. With two reserved subcarriers the reduction in power is approximately 2 dB for 16 QAM modulation with 64 subcarriers and 1dB for 256 subcarriers. We also describe techniques to improve the BER performance of grouped linear constellation precoding (GLCP) OFDM which is used to achieve frequency diversity. We present an Adaptive Weighting (AW) technique in which during MLSE, the distance of the possible constellation points from the received symbols are weighted according to the SNR of each subcarrier before the sequence with the minimum distance is chosen. We also analyze a sub optimum iterative decoding algorithm which improves the performance of an initial zero forcing detection iteratively on a symbol by symbol basis. Both techniques improve the performance of the GLCP-OFDM system considerably at the expense of increased complexity.

OFDM impairment mitigation techniques

In this thesis, we propose novel techniques to improve the performance of OFDM systems. We present a simple adaptive modulation technique to mitigate the nonlinear distortion effects of OFDM signals. Based on an estimation of the nonlinearity of the HPA/channel, for each OFDM symbol, a calculation is done at the transmitter side which identifies the subcarries with high distortion and correpsondingly reduces the modulation level on those subcarriers. This procedure is repeated until the nonlinear distortion is below a predetermined threshold. This technique is shown to improve the BER performance considerably while the reduction in data rate is small. The data rate is reduced by 4% for a system with 64 subcarriers and 16 QAM as primary and 4 QAM as secondary modulation levels. The tone reservation technique used in conventional PAPR reduction is suitably modified to provide a simple solution to reduce the average power requirement in intenstiy modulated optical OFDM systems. With two reserved subcarriers the reduction in power is approximately 2 dB for 16 QAM modulation with 64 subcarriers and 1dB for 256 subcarriers. We also describe techniques to improve the BER performance of grouped linear constellation precoding (GLCP) OFDM which is used to achieve frequency diversity. We present an Adaptive Weighting (AW) technique in which during MLSE, the distance of the possible constellation points from the received symbols are weighted according to the SNR of each subcarrier before the sequence with the minimum distance is chosen. We also analyze a sub optimum iterative decoding algorithm which improves the performance of an initial zero forcing detection iteratively on a symbol by symbol basis. Both techniques improve the performance of the GLCP-OFDM system considerably at the expense of increased complexity.

Turbo codes for multi-hop wireless sensor networks with decode-and-forward mechanism

Wireless channels are prone to many impairments, such as noise and fading. Weak channels between the nodes in the wireless sensor network (WSN) can cause reception of erroneous packets. Retransmission mechanisms are mainly mused to tackle the problem of erroneous reception in WSN communication protocols. Weak channels can cause high number of retransmissions in order to deliver a packet correctly, which will consume high energy of both the transmitting and the receiving nodes. Error correcting codes (ECCs) can be used to reduce number of retransmissions, but most ECCs have complex decoding algorithms, which leads to high processing energy consumption at the receiving nodes in the WSN. In this paper, we present a low power consumption decode-and-forward approach for the multi-hop WSNs; a serial concatenation convolutional codes (SCCC) encoder is implemented at the source node while the complex iterative decoding algorithm is shifted to the sink (base station). The intermediate nodes run a Viterbi decoding algorithm to decode only the inner code of the SCCC encoder. We investigate the effect of changing constraint length of both the inner and the outer codes and the effect of changing encoding block size. We show that most packets can be decoded at the base station at low signal-to-noise ratio (SNR) channels with the penalty of small energy loss in decoding the packet at the nodes in the network.

Turbo codes for multi-hop wireless sensor networks with decode-and-forward mechanism

Wireless channels are prone to many impairments, such as noise and fading. Weak channels between the nodes in the wireless sensor network (WSN) can cause reception of erroneous packets. Retransmission mechanisms are mainly mused to tackle the problem of erroneous reception in WSN communication protocols. Weak channels can cause high number of retransmissions in order to deliver a packet correctly, which will consume high energy of both the transmitting and the receiving nodes. Error correcting codes (ECCs) can be used to reduce number of retransmissions, but most ECCs have complex decoding algorithms, which leads to high processing energy consumption at the receiving nodes in the WSN. In this paper, we present a low power consumption decode-and-forward approach for the multi-hop WSNs; a serial concatenation convolutional codes (SCCC) encoder is implemented at the source node while the complex iterative decoding algorithm is shifted to the sink (base station). The intermediate nodes run a Viterbi decoding algorithm to decode only the inner code of the SCCC encoder. We investigate the effect of changing constraint length of both the inner and the outer codes and the effect of changing encoding block size. We show that most packets can be decoded at the base station at low signal-to-noise ratio (SNR) channels with the penalty of small energy loss in decoding the packet at the nodes in the network.

A Survey on Old and New Approximations to the Function ϕ(x) Involved in LDPC Codes Density Evolution Analysis Using a Gaussian Approximation

Low Density Parity Check (LDPC) codes are currently being deeply analyzed through algorithms that require the capability of addressing their iterative decoding convergence performance. Since it has been observed that the probability distribution function of the decoder’s log-likelihood ratio messages is roughly Gaussian, a multiplicity of moderate entanglement strategies to this analysis has been suggested. The first of them was proposed in Chung et al.’s 2001 paper, where the recurrent sequence, characterizing the passage of messages between variable and check nodes, concerns the function ϕ(x), therein specified, and its inverse. In this paper, we review this old approximation to the function ϕ(x), one variant on it obtained in the same period (proposed in Ha et al.’s 2004 paper), and some new ones, recently published in two 2019 papers by Vatta et al. The objective of this review is to analyze the differences among them and their characteristics in terms of accuracy and computational complexity. In particular, the explicitly invertible, not piecewise defined approximation of the function ϕ(x), published in the second of the two abovementioned 2019 papers, is shown to have less relative error in any x than most of the other approximations. Moreover, its use conducts to an important complexity reduction, and allows better Gaussian approximated thresholds to be obtained.

Sparse Signature Matrix Optimization for NOMA under Imperfect CSI

Non-orthogonal multiple access (NOMA) can support the rapid development of the Internet of Things (IoT) with its potential to support high spectral efficiency and massive connectivity. The low-density superposition modulation (LDSM) scheme is one of the NOMA schemes and uses the sparse signature matrix to reduce multiple access interferences (MAI). In order to improve the NOMA system performance in practice, this paper focuses on designing the sparse signature matrix with a large girth for LDSM under imperfect channel state information (CSI). Based on the orthogonal pilot and linear minimum mean square error (LMMSE) estimation, the LDSM optimized by bare-bone particle swarm optimization (BBPSO) algorithm has a larger girth and can gather more accurate information in the process of iterative decoding convergence. An extrinsic information transfer (EXIT) chart analysis is designed for the LDSM-OFDM system as a theoretical analysis tool. The simulation results show that the optimized LDSM outperforms the reference LDSM system, bringing about a 0.5 dB performance gain.