Trellis-Based QC-LDPC Convolutional Codes Enabling Low Power Decoders

A new rate 1/2 turbo code with short memory 2 is developed in this paper. The proposed turbo code consists of two 4-state parallel concatenated non-punctured systematic rate-2/3 convolutional codes. Using a modified maximum a posteriori (MAP) decoding algorithm working on dual codes, its bit error rate (BER) performance is comparable to that of the classic 16-state turbo code at short block lengths, such as k=1024, while its decoding complexity is less than 1/8 that of the classic 16-state turbo codes; for information block length k=504, its BER performance is better than that of the (1008, 3, 6) LDPC codes with comparable decoding complexity. The dual code decoding algorithm is intrinsically partial parallel and a considerably higher throughput of the turbo decoder can be obtained compared with classic turbo codes consisting of punctured codes. The simulation results show that the proposed turbo code can be a competitive technique for short block length applications.

Using a finite field approach, a novel algebraic construction of low-density parity-check (LDPC) convolutional codes with fast encoding property is proposed. According to the matrices of quasi-cyclic (QC) codes constructed based on the multiplicative groups of finite fields and the algebraic property that a binary circulant matrix is isomorphic to a finite ring, we first generate a polynomial-form parity-check matrix of an LDPC convolutional code under a given rate over a given finite field. Then some related modifications are made upon the original polynomial-form matrix to obtain the new one with fast encoding property. Simulation results show that the proposed LDPC convolutional codes have good performance with the iterative belief propagation decoding algorithm.

We consider a canonical model for coded code-division multiple access (CDMA) with random spreading, where the receiver makes use of iterative belief-propagation (BP) joint decoding. We provide simple density-evolution analysis in the large-system limit (large number of users) of the performance of the BP decoder and of some suboptimal approximations based on interference cancellation (IC). Based on this analysis, we optimize the received user signal-to-noise ratio (SNR) distribution in order to maximize the system spectral efficiency for given user channel codes, channel load (users per chip), and target user bit-error rate (BER). The optimization of the received SNR distribution is obtained by solving a simple linear program and can be easily incorporated into practical power control algorithms. Remarkably, under the optimized SNR assignment, the suboptimal minimum mean-square error (MMSE) IC-based decoder performs almost as well as the more complex BP decoder. Moreover, for a large class of commonly used convolutional codes, we observe that the optimized SNR distribution consists of a finite number of discrete SNR levels. Based on this observation, we provide a low-complexity approximation of the MMSE-IC decoder that suffers from very small performance degradation while attaining considerable savings in complexity. As by-products of this work, we obtain a closed-form expression of the multiuser efficiency (ME) of power-mismatched MMSE filters in the large-system limit, and we extend the analysis of the symbol-by-symbol maximum a posteriori probability (MAP) multiuser detector in the large-system limit to the case of nonconstant user powers and nonuniform symbol prior probabilities.

We propose a novel class of provably good codes which are a serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code. The proposed codes, termed product accumulate (PA) codes, are linear time encodable and linear time decodable. We show that the product code by itself does not have a positive threshold, but a PA code can provide arbitrarily low bit-error rate (BER) under both maximum-likelihood (ML) decoding and iterative decoding. Two message-passing decoding algorithms are proposed and it is shown that a particular update schedule for these message-passing algorithms is equivalent to conventional turbo decoding of the serial concatenated code, but with significantly lower complexity. Tight upper bounds on the ML performance using Divsalar's (1999) simple bound and thresholds under density evolution (DE) show that these codes are capable of performance within a few tenths of a decibel away from the Shannon limit. Simulation results confirm these claims and show that these codes provide performance similar to turbo codes but with significantly less decoding complexity and with a lower error floor. Hence, we propose PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1/2.

In the orthogonal frequency division multiplexing (OFDM) transmission system, when the digital symbols are transmitted in the wireless channel, it would be affected by a lot of noise interference due to the unsatisfactory condition characteristics of the wireless channel itself, therefore, the symbol error and bit error would be generated. To achieve a certain bit error rate (BER) under the condition of known signal-to-noise ratio (SNR), convolutional channel coding and block interleaver should be utilized to further reduce the BER. Moreover, convolutional code is almost utilized in all wireless communication systems. This paper proposes a convolutional code channel estimation method in multiple-input single-output (MISO)-based OFDM (MISO-OFDM) system with frequency-shift m-sequence (FSMS) as guard interval (GI) for avoiding inter-symbol interference (ISI). The proposed space-frequency block code (SFBC) MISO-OFDM system achieves higher transmit diversity gains and better BER performance. Simulation results verify that the proposed iterative threshold channel estimation (ITCE) method in octal representation generation vector (ORGV) convolutional code 4 × 1 MISO-OFDM system provides good BER and normalized mean squared error (NMSE) performance with significant coding gains in both static and dynamic multipath channels.

In digital communications, 90 or 180 degree phase ambiguity between the receiver and transmitter carrier is a serious problem for the coherent demodulation. To remove their phase ambiguity, differential quadrature phase shift keying (DQPSK) was proposed with the cost of a remarkable 2.4 dB performance degradation. Based on the iterative decoding (ID) scheme, an efficient joint convolutional code (CC)-coded DQPSK method is proposed to close the gap between quadrature phase shift keying (QPSK) and DQPSK. Using the extrinsic information transfer (EXIT) chart technique, we unveil that the low-complexity convolutional codes outperform the high-complexity Turbo codes for the ID scheme. Simulation results turn out that the proposed scheme can overcome the error-floor effect, and achieve almost 3.54 dB and 0.9 dB signal-to-noise ratio (SNR) gain compared with the non-iterative CC at 10−5 Bit Error Rate (BER)and iterative Turbo schemes at 10−7 BER, respectively.

Modulation techniques in 5G wireless communication systems play a crucial role in meeting demands for higher data rates, lower latency, and improved connectivity. This involves optimizing power spectral density (PSD), enhancing data transmission reliability, and reducing bit error rates (BER) and interference. The objective of this paper is to evaluate primary modulation schemes used in 5G—Orthogonal Frequency Division Multiplexing (OFDM), Filter-Orthogonal Frequency Division Multiplexing (F-OFDM), Filter Bank Multi-Carrier (FBMC), and Universal Filtered Multi-Carrier (UFMC)—based on performance metrics such as PSD, BER, and signal-to-noise ratio (SNR) using MATLAB. OFDM demonstrates low BER at high SNR but faces degradation at lower SNRs, necessitating a higher SNR for maintaining low BER. F-OFDM improves BER in noisy environments through reduced out-of-band emissions and improved spectral efficiency. FBMC shows lower BER than OFDM, especially in multipath fading scenarios, despite its higher complexity. UFMC provides balanced performance with moderate BER across varying SNRs, offering a trade-off between simplicity and efficiency, with stable BER and enhanced spectral efficiency, and reduced latency compared to OFDM. Each modulation scheme in 5G presents specific strengths and weaknesses. OFDM is robust and widely used, while F-OFDM, FBMC, and UFMC enhance spectral efficiency, BER, and SNR management. Selecting the appropriate technique depends on network requirements, with MATLAB simulations playing a crucial role in optimizing 5G network performance.

The codewords of a low-density parity-check (LDPC) convolutional code (LDPC-CC) are characterised into structured and non-structured. The number of the structured codewords is dominated by the size of the polynomial syndrome former matrix H T ( D ) , while the number of the non-structured ones depends on the particular monomials or polynomials in H T ( D ) . By evaluating the relationship of the codewords between the mother code and its super codes, the low weight non-structured codewords in the super codes can be eliminated by appropriately choosing the monomials or polynomials in H T ( D ) , resulting in improved distance spectrum of the mother code.

We newly design time-varying low-density parity-check convolutional codes (LDPC-CCs) based on parity check polynomials of the convolutional codes with a time period of 3, and show that BER (Bit Error Rate) performance in the time-varying LDPC-CCs with a time period of 3 is better than that in the conventional time-varying LDPC-CCs with a time period of 2 in the same coding rate with the nearly equal constraint length.

For space-time bit-interleaved coded modulation (ST-BICM) systems with iterative decoding, the overall perfor- mance is affected by the chosen mapping. In bit error rate (BER) curves, one mapping reaches an error floor at a low signal- to-noise ratio (SNR), while other mappings result in a lower error floor at a higher SNR. The constellation mappings are divided into groups where each group exhibits a distinctive BER curve. We show that the convergence abscissa of the system depends on the average total bit errors and the harmonic mean of the minimum squared Euclidean distance. In this paper, we characterize all mapping groups for ST-BICM with 8PSK and present the optimal selection for each mapping group over independent fading channels. I. INTRODUCTION Space-time coding techniques significantly improve trans- mission efficiency in radio channels by using multiple transmit and/or receive antennas and coordination of the signaling over these antennas. Bit-interleaved coded modulation with iterative decoding (BICM-ID) gives good diversity gains and Euclidean distance property with higher order modulation schemes using well known binary convolutional codes (1). Tonello (2) combined these two schemes as space-time BICM (ST-BICM) with Gray mapping. In this paper, we will first show that the asymptotic BER performance of ST-BICM system is equivalent to the single antenna BICM-ID case even when the throughput of ST-BICM is higher. This indicates that the total data rate of ST-BICM can be increased linearly with the number of transmit antennas while maintaining the same error probability as BICM-ID. This demonstrates the superior performance of ST-BICM. Motivated by the fact that the ST-BICM performance can be characterized by BICM-ID with the same code and mapping, we optimize the ST-BICM mappings based on the BICM-ID parameters. While the error floor (EF) bound (1) offers a good match for an error floor region, a heuristic analysis is still needed to study BER curve behaviors of BICM-ID for the water fall region. Thus, we derive design considerations based on both

This paper studies the performance of ultra-wideband (UWB) radio communications systems employing phase shift keying (PSK) modulation and fully saturated power amplifiers through additive white Gaussian noise (AWGN) channel or Rayleigh fading channel. An impulse response method is provided to analyze the signal-to-noise ratio (SNR) degradation. Both convolutional code and turbo code are employed with the Viterbi decoding and the iterative decoding, respectively. The decoding algorithms are modified for the Rayleigh fading channel. Near optimal bit error rate (BER) performance is achieved when employing either convolutional code or turbo code. The simulation results match the derivation. Therefore, fully saturated power amplifiers can be employed in UWB PSK systems to significantly reduce radio cost, simplify radio circuit, and increase battery life for portable terminals.

In this paper, we put forward the tree-structured expectation propagation (TEP) algorithm for decoding block and convolutional low-density parity-check codes over any binary channel. We have already shown that TEP improves belief propagation (BP) over the binary erasure channel (BEC) by imposing marginal constraints over a set of pairs of variables that form a tree or a forest. The TEP decoder is a message-passing algorithm that sequentially builds a tree/forest of erased variables to capture additional information disregarded by the standard BP decoder, which leads to a noticeable reduction of the error rate for finite-length codes. In this paper, we show how the TEP can be extended to any channel, specifically to binary memoryless symmetric (BMS) channels. We particularly focus on how the TEP algorithm can be adapted for any channel model and, more importantly, how to choose the tree/forest to keep the gains observed for block and convolutional LDPC codes over the BEC.

A new decoding strategy of belief propagation (BP) for low-density parity-check codes is presented by serially concatenating the traditional simultaneous decoding (also known as flooding) and the informed dynamic decoding (IDD) (e.g. node-wise residual belief propagation (NW RBP) or informed variable-to-check (IVC) RBP). The frame error rates (FER) and bit error rates (BER) of the concatenated BP decoder outperform that of the non-concatenated single decoder. In addition, as the signal-to-noise ratio (SNR) increases, the average number of decoding iterations required for the concatenated BP decoder decreases, and tends to merge with that of the first sub-decoder in the high SNR region. Moreover, since the IDD strategies concerned in this paper require extra effort for the residual computation, and the sequential updating of IDD is much more time consuming than the simultaneous updating of flooding. Therefore, compared with using a single IDD, serially concatenating flooding and IDD reduces both the approximate decoding complexity and the decoding latency because the concatenated decoder is still dominated by the sub-decoder flooding.

In this paper we consider the generalization of binary spatially coupled low-density parity-check (SC-LDPC) codes to finite fields GF$(q)$, $q\geq 2$, and develop design rules for $q$-ary SC-LDPC code ensembles based on their iterative belief propagation (BP) decoding thresholds, with particular emphasis on low-latency windowed decoding (WD). We consider transmission over both the binary erasure channel (BEC) and the binary-input additive white Gaussian noise channel (BIAWGNC) and present results for a variety of $(J,K)$-regular SC-LDPC code ensembles constructed over GF$(q)$ using protographs. Thresholds are calculated using protograph versions of $q$-ary density evolution (for the BEC) and $q$-ary extrinsic information transfer analysis (for the BIAWGNC). We show that WD of $q$-ary SC-LDPC codes provides significant threshold gains compared to corresponding (uncoupled) $q$-ary LDPC block code (LDPC-BC) ensembles when the window size $W$ is large enough and that these gains increase as the finite field size $q=2^m$ increases. Moreover, we demonstrate that the new design rules provide WD thresholds that are close to capacity, even when both $m$ and $W$ are relatively small (thereby reducing decoding complexity and latency). The analysis further shows that, compared to standard flooding-schedule decoding, WD of $q$-ary SC-LDPC code ensembles results in significant reductions in both decoding complexity and decoding latency, and that these reductions increase as $m$ increases. For applications with a near-threshold performance requirement and a constraint on decoding latency, we show that using $q$-ary SC-LDPC code ensembles, with moderate $q>2$, instead of their binary counterparts results in reduced decoding complexity.

Optimized polar-coded cooperation with an approximate prior probability-based threshold decision is proposed to improve the reliability and complexity in selective decode-and-forward (SDF) cooperation of multiple satellite constellation systems. First, an SDF scheme with polar coding is adopted in cooperative communications for efficient code construction and relay forwarding. Second, in the logarithmic belief propagation (BP) polar decoding, the variable iterative threshold is derived with independent and variable signal-to-noise ratio (SNR)-based approximate prior probability. This threshold reduces complexity by eliminating active nodes with high reliability in each decoding iteration. Third, the information detection factor is introduced to evaluate the accuracy of decoded bits, thereby limiting the average decoding iterations to improve decoding efficiency. Simulation results show that the proposed polar-coded SDF cooperation obtains 1.5 dB performance gain at a bit error rate (BER) of 10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−3</sup> compared with that of existing LDPC-related schemes. The complexity of the optimized logarithmic BP decoding is reduced by 25%–50% compared with that of the traditional BP decoding. Therefore, the proposed scheme has good BER performance and low complexity in cooperative communications of multisatellite and wireless integrated systems.