Parallel concatenated turbo codes for continuous phase modulation

In the paper, a class of LDPC coded continuous phase modulation (CPM) systems is proposed for reliable communication over burst-error channels. A series of binary LDPC codes with code rates 1/4, 1/2 and 2/3 are chosen for binary and quaternary CPM schemes. A non-recursive decomposition of CPM is incorporated to eliminate the error propagation caused by burst errors. To reduce the complexity, an improved demodulation algorithm for noncoherent soft in soft out (N-SISO) is considered. Simulation results show that the proposed LDPC coded CPM offers a better error performance and is abler to recover the transmitted information under severe burst errors than current systems.

Joint source and channel coding (JSCC) using combined trellis coded quantization (TCQ) and trellis coded continuous phase modulation (CPM) is studied. Optimal soft decoding based on the a posteriori probability (APP) algorithm for trellis coded CPM is developed for the considered systems. It has been demonstrated that the combined TCQ/CPM systems are both power and bandwidth efficient compared with the combined TCQ/TCM/8PSK systems. Furthermore, a TCQ design algorithm for the noisy channel is developed. The novelties of this work is the use of a soft decoder and the APP algorithm for combined TCQ/CPM systems.

In this paper, a doubly-iterative linear receiver, equipped with a soft-information aided frequency domain minimum mean-squared error (MMSE) equalizer, is proposed for the combined equalization and decoding of coded continuous phase modulation (CPM) signals over long multipath fading channels. In the proposed receiver architecture, the front-end frequency domain equalizer (FDE) is followed by the soft-input, softoutput (SISO) CPM demodulator and channel decoder modules. The receiver employs double turbo processing by performing back-end demodulation/decoding iterations per each equalization iteration to improve the a priori information for the front-end FDE. As presented by the computational complexity analysis and simulations, this process provides not only a significant reduction in the overall computational complexity, but also a performance improvement over the previously proposed iterative and noniterative MMSE receivers.

We study a serially interleaved concatenated code construction, where the outer code is a standard convolutional code, and the inner code is a recursive convolutional code of rate 1. We focus on the ubiquitous inner differential encoder (used, in particular, to resolve phase ambiguities), double differential encoder (used to resolve both phase and frequency ambiguities), and another rate 1 recursive convolutional code of memory 2. We substantiate analytically the rather surprising result, that the error probabilities corresponding to a maximum-likelihood (ML) coherently detected antipodal modulation over the additive white Gaussian noise (AWGN) channel for this construction are advantageous as compared to the stand-alone outer convolutional code. This is in spite of the fact that the inner code is of rate 1. The analysis is based on the tangential sphere upper bound of an ML decoder, incorporating the ensemble weight distribution (WD) of the concatenated code, where the ensemble is generated by all random and uniform interleavers. This surprising result is attributed to the WD thinning observed for the concatenated scheme which shapes the WD of the outer convolutional code to resemble more closely the binomial distribution (typical of a fully random code of the same length and rate). This gain is maintained regardless of a rather dramatic decrease, as demonstrated here, in the minimum distance of the concatenated scheme as compared to the minimum distance of the outer stand-alone convolutional code. The advantage of the examined serially interleaved concatenated code, given in terms of bit and/or block error probability which is decoded by a practical suboptimal decoder, over the optimally decoded standard convolutional code is demonstrated by simulations, and some insights into the performance of the iterative decoding algorithm are also discussed. Though we have investigated only specific constructions of constituent inner (rate 1) and outer codes, we trust, hinging on the rational of the arguments here, that these results extend to many other constituent convolutional outer codes and rate 1 inner recursive convolutional codes.

We track the density of extrinsic information in iterative turbo decoders by actual density evolution, and also approximate it by symmetric Gaussian density functions. The approximate model is verified by experimental measurements. We view the evolution of these density functions through an iterative decoder as a nonlinear dynamical system with feedback. Iterative decoding of turbo codes and of serially concatenated codes is analyzed by examining whether a signal-to-noise ratio (SNR) for the extrinsic information keeps growing with iterations. We define a for the iterative decoder, such that the turbo decoder will converge to the correct codeword if the noise figure is bounded by a number below zero dB. By decomposing the code's noise figure into individual curves of output SNR versus input SNR corresponding to the individual constituent codes, we gain many new insights into the performance of the iterative decoder for different constituents. Many mysteries of turbo codes are explained based on this analysis. For example, we show why certain codes converge better with iterative decoding than more powerful codes which are only suitable for maximum likelihood decoding. The roles of systematic bits and of recursive convolutional codes as constituents of turbo codes are crystallized. The analysis is generalized to serial concatenations of mixtures of complementary outer and inner constituent codes. Design examples are given to optimize mixture codes to achieve low iterative decoding thresholds on the signal-to-noise ratio of the channel.

The detection of convolutional codes over rings suitable for continuous phase modulation (CPM) are presented based on the Rimoldi's Decomposition of CPM. Because the ring convolutional codes are on the same ring as the inner codes of CPM, We can use reduced state sequence detection (RSSD) to analyze and detect the overall encoder. Numerical result shows the detection complexity of this RSSD is significantly reduced with a very small degradation in error performance.

The partial response channel can be viewed as a rate-1 encoder in which the output alphabet differs from the input alphabet. In serially concatenated coding schemes, the partial response channel can serve as the inner encoder. Recent work has focused on convolutional codes and parity-check codes as the outer code in such serial concatenation schemes. This work focuses instead on the use of product codes as the outer code. Systems using both hard and soft decoding, with both iterative and non-iterative decoding, are presented. Simulation results are presented comparing performance of product codes which use Reed-Solomon and BCH codes as the constituent codes.

Continuous phase modulation (CPM) is known for its attractive spectral properties. Furthermore, CPM has the property that the modulation signal maintains a constant envelope, so CPM is effective for satellite communications. Recently, generalized nonlinear CPM (GNCPM), which can achieve a larger minimum Euclidean distance than ordinary CPM, was introduced. In this paper, we propose a convolutional coded GNCPM to improve the bit error rate (BER) performance of uncoded GNCPM without expanding bandwidth. Combination CPM with convolutional coding causes an increased number of phase trajectory patterns which can cause the bandwidth expansion. Therefore, in our proposed model, to control the bandwidth, we pay attention to the phase trajectory pattern which is already owned by uncoded GNCPM and change the modulation index appropriately, depending on the input symbols, to keep the number of phase trajectory patterns the same as in uncoded GNCPM. First, we consider the most suitable assignment of the modulation index which can increase the Euclidean distances without bandwidth expansion. Next, we theoretically derive the upper bound on the error event probability of the proposed model in additive white Gaussian noise (AWGN). The performance of the proposed convolutional GNCPM, obtained by computer simulation, shows that the proposed model can improve BER performance without bandwidth expansion. © 1998 Scripta Technica. Electron Comm Jpn Pt 1, 81(8): 42–50, 1998

The neural networks offer iteration capability for low-density parity-check (LDPC) decoding with superior performance at transmission. However, to cope with increasing code length and rate, the complexity of the neural network increases significantly. This is due to the large amount of feature extraction required to maintain the error correction capability. Based on this gap, we design a new iterative LDPC decoding technique named graph model neural network-belief propagation (GMNN-BP). GMNN-BP uses graph models as a link between deep learning and belief propagation (BP) algorithms, combining the advantages of both. Compared to traditional fully connected neural network decoders, the GMNN-BP decoding has the substantial benefit of avoiding learning and judging codeword categories directly from a large amount of data and requiring less training data as well. The proposed algorithm is verified by simulation and experiment and is tested by using IEEE 802.3ca standard LDPC code word. The results show that the GMNN-BP decoding algorithm is superior to the BP-based iterative decoding method under the same number of iterations, and the maximum gain can reach 1.9dB. When achieving the same performance, the GMNN-BP decoding algorithm only requires half the number of iterations of other algorithms.

Iterative or Turbo decoding of parallel concatenated binary error control codes in Binary Phase Shift Keyed (BPSK) Communication System corrupted by both Additive White Gaussian Noise (AWGN) and oscillator phase noise is discussed. As an example of application of the discussed theory, iterative decoding technique of Parallel Concatenated block Codes (PCBC) is applied to a coherent Optical Code Division Multiple Access (OCDMA) network in the presence of Multiple Access Interference (MAI), detector shot noise and laser phase noise. Remarkable improvement in performance resulting from the use of turbo decoding in the OCDMA network is also discussed.

This paper consists of an overview of recent results on combined constant amplitude continuous phase modulation (CPM) and convolutional channel codes. We also compare the best coded CPM systems to trellis-coded amplitude/phase modulations. The ideal additive white Gaussian channel and systems with perfect carrier phase and symbol time synchronization are considered in this paper. Signals which have a constant amplitude at all times are sometimes needed when highly nonlinear amplifiers are used. Memory is introduced into the constant amplitude signals by means of continuous phase at all times, controlled intersymbol interference to further smooth the phase changes and combinations of CPM and convolutional codes. Analytical tools for calculating the power spectrum and upper bounds on the error probability are given. Results for the special case of Continuous Phase Frequency Shift Keying (CPFSK) with up to 256 levels are considered. Some new results on bounds on more advanced coded systems of higher complexity where the coding is performed jointly over several consecutive channel symbols are also given. Current research topics such as trellis-coded modulation for fading channels, and practical implementations and applications are also briefly discussed.

An iterative decoding approach to joint source and channel coding (JSCC) using combined trellis-coded quantization (TCQ) and continuous phase modulation (CPM) is proposed. The channel is assumed to be the additive white Gaussian noise channel. This iterative procedure exploits the structure of the TCQ encoder and the continuous phase modulator. The performance in terms of the signal-to-distortion ratio (SDR) is compared with that of a combined TCQ/trellis-coded modulation (TCM) system. It is shown that the combined TCQ/CPM systems are both power- and bandwidth-efficient, compared with the combined TCQ/TCM system. For source encoding rate R=2 b/sample, it is observed that the combined TCQ/CPM systems with iterative decoding working at symbol level converge faster than the systems working at bit level. The novelty of this work is the use of a soft decoder and an iterative decoding algorithm for TCQ-based JSCC systems. The combined TCQ/CPM with iterative decoding is considered for the first time.

Reed-Solomon convolutional concatenated (RSCC) code has been widely applied in wireless and space communications. However, iterative soft-decision decoding of the concatenated code is yet to be developed. This paper proposes a novel iterative soft decoding algorithm for the concatenated coding scheme. The maximum a posteriori (MAP) algorithm is used to decode the inner convolutional code. Its soft output will be deinterleaved and then passed to the soft-in-soft-out (SISO) decoding algorithm for the outer Reed-Solomon (RS) code. The outer SISO decoder integrates the adaptive belief propagation (ABP) algorithm and the Koetter-Vardy (KV) list decoding algorithm, attempting to find out the transmitted message. If it is found, the deterministic probabilities of the corresponding RS coded bits will be fed back. Otherwise, the extrinsic probabilities that are yielded by the ABP algorithm will be given as the feedback. With the proposed soft information exchange decoding mechanism, error-correction potential of the concatenated code can be better exploited. Our simulation results show that significant performance improvement can be achieved over the existing decoding algorithms.

The puncturing technique allows obtaining high-rate convolutional codes from low-rate convolutional codes used as mother codes. This technique has been successfully applied to generate good high-rate convolutional codes which are suitable for Viterbi and sequential decoding. In this paper, we investigate the puncturing technique for convolutional self-doubly orthogonal codes (CSO/sup 2/C) which are decoded using an iterative threshold-decoding algorithm. Based on an analysis of iterative threshold decoding of the rate-R=b/(b+1) punctured systematic CSO/sup 2/C, the required properties of the rate-R=1/2 systematic convolutional codes (SCCs) used as mother codes are derived. From this analysis, it is shown that there is no need for the punctured mother codes to respect all the required conditions, in order to maintain the double orthogonality at the second iteration step of the iterative threshold-decoding algorithm. The results of the search for the appropriate rate-R=1/2 SCCs used as mother codes to yield a large number of punctured codes of rates 2/3/spl les/R/spl les/6/7 are presented, and some of their error performances evaluated.

The performance of turbo-codes relies on two major concepts: code concatenation so as to build a powerful global code and iterative decoding in order to efficiently approximate the optimal decoding process. A turbo equalization (TE) scheme based on convolutional code and normalized least mean square equalizer for coherent optical communication links is proposed and experimentally demonstrated. For counteracting PDM 16 QAM impairments in dispersion uncompensated coherent transmission links, the iterative TE technique is proved effective.