Trellis-coded Modulation Schemes Research Articles

Implementation of Turbo Trellis Coding Modulation Scheme for Fading Channel

In the context of data communication, encountering fading channels can lead to errors occurring at the receiving end due to multipath propagation. To address this challenge, researchers have persistently worked towards developing Error Correction Schemes that effectively manage these errors and guarantee error-free data reception for the receiver. One area of focus lies in the implementation of Forward Error Correction Schemes directly at the transmitter end. Nonetheless, integrating error correction coding using these schemes comes with the drawback of increased bandwidth requirements since additional bits must be included to facilitate error correction. Fortunately, there exists a coding scheme known as Trellis Coded Modulation (TCM), which specifically tackles this concern. In the case of TCM, the modulation scheme has been chosen based on the rate of the convolutional coding scheme. Nevertheless, TCM has certain limitations when it comes to correcting a high number of errors, which prompted the emergence of Turbo Coding. Turbo Coding employs two coders at the transmitter, arranged either in a serial or parallel configuration, along with an appropriate decoder at the receiver. This paper introduces a Turbo Coding scheme design utilizing convolutional coders with a rate of 2/3, arranged in a serially concatenated configuration, resulting in an effective rate of 4/9. For preserving bandwidth, the Turbo Coding is applied to TCM scheme. Consequently, when employing the convolutional coding scheme with a rate of 2/3, the modulation scheme has to be 8-QAM. However, to maintain bandwidth after coding, when utilizing the Turbo coding scheme with a rate of 4/9, the modulation scheme is upgraded to 512-QAM. MATLAB simulations were conducted to evaluate the error correcting capabilities of the designed scheme compared to the convolutional coding scheme that uses the constituent convolutional encoder. The comparison has also been made with the uncoded data communication utilizing simple QPSK modulation scheme. The results indicate that under Rician fading channel conditions, the Turbo Trellis Coding Modulation Scheme provides an approximate gain of 5 dB compared to the convolutional coding scheme and approximately 8 dB gain compared to uncoded one.

Design of Turbo Trellis Coding Modulation Scheme of Rate 4/9 for Rician Fading Channel

When the fading channels are encountered during data communication, errors are likely to occur at the receiving end due to multipath propagation. Researchers have been consistently striving to develop Error Correction Schemes that can effectively handle these errors and ensure error-free data reception at the receiver end. Of particular interest are the Forward Error Correction Schemes that can be implemented at the transmitter end itself. However, the implementation of error correction coding through these schemes incurs additional costs in terms of bandwidth expansion, as extra bits need to be added to facilitate error correction. Fortunately, there exists one coding scheme called Trellis Coded Modulation (TCM), which addresses this issue. TCM selects a modulation scheme based on the rate of the convolutional coding scheme. However, this coding technique has limitations in correcting the number of errors, leading to the development of Turbo Coding. This scheme utilizes two coders at the transmitter, arranged in either serial or parallel configuration, and a suitable decoder at the receiver. A design of Turbo Coding scheme has been presented in this paper, that employs convolutional coders having rate 2/3, in a serially concatenated configuration, providing an effective rate of 4/9. This turbo coding scheme is then applied to TCM scheme in order to preserve the bandwidth. Therefore, if using the convolutional coding scheme of rate 2/3, the modulation scheme is 8-QAM and in order to preserve bandwidth after coding, using the Turbo coding scheme of rate 4/9, then the modulation scheme will be 512-QAM. The simulations have been conducted in MATLAB and the error correcting capabilities of the designed scheme in comparison with convolutional coding scheme using the constituent convolutional encoder have also been compared. It has been observed that in the Rician fading channel conditions, the Turbo Trellis Coding Modulation Scheme provides approximately 5 dB gain compared to the convolutional coding scheme.

150 m/500 Mbps Underwater Wireless Optical Communication Enabled by Sensitive Detection and the Combination of Receiver-Side Partial Response Shaping and TCM Technology

In this paper, a joint digital signal processing (DSP) scheme including partial response shaping and trellis coded modulation (TCM) technology is proposed to mitigate the bandwidth limitation of the long-reach underwater wireless optical communication (UWOC) system. The similarity of spectral responses between the partial response filter and the communication system is utilized to suppress the enhancement of noise and distortion induced by the full-response feed-forward equalizer. A random interleaver and a precoder are applied to whiten the noise and distortion. In a laboratory experiment, the minimal required received optical power of -29.8 dBm (at a BER of 3.80 ×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> - 3</sup> ) is realized at a data rate of 500 Mbps. In a standard swimming pool, the proposed system successfully achieves a data rate of 500 Mbps with a transmission distance up to 150 m, at which the total attenuation is measured to be 53.47 dB. Such a data rate, enabled by the proposed joint DSP scheme, is 8.0%, 9.2%, and 14.2% higher than those achieved by solely using partial response shaping scheme, TCM scheme, and least square equalization scheme, respectively. To the best of our knowledge, this is the first time to employ the combination of partial response shaping and TCM technology in UWOC for high-speed long-reach transmission.

A Symbolic Dynamics Approach to Trellis-Coded Chaotic Modulation

We propose a trellis-coded chaotic modulation scheme employing the symbolic dynamics generated by three-dimensional chaotic flows. The continuous chaotic trajectories are discretized using a labeled partition of a Poincare section. The discrete dynamics is modeled by a graph representing the evolution mechanism of the chaotic trajectories according to the restrictions imposed by the chaotic flow. This graph is employed to design finite-state encoders to transmit binary information sequences using the restricted discrete chaotic dynamics. We show that the proposed system outperforms a recently proposed trellis-coded chaotic modulation scheme.

Four-dimensional trellis-coded modulation using sphere packing non-cubic constellations

In the paper, we introduce the 8-state trellis-coded modulation (TCM) scheme using sphere packing four-dimensional (4D) non-cubic constellations on the basis of a novel set-partitioning (SP) method. Sphere packing four-dimensional formats have a higher asymptotic power efficiency (APE) because the spatial arrangement of constellation points is more dense. The scheme can further alleviate the contradiction between spectral efficiency (SE) and APE in 4D modulation format. The SP process of 4D non-cubic constellations is completed in the condition that the minimum Euclidean distance between the constellation points and the number of nearest neighbors are adequately considered. We compared these 4D TCM formats to their corresponding 4D formats (i.e., dicyclic4_16, b4_32, b4_64, SP-QAM4_128 and 256-D4) in the 800 km standard single-mode fiber (SSMF) transmission system. Through measurements of bit error rate (BER) performance, at the BER = 1 × 10−3, the coding gains are 5.7 dB, 3.8 dB, 3.6 dB, 3.9 dB and 4.1 dB respectively.

4D PAM-7 Trellis Coded Modulation for Data Centers

We propose a novel seven-level pulse amplitude modulation (PAM-7) combined with trellis coded modulation (TCM) for data center applications. Four symbols are combined in the 4D space to encode ten information bits. The novel scheme called 4D PAM-7 TCM is experimentally demonstrated with commercially available devices at 1550 nm at rates of 210/225 Gbit/s. Excellent performance is achieved by employing advanced digital signal processing algorithms both at transmitter and receiver. The TCM scheme is compared with the PAM-6 modulation format which has the same spectral efficiency. The 4D PAM-7 TCM format improves the sensitivity by 5.5 dB compared to the best PAM-6 results assuming that the system works with the KP4 FEC. The TCM solution may transport the next Ethernet data rate of 800G using $4\times 200\text{G}$ transceivers.

Hybrid trellis coded modulation (HTCM) for visible light communications

The radio frequency spectrum has become very congested and scarce. A response to this dilemma is the implementation of visible light communications (VLC) technology, which is enabled by the dramatic development of light emitting diodes (LEDs) and laser diodes (LDs). VLC has become the most popular emerging telecommunication technology. This is due to the interesting advantages that it provides, which include an unlicensed and large bandwidth, a high throughput capability and a low implementation cost. VLC needs a pivot network in medium and long distance transmissions. The amplify-and-forward scenario between the backbone network and VLC is cost-effective owing to its simplicity when compared to the decode-and-forward scenario. MPSK-CSK is a typical example of cascaded systems in AF scenario with VLC where the backbone channel utilises PSK to convey the message. In this paper, we investigate a forward error correction scheme for cascaded MPSK-CSK systems. A convolutional encoder is added to the MPSK-CSK scheme to construct the hybrid trellis coded modulation scheme. Selected 8HTCM systems using set partitioning are investigated and results for a Gaussian channel are presented. Numerical results reveal that 8HTCM achieves up to 2.129 dB of asymptotic coding gain when compared to the corresponding un-coded MPSK-CSK system.

Turbo Trellis-Coded Differential Chaotic Modulation

In this brief, a novel turbo trellis-coded differential chaotic modulation (TTC-DCM) system is proposed, where parallel concatenated trellis codes are combined with the M-ary differential chaotic shift keying (M-ary DCSK) scheme. An extrinsic information transfer chart is employed to analyze the convergence over additive white Gaussian noise channel and multipath Rayleigh channels. Simulation results show that the new scheme can obtain considerable coding gains without impairing the bandwidth efficiency in comparison with the M-ary DCSK scheme and the trellis-coded differential chaotic modulation scheme. Moreover, compared to the direct-sequence spread-spectrum turbo trellis-coded modulation scheme, TTCDCM has lower complexity and better robustness in the absence of channel state information over multipath Rayleigh channels. Overall, because of the merits of promising performance, high bandwidth efficiency, robustness to poor channel conditions, and an easy-to-implement property, the TTC-DCM scheme is suitable for bandlimited communication applications under poor channel conditions.

Capacity-Approaching Non-Binary Turbo Codes: A Hybrid Design Based on EXIT Charts and Union Bounds

In this paper, we introduce a novel design approach for capacity-approaching non-binary turbo codes. There are two important factors that impact the performance of turbo codes in general: 1) the convergence behavior of iterative decoding in the low signal-to-noise ratio (SNR) and 2) the error-floor effect in the high SNR. We thus design the non-binary turbo codes by means of the EXIT charts and truncated union bounds. We first reduce the search space of component recursive convolutional codes by the analysis based on the truncated union bounds in conjunction with the uniform interleaver, followed by its optimization through the EXIT chart analysis. The construction of the EXIT chart for non-binary turbo codes with fixed code coefficients is a non-trivial task by the fact that these messages have multiple parameters to identify. Therefore, we develop a new EXIT chart analysis for non-binary messages which does not rely on any specific message model. It is demonstrated through computer simulations that the well-designed non-binary turbo codes achieve a better performance than their binary counterparts as well as the conventional non-binary LDPC codes of the same field size. Furthermore, the code design is extended to high-order modulation, and our turbo codes designed for quadrature amplitude modulation are shown to outperform the conventional turbo trellis coded modulation schemes.

User Pairing for Downlink Non-Orthogonal Multiple Access Networks Using Matching Algorithm

In this paper, we study the user pairing in a downlink non-orthogonal multiple access (NOMA) network, where the base station allocates the power to the pairwise users within the cluster. In the considered NOMA network, a user with poor channel condition is paired with a user with good channel condition, when both their rate requirements are satisfied. Specifically, the quality of service for weak users can be guaranteed, since the transmit power allocated to strong users is constrained following the concept of cognitive radio. A distributed matching algorithm is proposed in the downlink NOMA network, aiming to optimize the user pairing and power allocation between weak users and strong users, subject to the users’ targeted rate requirements. Our results show that the proposed algorithm outperforms the conventional orthogonal multiple access scheme and approaches the performance of the centralized algorithm, despite its low complexity. In order to improve the system’s throughput, we design a practical adaptive turbo trellis coded modulation scheme for the considered network, which adaptively adjusts the code rate and the modulation mode based on the instantaneous channel conditions. The joint design work leads to significant mutual benefits for all the users as well as the improved system throughput.

Pragmatic TCMs With General Cross-Type M-QAM Constellations

Recent applications of pragmatic trellis-coded modulation (TCM) to the $\boldsymbol {2^{k}}$ -quadrature amplitude modulation (QAM) (where ${k}$ is an even integer) have been preferred to utilize the square-type constellations due to its simplicity for practical implementation. However, these schemes limit a degree of freedom in designing transceivers since the cross-type constellations cannot be used. In this paper, pragmatic TCM having cross-type $\boldsymbol {2^{k}}$ -QAM constellations with the odd integer ${k}$ ’s greater than 4 are proposed. The proposed work includes details on the transceiver structures of pragmatic TCM based on the required constellation remapping rules. In addition, the approximate bit error rates (BERs) of 32 ( $\boldsymbol {k=5}$ ) and 128 ( $\boldsymbol {k=7}$ )-QAM utilizing the proposed rules are analytically derived and their BER performances are evaluated by the Monte-Carlo simulation. Simulation results of comparable performances to the conventional TCM schemes confirm the validity of the proposed transceiver design and the soundness of the BER analyses for the cross-type M-QAM constellations.

A Genetic Algorithm for Optimizing TCM Encoder

This article describes a genetic algorithm for the optimization of the Trellis Coded Modulation (TCM) schemes with a view to achieve a higher performance in the multipath fading channel. The use of genetic algorithms is motivated by the fact that they are capable of performing global searches to retrieve an approximate solution to an optimization problem and if the solution is unknown to provide one within a reasonable time lapse. The TCM schemes are indeed optimized by the Rouane and Costello algorithm but the latter has as major disadvantage high requirements in both computation time and memory storage. This is further exacerbated by an increase in the encoder rate, the number of memory piles and the depth of the trellis. We describe a genetic algorithm which is especially well suited to combinatorial optimization, in particular to the optimization of NP-complete problems for which the computation time grows with the complexity of the problem, in a non-polynomial way. Furthermore this opens up the possibility of using the method for the generation of codes for channel characteristics for which no optimization codes are yet known. Simulation results are presented, that show the evolutionary programming algorithm on several generations of populations which only exhibit a medium probability of exchanging genetic information.

Full Frame Encryption and Modulation Obfuscation Using Channel-Independent Preamble Identifier

The broadcast nature of wireless communications exposes various transmission attributes, such as the packet size, inter-packet times, and the modulation scheme. These attributes can be exploited by an adversary to launch passive (e.g., traffic analysis) or selective jamming attacks. This security problem is present even when frame headers and payloads can be encrypted. For example, by determining the modulation scheme, the attacker can estimate the data rate, and hence the payload size. In this paper, we propose Friendly CryptoJam (FCJ), a scheme that decorrelates the payload’s modulation scheme from other transmission attributes by embedding information symbols into the constellation map of the highest-order modulation scheme supported by the system (a concept we refer to as indistinguishable modulation unification). Such unification is done using the least-complex trellis-coded modulation schemes, which are combined with a secret pseudo-random sequence in FCJ to conceal the rate-dependent pattern imposed by the code. It also preserves the bit error rate performance of the payload’s original modulation scheme. At the same time, modulated symbols are encrypted to hide PHY-/MAC layer fields. To identify the Tx and synchronously generate the secret sequence at the Tx and Rx, an efficient identifier embedding technique based on Barker sequences is proposed, which exploits the structure of the preamble and overlays a frame-specific identifier on it. We study the implications of the scheme on PHY-layer functions through simulations and testbed experiments. Our results confirm the efficiency of FCJ in hiding the targeted attributes.

Performance Comparison Between 4D Trellis Coded Modulation and PAM-4 for Low-Cost 400 Gbps WDM Optical Networks

We investigate two trellis-coded modulation (TCM) schemes for use in next-generation low-cost 400G optical networks. Their performance is evaluated against that of four-level pulse amplitude modulation (PAM-4). We experimentally demonstrate that TCM outperforms PAM-4 at bit rates between 56 and 80 Gbps and thus is a valid candidate for $\text{8}\lambda \times \text{50G}$ implementations of future 400G wave division multiplexing (WDM) networks. Due to the severe bandwidth limitations of the experimental setup, the feed-forward equalizer and the maximum likelihood sequence estimation equalizer are employed in order to achieve bit error rates below the KP4 threshold of $3\times 10^{-4}$ . We also show that, at 56 Gbps and 1300 nm wavelength, TCM enables optical links of up to 40 km, whereas PAM-4 can only provide transmissions of up to 30 km. We observe that TCM performance degrades faster than that of PAM-4 when we increase the bit rate. For rates higher than 80 Gbps, TCM is not able to improve upon PAM-4 anymore. Thus, only PAM-4 is fit for $\text{4}\lambda \times \text{100G}$ WDM networks, unless higher bandwidth components are used.

Multiple trellis-coded modulation, per-survivor processing and Reed–Solomon coding in the presence of phase noise

The aim of this paper is to consider trellis coded modulation (TCM) in the presence of phase noise. The starting point is a two-dimensional 32 point cross (32-CR) signal set that has served as a benchmark for other power and bandwidth efficient modulation schemes. Per-survivor processing (PSP) is used for carrier phase estimation, and both the phase acquisition (transient state) and phase tracking (steady state) performances are considered in an additive white Gaussian noise (AWGN) channel, in which phase offset or time varying phase noise is introduced. Based on the theoretical and simulation results it can be said that the 32-CR constellation is itself more sensitive to a phase error rather than the PSP algorithm. Due to the phase error the TCM scheme becomes a catastrophic code. Possible solutions include stringent phase noise requirements for oscillators, multiple trellis-coded modulation (MTCM) and concatenated TCM and Reed–Solomon (RS) coding. Our simulation results show that a simple combined MTCM, PSP and RS scheme has around 3 dB advantage compared to the pure TCM and PSP in the presence of phase noise. A semianalytical approach is used for performance evaluation, and the method is a particularly convenient tool to determine the rate of RS coding in detail.

Turbo Trellis-Coded Hierarchical-Modulation Assisted Decode-and-Forward Cooperation

Hierarchical modulation (HM), which is also known as layered modulation, has been widely adopted across the telecommunication industry. Its strict backward compatibility with single-layer modems and its low complexity facilitate the seamless upgrading of wireless communication services. The potential employment of HM in cooperative communications has the promise of increasing the achievable throughput at low power consumption. In this paper, we propose a single-relay-aided hierarchical-modulation-based cooperative communication system. The source employs a pair of turbo trellis-coded modulation (TTCM) schemes relying on specially designed HM, whereas the relay invokes the decode-and-forward (DAF) protocol. We have analyzed the system's achievable rate, as well as its bit error ratio (BER), using Monte Carlo simulations. The results demonstrate that the power consumption of the entire system is reduced to 3.62 dB per time slot (TS) by our scheme.

Eight-state trellis-coded optical modulation with signal constellations of four-dimensional M-ary quadrature-amplitude modulation.

We apply the eight-state trellis-coded modulation (TCM) using signal constellations of four-dimensional M-ary quadrature-amplitude modulation (4D-MQAM) to optical communication systems for the first time to our knowledge. In the TCM scheme, the free distance of the trellis diagram is equal to the minimum distance between constellation points in partitioned subsets, which enlarges the coding gain effectively. In fact, its asymptotic power efficiency is 3-dB larger than that of the set-partitioned 4D-MQAM (SP-4D-MQAM) format, while their spectral efficiencies are the same. Such theoretical predictions are confirmed through computer simulations on eight-state TCM with constellations of 4D-4QAM (i.e., 4D quadrature phase-shift keying: 4D-QPSK) and 4D-16QAM. In particular, eight-state TCM with 4D-QPSK constellations is practically important because of its simple encoder structure, relatively low computational cost, and high coding gain against dual-polarization QPSK (DP-QPSK) and SP-4D-QPSK. Through measurements of its bit-error rate (BER) performance, we confirm that the coding gain against DP-QPSK is about 3 dB at BER=10(-3).

Two-Dimensional 8/9 Error Correcting Modulation Code

In holographic data storage (HDS), a high transmission rate is accomplished through the use of a charge coupled device array for reading two-dimensional (2D) pixel image data. Although HDS has many advantages in terms of storage capacity and data transmission rates, it also features problems, such as 2D intersymbol interference (ISI) by neighboring pixels and interpage interference (IPI) by multiple images stored in the same holographic volume. Modulation codes can be used to remove these problems. We introduce a 2D 8/9 error-correcting modulation code. The proposed modulation code exploits the trellis-coded modulation scheme, and the code rate is larger (about 0.889) than that of the conventional 6/8 balanced modulation code (an increase of approximately 13.9%). The performance of the bit error rate (BER) with the proposed scheme was improved compared with that of the 6/8 balanced modulation code and the simple 8/9 code without the trellis scheme.

Pragmatic Distributed Algorithm for Spectral Access in Cooperative Cognitive Radio Networks

A pragmatic distributed algorithm (PDA) is proposed for supporting the efficient spectral access of multiple Primary Users (PUs) and Cognitive Users (CUs) in cooperative Cognitive Radio (CR) networks. The novelty of our PDA is that the PUs negotiate with the CUs concerning the specific amount of relaying and transmission time, the CU is granted, which the CU will either accept or decline. The CUs may serve as relay nodes for relaying the signal received from the PUs to their destinations, while both the PUs' and the CUs' minimum rate requirements are satisfied. This will reduce the required transmission power and/or increase the transmission rate of the PU. Our results show that the proposed scheme performs better than the benchmarker, despite its significantly lower overhead and complexity. Moreover, we show that the cooperative spectral access based on our PDA reaches an equilibrium, when it is repeated for a sufficiently long duration. These benefits are achieved, because the PUs are motivated to cooperate by the incentive of achieving a higher PU rate, whilst non-cooperation can be discouraged with the aid of a limited-duration punishment. Furthermore, we invoke an attractive practical adaptive Turbo Trellis Coded Modulation (ATTCM) scheme, which appropriately adjusts the code rate and the modulation mode according to the near-instantaneous channel conditions. It was found that the joint design of coding, modulation and user-cooperation may lead to significant mutual benefits for all the PUs and the CUs.

Evaluation of the Effects of Co-Channel Interference on the Bit Error Rate of Wireless Networks with Error Correcting Codes in Fading Channels

This paper presents a performance analysis of wireless networks using error correcting codes on channels with Rayleigh fading in the presence of co-channel interference. The performance is evaluated in terms of the average bit error rate (BER) using TCM (Trellis-Coded Modulation) and TTCM (Turbo Trellis-Coded Modulation) schemes for QAM modulations. The effects of co-channel interference are evaluated through Monte Carlo simulation in scenarios where the system is affected by a dominant interfering synchronous and similar to the target user. For each coded-modulation schemes, the results show that there are BER floors, which vary according to the signal-interference (S/I).