Semantic Communication on Digital Wireless Communication Systems

Abstract

Semantic communication is an effective technological approach for the integration of intelligence and communication, enabling more efficient and context-aware data transmission. In this paper, we propose a bit-conversion-based semantic communication transmission framework to ensure compatibility with existing wireless systems. Specifically, a series of physical layer processing modules in end-to-end transmission are designed. Additionally, we develop a semantic communication simulator to implement and evaluate this framework. To optimize the performance of this framework, we introduce a novel physical layer metric, termed Integer Error Rate (IER), which provides a more suitable evaluation criterion for semantic communication compared to the conventional bit error rate (BER). On the basis of the IER, a minimum Manhattan distance constellation mapping scheme is proposed, which can improve the transmission quality of semantic communication under the same BER condition. Furthermore, we propose a hybrid joint source–channel coding (JSCC) and separate source–channel coding (SSCC) transmission scheme. This scheme decouples the semantic quantization output from the modulation order by segmenting the bits to be transmitted. Simulation results demonstrate that the hybrid JSCC/SSCC transmission scheme can improve the semantic performance, such as the Peak Signal-to-Noise Ratio (PSNR), in low Signal-to-Noise Ratio (SNR) environments while reducing bandwidth usage by up to 50% compared to the benchmark scheme.

1. Introduction

In recent years, semantic communication, as one of the potential key technologies for 6G mobile communications, has garnered widespread attention from academia and industry. It is anticipated that semantic communication will become a novel paradigm in the development of end-to-end communication systems for 6G mobile communications [1,2,3,4].

In the research on semantic communication, many end-to-end transmission frameworks have been proposed [5,6,7,8,9,10]. The design of these end-to-end transmission frameworks all involve the same issue: the output of semantic encoding based on neural networks (NNs) is a continuous signal, leading to the following question: how can it be transmitted via existing wireless communication systems? To solve this issue, current raised frameworks can be divided into two main approaches. One approach is to change the existing system’s modulation method to analog modulation [8,9,10,11,12,13]. The advantage of this approach is that it can preserve the information after semantic encoding and reduce quantization error. However, the disadvantage is that it is extremely different from the existing systems, requiring significant changes to both hardware equipment and software protocols. The other approach still utilizes digital modulation, quantizing the output after semantic encoding before transmission [5,6,7,14,15,16]. We can call it the quantized approach. The disadvantage of the quantized approach is that, from a conventional perspective, quantization tends to introduce certain performance losses. And the magnitude of the performance loss depends on different quantization methods [17,18]. Conversely, the advantage of the quantized approach is that its compatibility with existing system protocols is convenient. Moreover, there are currently many studies on quantization methods for semantic communication to improve the performance of quantization [5,14,15,16,19]. Comprehensively, the quantized approach is a more feasible path for the evolution of semantic communication systems onexisting systems.

Furthermore, many transmission schemes have been proposed within the quantized approach, which can be divided into two major categories based on whether traditional channel coding is utilized. One category of the schemes still adopts the separate source–channel coding (SSCC) scheme, called the SSCC transmission scheme [1,6,7]. The transmission framework of this scheme is illustrated in Figure 1a. It is only necessary to transmit the content of semantic encoding as the payload data of the existing system, without any modification of the existing wireless communication systems needed. However, the disadvantage of the SSCC transmission scheme is the so-called “Cliff Effect”. This refers to a sharp decline in distortion or decoding accuracy when the channel quality drops below a certain quality threshold. This issue has been mentioned in many studies on semantic communication, and corresponding references have been provided [14,20,21,22]. The other category of the transmission schemes eliminate traditional channel coding replacing with the JSCC (joint source–channel coding) scheme, called the JSCC transmission scheme. For example, the JSCC image transmission schemes were proposed by Bourtsoulatze, Yang, and others [14,20]; The JSCC video transmission schemes were proposed by Wang, Jiang, and others [23,24]; The speech transmission schemes were proposed by Han and others [8]. All these schemes have demonstrated that the JSCC transmission scheme for semantic communication can avoid the “Cliff Effect” and save transmission bandwidth, compared to the SSCC transmission scheme.

However, since the JSCC transmission scheme removes traditional channel coding, the existing wireless communication systems are modified. The extent of the impact depends on the specific function designs. Most of the current research using the JSCC transmission scheme [5,8,14,15,16,23,24] have proposed a transmission framework, as shown in Figure 1b, called the non-bit-conversion JSCC transmission framework. In this framework, at the transmitter, the range of the quantization output needs to be determined based on the modulation order (e.g., QPSK,16QAM,64QAM … …). Semantic encoding and quantization are jointly designed to map the encoded quantization output directly to the modulation constellation points. At the receiver, this framework does not require restoring the demodulated constellation points into bits, but instead sends the demodulated constellation points, represented by complex numbers, for decoding in a semantic decoder. The advantage of this framework is that it can avoid the performance loss caused by the bit decision at the receiver while retaining some of the channel state information. However, the disadvantage is that it makes significant changes to the existing wireless communication system protocols and network architecture. For example, at the receiver, the input of the semantic decoder in this scheme is complex numbers, which faces the problem of how to handle complex numbers above the physical layer if the semantic decoding algorithm is not feasible in the base station’s physical layer. If the semantic decoding server is deployed in the base station’s physical layer, it will face the problem of how to handle the user data in base stations, which conflicts with the existing system specifications. At the transmitter, since this scheme has already been quantized, whether to convert the semantic output to bits will not lead to differences in information loss. However, this framework also brings compiling issues, e.g., where to deploy the encoding algorithm and how to exchange information between nodes in the network architecture.

Based on the impact of the non-bit-conversion transmission scheme on the semantic communication system, we believe that bit conversion is indispensable. The reason for this is that existing wireless communication systems, with all layers of the protocols and information exchange between nodes, are designed for bit-oriented transmission. To minimize the impact on existing wireless communication systems, we propose a transmission framework, as shown in Figure 1c, called the bit-conversion-based JSCC transmission framework. In this framework, at the transmitter, the quantization result is converted into bits, and the existing system’s bit constellation mapping module is retained. At the receiver, the demodulated constellation points are restored into bits, and then the bits are converted into integers before being sent into the semantic decoder. The advantage of this transmission framework is that it is convenient to integrate with the existing system and retain the advantages of the JSCC transmission scheme. We will introduce the specific physical layer procedure designed in this framework in the following part of this paper.

Based on the above work, the main contributions of this paper mainly include the following:

• The specific physical layer procedure of the bit-conversion JSCC transmission framework for semantic communication is designed. Furthermore, a semantic communication simulator is developed to implement and verify this transmission framework.
• A novel physical layer metric, the IER (Integer Error Rate), is proposed as a physical layer metric for semantic information transmission. And we prove that the IER is more suitable than the BER for semantic communication by simulation.
• We present a minimum Manhattan distance constellation mapping scheme for m-QAM modulation to optimize the transmission quality in the bit-conversion JSCC transmission framework.
• Lastly, based upon this minimum Manhattan distance constellation mapping scheme, we propose a hybrid transmission scheme to adapt different quantization levels, which can separate the semantic quantization output from the modulation order. Meanwhile, this hybrid transmission scheme can improve the transmission quality of semantic communication at the low SNR range while leveraging the bandwidth-saving advantage of semantic communication [14,20,23,24].

The rest of this paper is organized as follows. In Section 2, we propose the specific physical layer procedure design for the bit-conversion-based JSCC transmission framework for semantic communication and introduce the corresponding simulator. In Section 3, we propose a novel physical layer indicator IER based on the bit-conversion-based JSCC transmission framework, as well as its simulation verification. In Section 4, the optimization methods for the bit-conversion-based JSCC transmission framework and their simulation verification are presented, including minimum Manhattan distance constellation mapping and hybrid JSCC and SSCC transmission schemes. Finally, conclusions are drawn in Section 5.

2. Bit-Conversion-Based JSCC Transmission Framework and Simulator

2.1. Bit-Conversion-Based JSCC Transmission Framework

To better adapt to the existing wireless communication systems, the specific physical layer procedure of the bit-conversion JSCC transmission framework for semantic communication is designed. Since the JSCC approach eliminates traditional channel encoding and decoding, we need to add an adaptation module between the physical layer digital modulation interface of the existing system and the semantic encoder/decoder. This transmission framework does not require changes to the physical layer processing flow after bit mapping at the transmitter or before digital demodulation at the receiver, as shown in Figure 2.

The specific process design of the adaptation module is illustrated in Figure 3. The functions of the transmitter adaptation module include integer-to-bit conversion, end-of-data indication attachment, rate matching, and data segmentation. The functions of the receiver adaptation module include hard-decision demodulation, data concatenation, end-of-data indication detection, and bit-to-integer conversion.

Functions in the transmitter adaption module include the following:

• Integer-to-bit conversion: based on the output range of semantic encoding quantization, determine the minimum number of bits required to represent each integer. Select a specific encoding method, such as natural binary coding, binary complement coding, etc., to convert the integer to then be transmitted into binary.
• Adding end of data indication: for semantic transmission, bit error is allowed when the physical layer sends the received data to the semantic decoder, while the number of bits (or data) should not be changed. For the JSCC scheme, CRC is not required; thus, an end-of-data indication function makes the receiver identify the end of data flow. A special sequence is adopted as the end-of-data indication and is repeated multiple times to improve the robust of detection.
• Rate matching and data segmentation: rate matching and data segmentation are designed with the code rate of channel coding in the traditional system. As there is no channel coding/decoding in the JSCC scheme, the rate matching and data segmentation should be re-designed to adapt the physical layer with no channel coding. Here, we adopt the zero-padding method to make the data fit the scheduled resource.

Functions in the receiver adaption module include the following:

• Hard-decision de-mapper: since there is no channel coding/decoding, the output LLRs of de-modulation should be converted to bits with a simple algorithm. A hard decision de-mapper function is added here to convert the LLRs to bits.
• Data concatenation: the reverse process of data segmentation in the transmitter.
• End of data detection: we employed a simple character comparison algorithm here to identify the special sequence adopted in the transmitter.
• Bits-to-integer conversion: convert the bits to integers with the same binary coding employed in the transmitter.

Comparing this framework with the SSCC transmission framework shown in Figure 4, which has no impact on the existing system, it can be observed that this framework involves minimal modifications to the existing system, while, since the channel coding is removed in the JSCC transmission framework, the computational complexity at the physical layer of this framework is significantly reduced. And the key consideration is whether the proposed transmission framework has an advantage in transmission performance compared with the SSCC transmission framework. The simulation tools and the evaluation will be introduced in the following sections.

2.2. Simulation Platform for E2E Semantic Communication

There is a common issue in the semantic communication simulation tools, which is that traditional simulation tools implement complete physical layer processing but do not transmit the real payload data; random bits are used as the payload for transmission. In contrast, numerical simulations mentioned in most semantic communication papers emphasize the encoding and decoding algorithms, while the physical layer processing is relatively simplified and cannot reflect the impact of complete physical layer algorithms on semantic transmission performance.

To solve this problem, based on the transmission frameworks we designed, we develop a semantic communication simulation platform. The software architecture of the simulation platform is illustrated in Figure 5. By configuration, this simulation platform can support the semantic SSCC and JSCC transmission schemes, as well as the traditional bit transmission. And this is different from most of the traditional physical layer simulation systems or semantic communication simulation systems at present; with the adaption module, we can simulate the transmission of the real payload on the physical layer, not only of random bits.

The simulation procedure is illustrated in Figure 6. To be specific, the input original data are firstly processed by the semantic or source encoder. After that, the encoded data proceeds to execute the remaining physical layer functions. Then, differences in the data files can be received with customized configurations (e.g., JSCC, SSCC, modulation, … …) under changing channel conditions. Finally, the semantic decoder outputs the final result and compares this with the source files to calculate the semantic key performance indicators (KPIs). In addition, the physical KPIs can also be obtained during the simulation procedure.

Taking image transmission as an example, we simulate the semantic transmission with QPSK/16QAM/64QAM using both the JSCC and SSCC transmission schemes in this simulation platform. For the SSCC transmission scheme, a 0.5 code rate LDPC is adopted. And for JSCC, there is no channel coding. A layer-based semantic communication system for images (LSCI) is chosen for the semantic coding algorithm [25].

It is observed from simulation results that, as shown in Figure 7a,c,d, for SSCC, when the SNR is in the range where LDPC can work, there is no bit error and the PSNR and SSIM maintain perfect performance as well. Below a certain SNR threshold, LDPC could not correct the bit error and suffers from the “Cliff Effect”. The BER, PSNR, and SSIM decrease sharply. For JSCC, since it does not include channel coding, few error bits exist, even in a good SNR range, but PSNR and SSIM perform well. The BER, PSNR, and SSIM decrease smoothly when the SNR decreases; thus, the PSNR of JSCC can remain acceptable in an SNR range lower than the “Cliff Effect” point of SSCC. At the same time, JSCC can achieve two times the spectrum efficiency of SSCC with different modulation orders, as shown in Figure 7b, since there is no channel coding overhead.

Together with other papers [14,20], the results obtained from our semantic simulation platform show the same trend of the semantic transmission of JSCC and SSCC. This demonstrates the accuracy of this simulation platform. Furthermore, we can leverage this simulation platform to study the impact of physical layer algorithms and semantic algorithms on the end-to-end semantic communication system.

3. IER—A Novel Physical Layer Semantic Metric

For the traditional wireless system, the BER (bits error rate) is a basic physical layer metric to measure the reliability of the E2E communication link. One of the main principles for designing communication systems is to reduce the BER metric to as low as possible from 1G to 5G. However, the BER is not suitable to measure the quality of the physical layer semantic communication because semantic communication is not anticipated to recover information without errors in the bit level. Thus, a new semantic metric should be defined and should focus on the preservation of the semantics in the regenerated content. In this chapter, we will try to define a novel loss function to measure the semantic transmission quality and verify this novel loss function with our simulation platform.

3.1. Definition of IER (Integer Error Rate)

First of all, we should consider how to define the error distance between the sending/received message for the semantic codec. As illustrated in Figure 8, assume that the sending message is sequence S and the received message is sequence R. Then, the error distance between the sending/received message for the semantic codec can be defined as the distance between sequences S and R. In mathematics, there are many ways to define the distance between two sequences, e.g., Euclidean distance, Manhattan distance, Hamming distance…, etc. Hamming distance is the commonly adopted metric in the current communication system, but it is not the best one for semantic communication. We are going to analyze this in the following.

• Hamming distance and BER (bit error rate)

In most of the digital wireless system, binary coding is used. And for binary coding, Hamming distance is the commonly used metric to define the error distance between transmitted/received messages. Assume that the transmitted message S = [1,0,0, 1,1,0, 0,0,0, 0,1,1] and the received message R = [0,0,0, 1,0,0, 0,0,0, 1,1,1]. In this case, the Hamming distance is three, which is the number of the different bits between S and R. And the BER can also be defined as the ratio of the Hamming distance and the total length of the transmitted message, as shown in Equation (1), where Len(S) is the total length of the transmitted message.

$$\mathrm{B}\mathrm{E}\mathrm{R}=\mathrm{H}\mathrm{a}\mathrm{m}\mathrm{m}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{D}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{c}\mathrm{e} (\mathrm{S},\mathrm{R}) / \mathrm{L}\mathrm{e}\mathrm{n}\left(\mathrm{S}\right)$$

(1)

• Manhattan distance and IER (Integer Error Rate)

For non-binary coding, Hamming distance is not suitable to define the error distance. Here, we suggest the adoption of Manhattan distance [26] to measure the error distance between the transmitted/received messages. The Manhattan distance is defined below.

Let $\mathrm{x}=\left({\mathrm{x}}_{1,}{\mathrm{x}}_{2,\dots \dots ,}{\mathrm{x}}_{\mathrm{n}}\right)$ and $\mathrm{y}=({\mathrm{y}}_{1,}{\mathrm{y}}_{2,\dots \dots ,}{\mathrm{y}}_{\mathrm{n}})$ be the integer-valued vectors at the transmitter and receiver, respectively, ${\mathrm{x}}_{\mathrm{i}},{\mathrm{y}}_{\mathrm{i}} \mathsf{ϵ} \left\{0,1,\dots \dots ,\mathrm{q}-1\right\},\mathrm{i}=\mathrm{1,2},\dots \dots \mathrm{n}.$ Then, the distance function is defined by

$${\mathrm{d}}_{\mathrm{M}}\left(\mathrm{x},\mathrm{y}\right)=\sum _{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{x}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}\right|$$

(2)

Based on the Manhattan distance, we can define a new metric IER in the physical layers to measure the semantic transmission quality. The IER is defined in Equation (3), where x is the transmitted message and y is the received message. Let $\mathrm{x}=\left({\mathrm{x}}_{1,}{\mathrm{x}}_{2,\dots \dots ,}{\mathrm{x}}_{\mathrm{n}}\right)$ and $\mathrm{y}=\left({\mathrm{y}}_{1,}{\mathrm{y}}_{2,\dots \dots ,}{\mathrm{y}}_{\mathrm{n}}\right)$ be integer-valued vectors, ${\mathrm{x}}_{\mathrm{i}},{\mathrm{y}}_{\mathrm{i}} \mathsf{ϵ} \left\{0,1,\dots \dots ,\mathrm{q}-1\right\},\mathrm{i}=\mathrm{1,2},\dots \dots \mathrm{n}.$

$$\mathrm{I}\mathrm{E}\mathrm{R}={\displaystyle \frac{{\mathrm{d}}_{\mathrm{M}}\left(\mathrm{x},\mathrm{y}\right)}{\mathrm{l}\mathrm{e}\mathrm{n}\left(\mathrm{x}\right)\times \mathrm{q}}}={\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}\left|{\mathrm{x}}_{\mathrm{i}}-{\mathrm{y}}_{\mathrm{i}}\right|}{\mathrm{n}\times \mathrm{q}}}$$

(3)

3.2. Relation Between BER and IER

Two received messages with the same BER may result in different IERs, as

Table 1. Comparison of the BER and IER.

Message Vector	Integer- Valued	Manhattan Distance to Vector S	Natural Binary Coding	Hamming Distance to Vector S	BER	IER
S	[1, 2, 5, 7]	0	[001, 010, 101, 111]	0	0%	0%
R1	[0, 3, 5, 6]	3	[000, 011, 101, 110]	3	25%	9%
R2	[5, 2, 1, 3]	12	[101, 010, 001, 011]	3	25%	37%
R3	[5, 6, 5, 7]	8	[101, 110, 101, 111]	2	16%	13%

illustrates, for example. From the BER perspective, received message R1 and R2 have the same quality, while from the IER perspective, received message R1 is better than R2. Even for some special cases, e.g., R3 is better than R1 in the BER, while it is worse than R1 in terms of the IER.

Since the final input and output data for the semantic codec is the integer value, not the bits value, intuitively, the IER is a better error distance function than the BER for semantic transmission, and we can verify this assumption with the simulation platform.

3.3. Relation Between IER, BER, and Semantic Metric

In order to verify the relation between the IER, BER, and semantic communication metric, we designed a test case, as shown below. We chose the bit-conversion JSCC transmission scheme we proposed in Section 2. And the measurement points of the BER, IER, and PSNR at the simulation link are shown in Figure 9.

In this simulation link, if we keep the bits-to-constellation point mapping unchanged (the mapper and de-mapper module) and employ the 3GPP 5G bit constellation point mapping scheme [27], then different integer-to-bit conversion coding results cause different integer constellation point mapping results. Obviously, different integer-to-bit conversion coding methods will impact the received data directly. We choose two different integer-to-bit conversion codecs: one is the natural binary coding shown in Figure 10a, and the other is the Manhattan distance binary coding, as shown in Figure 10b, which is designed to make the Manhattan distance of adjacent constellation points smaller. We will introduce more details of this constellation mapping scheme in Section 4.

The simulation configuration is illustrated in

Table 2. Simulation configuration for BER/IER comparison.

Test Case	Natural binary coding scheme	Manhattan distance binary coding scheme
Transmission Framework	bit-conversion JSCC	bit-conversion JSCC
Source File	image	image
Semantic Codec	LSCI	LSCI
Quantization Output Range	[0–7]	[0–7]
Integer-to-Bit Coding	natural binary coding	Manhattan distance binary coding
Channel Coding	NO	NO
Bit constellation mapping	3GPP 5G	3GPP 5G
Modulation	64QAM	64QAM
Simulation SNR Range	[−5~30]	[−5~30]
Channel Model	AWGN	AWGN
Channel Equalization	LMMSE	LMMSE

. In order to evaluate the relation between the IER, BER, and semantic metric, two identical configurations are employed, except for the different integer-to-bit conversion coding schemes. The transmission framework both used bit-conversion JSCC, which is described in Section 2.1. The quantization output range is [0–7], which is used to adopt the 64QAM modulation for the Manhattan distance binary coding. And the channel equalization is LMMSE for both cases, so as to eliminate the impact of different channel types. In a simple way, we choose image as the source file, and then we can compare the simulation results of these two test cases to analyze the relation between the BER, IER, PSNR, and SSIM. And for the semantic codec, the LSCI is chosen for the semantic coding algorithm, which can be used for image and video semantic communication.

The physical layer metrics simulation results are shown in Figure 11. It is observed that, since the physical layer procedure is the same for two test cases, the Hamming distance and BER are almost the same for the two test cases. It can be observed that the BER starts to increase when the SNR is lower than 20 for both cases, which is consistent with the traditional communication performance, since both cases utilized 64QAM and did not use channel coding.

While measured with Manhattan distance and the IER, the case utilizing Manhattan distance binary coding obtained a better IER when the SNR was lower than 20. In addition, comparing natural binary coding and Manhattan distance binary coding from the perspective of semantic metrics, Manhattan distance binary coding can achieve a better PSNR and SSIM at the same BER condition. According to the BER, IER, PSNR, and SSIM curves shown in Figure 12, it can be observed that the IER is more relative to the semantics metric than the BER. This validates that the IER is a better evaluation metric than the BER for E2E semantic communication, especially in image semantic transmission scenarios.

4. Optimization for the Bit-Conversion JSCC Scheme

4.1. Minimum Manhattan Distance Constellation Mapping Scheme

Based on the simulation in Section 3.3, it can be observed that different integer-to-bit conversion coding methods will impact the received data directly. The key factor of this phenomenon is the numerical difference in the integers mapped onto adjacent constellation points. In existing wireless systems, error correction is based on bit-level and channel coding. Therefore, the bits mapped onto adjacent constellation points are based on Gray- code mapping, meaning that adjacent constellation points differ by only one bit. However, in JSCC, the channel coding is removed, and the received symbols will be directly converted to the mapped integers and then sent to the JSCC decoder. Thus, the principle of the JSCC constellation mapping scheme design should be changed to the numerical difference in integers mapped onto adjacent constellation points instead of the difference in bits.

According to this JSCC constellation mapping scheme design principle, the minimum Manhattan distance constellation mapping scheme of m-QAM modulation is proposed. And the algorithm to generate the binary encoding table of this constellation mapping scheme to be compatible with the current system, called Manhattan distance binary coding, is described.

For regular m-QAM modulation, we design a minimum Manhattan distance constellation mapper. This mapper maps the integer number pair to the constellation point according to Formula (4).

$$\mathrm{M}\left(\mathrm{p},\mathrm{q},{\mathrm{K}}_{\mathrm{m}\mathrm{o}\mathrm{d}},{\mathrm{Q}}_{\mathrm{m}}\right)=-{\mathrm{K}}_{\mathrm{m}\mathrm{o}\mathrm{d}}\times \{\left(2\mathrm{p}-{\mathrm{Q}}_{\mathrm{m}}+1\right)+\mathrm{j}\left(2\mathrm{q}-{\mathrm{Q}}_{\mathrm{m}}+1\right)\}$$

(4)

Here, ${\mathrm{Q}}_{\mathrm{m}}$ is the modulation order and ${\mathrm{K}}_{\mathrm{m}\mathrm{o}\mathrm{d}}$ is the normalization parameter of the adopted system for different m-QAM. Function $\mathrm{M}(\mathrm{p},\mathrm{q},{\mathrm{K}}_{\mathrm{m}\mathrm{o}\mathrm{d}},{\mathrm{Q}}_{\mathrm{m}})$ takes $\mathrm{p},\mathrm{q}$, the non-negative integer in the range $[0,{\mathrm{Q}}_{\mathrm{m}}+1$], as the input and produces complex-valued modulation symbols as the output. For example, in the case of 5G-64QAM,5G-16QAM modulation, the integer constellation mapping scheme generated by this formula is shown in Figure 13.

Then, for compatibility with the adopted system, binary coding should be introduced. We design an algorithm for Manhattan distance binary coding generation, as Algorithm 1 illustrates.

Algorithm 1. Manhattan distance binary coding generation
1.	Input:
2.	$\mathrm{m}-\mathrm{QAM} \mathrm{modulation} \mathrm{order} Q_m$
3.	$\mathrm{m}-\mathrm{QAM} \mathrm{standard} \mathrm{bit} \mathrm{constellation} \mathrm{mapper} d(i)$
4.	$\mathrm{Integer} \mathrm{constellation} \mathrm{mapper} M(p,q,K_{mod},Q_m)$
5.	data process:
6.	$Q_m$$-> K_{mod}$
7.	for$\mathrm{i} \mathrm{from} 0 \mathrm{to} Q_m^2-1$:
8.	$\mathbf{for} \mathrm{integer} p,q$ in range [0, $Q_m$ − 1]:
9.	$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathbf{find} p,q$$\mathrm{that} M\left(p,q,K_{mod},Q_m \right)$$==d(i)$
10.	$\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\mathbf{then} \mathrm{mapping} (p,q$$): (b\left(Q_m\ast i\right),\dots ,b\left(Q_m\ast i+Q_m-1\right))$
11.	End for
12.	End for
13.	output:
14.	Manhattan distance binary coding mapping table

The input of this algorithm, besides the m-QAM integer constellation mapper, is the modulation order ${\mathrm{Q}}_{\mathrm{m}}$ and the responding m-QAM bit constellation mapping scheme d(i) of the adopted system. The modulation mapper $\mathrm{d}\left(\mathrm{i}\right)$ takes binary digits as the input and produces complex-valued modulation symbols as the output. For example, in the case of 5G-64QAM modulation, hextuplets of bits, $\mathrm{b}\left(6\mathrm{i}\right), \mathrm{b}(6\mathrm{i}+1), \mathrm{b}(6\mathrm{i}+2), \mathrm{b}(6\mathrm{i}+3), \mathrm{b}(6\mathrm{i}+4), \mathrm{b}(6\mathrm{i}+5)$, are mapped to complex-valued modulation symbols d(i), according to Formula (5) [27]. Here, b(x) is the Gary code and x is the non-negative integer in the range $[0,{\mathrm{Q}}_{\mathrm{m}}^2-1$]. The constellation mapping scheme generated by Formula (5) is shown in Figure 14a.

$$\begin{gathered} \mathrm{d}\left(\mathrm{i}\right)={\displaystyle \frac{1}{\sqrt{42}}}\left\{(1-2\mathrm{b}\left(6\mathrm{i}\right)\left[4-(1-2\mathrm{b}\left(6\mathrm{i}+2\right)\left[2-2\mathrm{b}\left(\mathrm{b}\mathrm{i}+4\right)\right]\right]+\mathrm{j}(1 \\ -2\mathrm{b}\left(6\mathrm{i}+1\right))\left[4-(1-2\mathrm{b}\left(6\mathrm{i}+3\right)\left[2-2\mathrm{b}\left(\mathrm{b}\mathrm{i}+5\right)\right]\right]\right\} \end{gathered}$$

(5)

Then, follow the data process in the algorithm, determine the ${\mathrm{K}}_{\mathrm{m}\mathrm{o}\mathrm{d}}$ according to ${\mathrm{Q}}_{\mathrm{m}}$, and map the integer number pairs ($\mathrm{p},\mathrm{q})$ with the bits at the same constellation points; following this, the binary coding table can be generated. For example, in the case of 5G-64QAM modulation, this algorithm can generate the Manhattan distance binary coding table, as Figure 14b illustrates.

To evaluate the enhancement of this proposed scheme on the performance of semantic communication, the semantic metric and the physical layer metric introduced in Section 3 are simulated with the following three schemes: SSCC–natural binary coding, JSCC–natural binary coding, and JSCC–Manhattan distance binary coding. These three schemes all transmit with 64QAM, and the SSCC–natural binary coding scheme uses 0.5 code rate LDPC channel coding. And all three schemes retain the channel estimation and equalization of 3GPP 5G physical layers to eliminate the impact of different channel types. Simulation configurations are listed in

Table 3. Simulation configurations for the evaluation of the proposed scheme.

Test Case	JSCC–Natural Binary Coding	JSCC–Manhattan Distance Binary Coding	SSCC–Natural Binary Coding
Semantic transmission framework	bit-conversion JSCC	bit-conversion JSCC	bit-conversion SSCC
Source file	image	image	image
Semantic codec:	LSCI	LSCI	LSCI
Quantization range	[0–7]	[0–7]	[0–7]
Data-to-binary codec	natural binary coding	Manhattan distance binary coding	natural binary coding
Channel coding	NO	NO	LDPC CR = 0.5
Bit constellation mapping	3GPP 5G	3GPP 5G	3GPP 5G
Modulation	64QAM	64QAM	64QAM
Simulation SNR range	[−5~30]	[−5~30]	[−5~30]
Channel model	AWGN	AWGN	AWGN
Channel equalization	LMMSE	LMMSE	LMMSE

.

The simulation results are shown in Figure 15. As shown in Figure 15a, it can be observed that the SSCC–natural binary coding scheme has the best performance in terms of the BER. The BERs of both JSCC cases start to increase when the SNR is lower than 20, while the SSCC cases maintain no bit error until the SNR is lower than 11, which is consistent with the traditional communication performance since the SSCC uses LDPC channel coding. In addition, the JSCC–natural binary coding and JSCC–Manhattan distance binary coding achieve the same BER. However, as shown in Figure 15b, the JSCC–Manhattan distance binary coding scheme is superior in terms of IER performance to the JSCC–natural binary coding scheme. Moreover, as shown in Figure 15c, the JSCC–Manhattan distance binary coding scheme also significantly outperforms the SSCC–natural binary coding scheme within an SNR range of [5–10]. In terms of semantic performance metrics, within the SNR range of [5–10], the JSCC–Manhattan distance binary coding scheme is also significantly better than the other two schemes, by 4–6 dB. At the same time, as shown in Figure 15d, as the SSCC scheme adopts LDPC code with a code rate of 0.5, the JSCC–Manhattan distance binary coding scheme has twice the spectral efficiency of this SSCC–natural binary coding scheme.

Through the above analysis, it can be further seen that a well-designed constellation mapping can be utilized to improve the performance of semantic information transmission, and JSCC is more suitable for leveraging the advantages of semantic communication compared to SSCC. However, this minimum Manhattan distance constellation mapping scheme has a limitation: the quantization output range of semantic encoding has to be bounded to the modulation order. In other words, a lower-order modulation is required when the SNR decreases. Meanwhile, the output range of semantic quantization must also be correspondingly reduced. To address this issue, based on the minimum Manhattan distance constellation mapping scheme, we further propose a hybrid transmission scheme of JSCC and SSCC.

4.2. Hybrid JSCC/SSCC Transmission Scheme

In this chapter, a hybrid JSCC/SSCC transmission scheme for semantic communication is proposed. The principle of the hybrid scheme is that, at the transmitter, the quantized data after semantic encoding are converted into bits, and the integer-corresponding bit data are divided into two parts for transmission. The “higher-order bits” part is transmitted with a lower-order modulation concatenated channel coding to ensure transmission reliability, for which the SSCC–natural binary coding scheme can be adopted. The “lower-order bits” part can be transmitted using the JSCC–Manhattan distance binary coding scheme. The splitting position between the “higher-order and lower-order” bits can be adjusted according to the value range of the quantized output and the modulation order, thus solving the limitation that the range of the semantic quantization output must be bound to the modulation. At the receiver, the received bit data are combined and then converted back into integer data, which are sent to the upper layer of the receiver for semantic decoding. The specific data processing flow for transmission and reception are shown in Figure 16.

The data procedure step is described as below. It is assumed that the output integer data range of semantic coding and quantization is [0–7].

• The procedure steps in transmitter as following:

• Step1: convert the integer data into binary with natural binary coding.
• Step2: split the bit data blocks into two blocks; the first bit of each of the three bits is put into the “part one” block, and the last two bits are put into the “part two” block.
• Step3: transmit the “part one” block with the SSCC scheme (QPSK and 0.5 code rate LDPC coding); transmit the “part two” block with the JSCC–Manhattan distance constellation mapping scheme (16QAM and no channel coding).

• The procedure step in receiver as following:

• Step1: receive the two bits data blocks and merge them back to a whole bit data block.
• Step2: convert the received bit data into integer values with natural binary coding.

This hybrid JSCC/SSCC transmission scheme can fix the problem of the quantization output range of semantic encoding having to be bounded to the modulation order if we want to adopt the dedicated integer constellation mapping scheme. Take an example: assume the quantized output of the semantic encoding is [0–7]; if we adopt the JSCC–Manhattan distance binary coding scheme for transmission, we can only use 64QAM modulation rather than QPSK or 16QAM. When adopting the hybrid JSCC/SSCC transmission scheme, a lower-order modulation can be used. In order to evaluate the performance of this hybrid JSCC/SSCC transmission scheme, the bit-conversion SSCC and bit-conversion JSCC transmission schemes are simulated, respectively, as the baselines. In this simulation, the previous LSCI semantic encoding scheme is adopted for image transmission, and the quantized output of the semantic encoding is [0–7]. A detailed configuration of the simulation is included below:

Simulation verification-1.

The simulation configurations comparing the hybrid JSCC-SSCC transmission scheme with the bit-conversion SSCC scheme are shown in

Table 4. Simulation configurations for hybrid scheme vs. SSCC scheme.

Test Case	Modulation	Binary Codec	Channel Coding
Hybrid JSCC/SSCC transmission (QPSK + 16QAM)	QPSK (1/3 data)	natural binary coding	LDPC (CR = 0.5)
	16QAM (2/3 data)	Manhattan distance binary coding	NO
SSCC-QPSK	QPSK	natural binary coding	LDPC (CR = 0.5)
SSCC-16QAM	16QAM	natural binary coding	LDPC (CR = 0.5)

.

The simulation result is show in Figure 17. It can be observed that the BER of the hybrid JSCC/SSCC transmission scheme is better than the SSCC 16qam and worse than the SSCC-QPSK. This is consistent with the traditional communication performance, since the hybrid JSCC/SCC transmission scheme employs a portion of QPSK. In terms of the IER, the hybrid JSCC/SSCC transmission scheme shows a significant improvement, approaching the performance of the SSCC-QPSK scheme. Finally, the PSNR of the hybrid JSCC/SSCC transmission scheme is essentially close to that of the SSCC-QPSK scheme. At the same time, the JSCC/SSCC hybrid transmission scheme demonstrates approximately twice the spectrum efficiency of the SSCC-QPSK scheme, comparable to the SSCC-16QAM scheme, as shown in Figure 17d.

Simulation verification-2.

The simulation configurations comparing the hybrid JSCC-SSCC transmission scheme with the bit-conversion JSCC scheme are shown in

Table 5. Simulation configurations for hybrid scheme vs. JSCC scheme.

Test Case	Modulation	Binary Codec	Channel Coding
Hybrid JSCC/SSCC transmission (QPSK + 16QAM)	QPSK (1/3 data)	natural binary coding	LDPC(CR = 0.5)
	16QAM (2/3 data)	Manhattan distance binary coding	NO
JSCC-QPSK	QPSK	natural binary coding	NO
JSCC-16QAM	16QAM	natural binary coding	NO

.

The simulation result is shown in Figure 18. It can be observed that the BER of the hybrid JSCC/SSCC transmission scheme is better than the JSCC 16qam and worse than the JSCC-QPSK. In terms of IER metrics, the hybrid JSCC/SSCC transmission scheme demonstrates a great improvement and performs better than the JSCC-QPSK scheme. Finally, the hybrid JSCC/SSCC transmission scheme outperforms the JSCC-QPSK scheme in terms of the PSNR, with a performance gain of 3–5 dB in an SNR range of [0–5], as shown in Figure 18c. At same time, the hybrid JSCC/SSCC transmission scheme has the same spectrum efficiency as the JSCC-QPSK scheme, as shown in Figure 18d.

Based on the simulation above, it is evident that the hybrid JSCC/SSCC transmission scheme can resolve the issue that the quantization output range of semantic encoding has to be bound to the modulation order. Additionally, within the SNR range of [0–5], the semantic transmission performance is comparable to the SSCC-QPSK scheme, and the spectrum efficiency of this hybrid JSCC/SSCC scheme is twice that of the SSCC-QPSK scheme. It still maintains the advantage of the JSCC scheme in terms of bandwidth conservation. This indicates that this hybrid JSCC/SSCC scheme has specific application scenarios, especially for semantic imaging transmission in lower SNR scenarios.

5. Conclusions

To address the issue of how the semantic information can be compatible with existing wireless communication systems, we design a bit-conversion-based JSCC transmission framework and develop the specific physical layer procedures. After this, we develop a semantic communication simulation platform. Based on the bit-conversion-based JSCC transmission framework, we propose a new physical layer semantic metric, the IER. Simulations reveal that the IER is more suitable than the BER as a physical layer metric for evaluating the transmission quality of semantic communication, especially for semantic image transmission. Regarding the IER, we optimize the bit-conversion-based JSCC transmission framework. We propose a minimum Manhattan distance constellation mapping scheme for semantic communication. The simulation results indicate that this scheme could enhance the IER without compromising the BER, thereby improving the transmission quality of semantic communication. Furthermore, to address the issue regarding the coupling requirement between the quantization output range of semantic encoding and modulation order in the minimum Manhattan distance constellation mapping scheme, we propose a hybrid JSCC/SSCC transmission scheme. This scheme further decouples the semantic quantization output from the modulation method by segmenting the bits for transmission and providing a framework for the separate optimization of the semantic quantization output and transmission modulation order. Simulations demonstrate that this scheme could enhance the transmission quality of semantic communication in low SNR scenarios while saving much bandwidth and illustrating the feasibility of the bit-conversion-based JSCC transmission framework for evolution within existing wireless communication systems.

For future research directions, whether the IER has a significant correlation with all semantic encoding algorithms is expected to be studied. Additionally, the performance enhancement of the bit-conversion-based JSCC transmission framework can be a subject of ongoing research efforts.