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Abstract

High reliable and efficient image transmission is of primary importance for space communications. In the traditional space image transmission system design, the source coding module and channel coding module are separated. This separate design, although simple to be implemented, cannot explore the transmission performance to the most. In this article, we propose a joint source–channel rate allocation framework to improve the space image transmission performance. A joint rate allocation algorithm based on the packet loss rate is proposed. For certain required system transmission rate, the optimal source coding and channel coding rate pair can be selected from pre-configured code rate sets by sliding search. In addition, our design has taken into account the progressive scalability feature of the image compression results. Each of the source coding output packets is divided into several sub-packets with different levels of significance and then channel coding with different rates is applied on these sub-packets to achieve unequal error protection. Simulation results show that the proposed joint design can significantly improve the image reconstruction quality. Compared with the traditional separate design, the proposed joint design can achieve 3–5 dB performance gain in terms of peak signal-to-noise ratio.

Keywords

Space image transmission joint source–channel rate allocation unequal error protection source coding channel coding

Introduction

With the acceleration of global informatization in our society, the scope of information sensing and communication has been rapidly expanded from terrene to air, space, and even deep space. The space information networks (SIN), including the space range–related satellite communication networks and the deep space range–related remote probe communications, have drawn extensive research interests as well as large amounts of industrial capital invests in recent years. Different from communication links, the space communication links are characterized by features of significant latency, frequent disruptions, extremely low signal-to-noise ratios (SNRs), limited node resources, and so on. Due to these critical characteristics, a lot of key enabling technologies are needed to promote the development and application of SIN. Among the various technologies, high reliable and efficient image transmission technology is of primary importance, especially for deep space communication scenarios. On one hand, the remote captured images can provide the most intuitive information for human beings to understand the unknown space environment, it is highly required that the images are transmitted back to the Earth station reliably. On the other hand, the images to be transmitted are of immense amount, especially for real-time transmission cases, which puts rigorous pressure on the efficiency of the communication links.¹

Traditionally, high efficient image compression algorithms including lossless and lossy ones and advanced channel coding techniques are employed to accomplish the high reliable and efficient space image transmission. In the system design, the source coding module for image compression and the channel coding module for error protection are implemented separately. The advantage of separate design is the implementation simplicity, and the two modules can be optimized separately. However, there are also some shortcomings that hinder further promotion of the traditional separate source–channel coding system. First, when the transmission rate of the entire system is constant, the source and channel code rates are also fixed, which cannot dynamically adapt to the varying channel conditions. Second, most of the source coding techniques for the image compression have the characteristic of progressive scalability. The progressive scalability refers to the feature that the significance of the source coding output bitstream decreases gradually as the bit index corresponding to one image frame grows. Nevertheless, the traditional separate coding system which uses equal channel coding rate for different segments of the source coding output bitstreams has not considered the significant difference; it simply applies the same degree of error protection for all phases of the code stream. Obviously, the quality of image reconstruction cannot reach the optimal with this kind of equal error protection (EEP) scheme.

There is much room for the traditional separate coding system for image transmission to improve. The most efficient and direct way is to jointly design the source and channel coding modules from a systematic point of view. In fact, the idea of joint source–channel coding can be dated back to the invent of information theory, in which Shannon stated that for discrete memoryless channels (DMC) and stationary ergodic sources, joint design can be no better than separate design; but for other cases like correlated sources, such as images and videos, joint design may bring performance gains compared with separate source–channel coding. There are mainly two types of joint design. One is the integrated coding approach, by which codewords that can simultaneously accomplish the tasks of source compression and channel error protection are designed. The other is the joint configuration approach, by which parameters such as the coding rate of the two modules are jointly configured to tune the entire system to best match the channels. Both the types of approaches have been investigated extensively in the context of terrestrial communication scenarios. For example, Chande and colleagues² divided the source compression output stream into fixed bit lengths and used different channel coding rate for each source packet. Nosratinia et al.³ established an empirical model based on the channel decoding error probability to achieve the optimal rate allocation for joint source–channel coding. However, very limited work has been done on the joint source–channel coding design for space image transmission.

In this work, we aim to propose a joint source–channel coding design for high reliable and efficient space image transmission. Specifically, our design is based on the joint rate allocation approach due to its lower complexity than the integrated coding approach. A joint rate allocation algorithm based on the packet loss rate is proposed. For certain required system transmission rate, the optimal source coding and channel coding rate pair can be selected from pre-configured code rate sets by the proposed algorithm. In addition, our design has taken into account the progressive scalability feature of the image compression results. Each of the source coding output packets is divided into several sub-packets with different levels of significance and then channel coding with rates from lower to higher is applied on these sub-packets to achieve unequal error protection (UEP)⁴ of the source. Simulation results show that the proposed scheme can significantly improve the image reconstruction quality by 3–5 dB compared with the traditional separate coding system.

The rest of this article is organized as follows. Section “Related work” summarizes the state-of-art of the space image transmission technologies. In section “The framework of joint source–channel rate allocation for space image transmission,” the system model of space image transmission and the proposed joint source–channel rate allocation framework are presented. Details about the joint rate allocation scheme, the UEP operations, and the algorithm for selection of the optimal rate pair are presented in section “The proposed joint source–channel rate allocation scheme.” Section “Simulation results” evaluates the proposed joint source–channel rate allocation–based transmission system with extensive simulations, followed by the concluding remarks and future research plans in section “Conclusion and future work.”

Related work

The traditional space image transmission system is mainly composed of two separate modules: high efficient source coding module for image compression and the high gain channel coding module for error protection.

For the source coding module, the widely used image compression techniques include Joint Photographic Experts Group (JPEG),⁵ JPEG2000,⁶ ICER,⁷ and Set Partitioning in Hierarchical Trees (SPIHT),⁸ in which the JPEG is a lossy image compression algorithm based on Discrete Cosine Transform (DCT). In high bit rate, the image restoration is better, while in low bit rate, the image has obvious block effect. The JPEG2000 is based on Discrete Wavelet Transform (DWT), when the bit rate is high, the image restoration quality is better, and the image restoration quality is still good in low bit rate. However, the encoding of the algorithm suffers from high complexity. The high complexity of the algorithm poses a serious problem for hardware implementation. The ICER image compression algorithm proposed by NASA is basically very similar to the JPEG2000 algorithm, so ICER holds the same pros and cons as JPEG2000. The complexity of the SPIHT algorithm is low and the image restoration quality can approximate to JPEG2000 at the same compression bit rate.

For the channel coding module, traditionally used codes include the Reed–Solomon (RS) codes,⁹ convolution codes,¹⁰ and concatenated codes.¹¹ In recent years, advanced codes such as the Turbo codes¹² and Low-Density Parity Check (LDPC) codes¹³ have been used more and more frequently. For the decoding of Turbo and LDPC codes, when using the Belief Propagation (BP) decoding method¹⁴ and if the number of decoding iterations is enough, the decoding performance can approach the Shannon limit at the expense of high complexity requirements. E Arikan¹⁵ proposed Polar codes in 2009 and the construction of which is based on channel polarization. Polar codes are proved to achieve the symmetric capacity of the binary-input discrete memoryless channels (BDMCs), with low encoding and decoding complexity. In addition, when using the Successive Cancelation List–Cyclic Redundancy Check (SCL-CRC) decoding method¹⁶ of Polar codes, the decoding performance of Polar codes is better than the LDPC codes under BP decoder.

For the joint source–channel rate allocation transmission system, Chande and Nosratinia have proposed some joint transmission schemes in Kwasinski et al.² and Nosratinia et al.,³ respectively, for the terrestrial communication scenarios. Compared with the terrestrial channels, space channels are characterized by features of significant latency, frequent link disconnections, high error rate, and limited network resources (e.g. downlink/uplink bandwidth and spacecraft/satellite onboard-processing capability). Therefore, the joint source–channel rate allocation scheme with low computational complexity and high image reconstruction quality has become the focus of the research. To the best of the authors’ knowledge, the design of the joint source–channel coding scheme for space image transmission is very limited. Abdessalem et al.¹⁷ analyzed the joint source–channel coding scheme based on LDPC codes. LDPC codes can approach the Shannon limit and perform well under moderate SNR conditions, but not so good at low SNR regime. In addition, as mentioned above, the decoding complexity of LDPC codes is usually high.

The framework of joint source–channel rate allocation for space image transmission

System model of space image transmission

Figure 1 shows the system model of space image transmission. The various types of space images are first compressed by the source coding module and then feed into the channel coding module. After being transmitted through the space channels, the space images are reconstructed at the receiver end by inverse playing the operations of the transmitter, that is, the channel decoding followed by the source decoding. As is introduced in the “Related work” part, both modules have various choices of techniques. In this work, we adopt the SPIHT algorithm and the Polar codes to implement the source coding and channel coding modules, respectively, due to their superiorities over their counterparts. Next, we will briefly introduce the SPIHT algorithm and the Polar codes.

Figure 1.

System model of the space image transmission.

The basic idea of the SPIHT algorithm is that the image data are first decomposed by multi-layer wavelet and then the different sub-band coefficients with multi-resolution characteristics are used to constitute a tree structure. Specifically, the sub-band coefficients in low frequency constitute the set of root node of the tree, and the sub-band coefficients in high frequency constitute the descendant node set of the root nodes. The encoding process begins at the root node set of the tree structure and then encoding along the tree structure layer by layer. The coefficients in low frequency that represent the image information are encoded first, and the coefficients in high frequency which represent the detail information of the image are then encoded. The output stream has the characteristic of progressive scalability. The notable feature of the SPIHT algorithm is that it has low complexity and high image restoration quality; thus, it is suitable for deep space communication.

Polar codes are the first ever provably capacity achieving codes, which are applicable to any BDMC and also have good performance under the additive white Gaussian noise (AWGN) channel. Compared with other advanced channel codes, such as the LDPC codes and Turbo codes, Polar codes have multiple advantages: first, Polar codes are theoretically capacity achieving, while LDPC codes and Turbo codes are just capacity approaching; second, the recursive encoding and decoding structure of Polar codes leads to low implementation complexity; third, Polar codes can achieve remarkable performance without random coding; finally, the rate of Polar codes can be adjusted easily and consistently to adapt to different channel conditions.

The joint source–channel rate allocation framework

Different from the traditional separate design of the source and channel coding modules, we aim to propose a joint rate allocation–based transmission system. Specifically, the rate of SPIHT and Polar codes are jointly configured, and the source coding output packets are divided into sub-packets for UEP purpose. Figure 2 shows the general framework of the proposed design.

Figure 2.

Framework of the proposed joint source–channel rate allocation–based space image transmission system.

As is shown in Figure 2, the bitstream of the original images after source coding is divided into several successive packets, and each packet has equal length of $L$ bits. Then, every packet is further divided into $N$ sub-packets with length of $K$ bits, so $L = NK$ . For each sub-packet, a 16-bit CRC header is added. The sub-packet together with its CRC header is dumped into the channel coding module, where the input bits are encoded by Polar codes, with code rate appropriately selected from a channel coding rate set, denoted by $ℝ_{c}$ . After being transmitted through the deep space channel, the first step at the decoding end is to decode the $N$ sub-packets and then check each sub-packet with CRC. During this receiving process, if an error is checked, we will end the receiving process of the current packet and discard the erroneous sub-packet and all the subsequent packets in order to prevent the error propagation. The SPIHT source decoder restores the image using the correctly received data only. Meanwhile, the packet loss rate of the channel feedback can be received at the transmitter. In order to simplify the description, we use $g$ to denote the packet loss rate in this article.

The packet loss rate¹⁸ is defined as the ratio of the number of packets discarded by the receiver to the total number of packets generated by the SPIHT encoder. The value of the parameter $g$ can not only reflect the channel condition but also indicate whether the selected code rate combination is optimal. When the packet loss rate is high, it means that the channel environment is poor and the selected bit rate combination is not optimal, while the low packet loss rate indicates that the channel condition is well and the selected bit rate combination is suitable for the channel condition. Therefore, the key issue is how to dynamically adjust the source and channel coding rate and the level of error protection for each packet.

The proposed joint source–channel rate allocation scheme

The necessity of joint source–channel coding rate allocation

For the progressive scalability of image compression stream, the relationship between the distortion and the coding rate satisfies the rate distortion theory.¹⁹ As shown in Figure 3(a), the distortion of the image compression stream ( $D_{s}$ ) decreases as the image compression ratio ( $R_{s}$ ) goes up. During the channel coding process, the channel decoding error probability ( $P_{b}$ ) increases along with the channel coding rate ( $R_{c}$ ), as shown in Figure 3(b).

Figure 3.

The rate distortion curve: (a) the source rate distortion curve, (b) the channel bit error rate curve, and (c) the rate distortion curve of transmission system.

The relationship of system transmission rate ( $R_{T}$ ), source compression ratio, and channel coding rate is $R_{T} = R_{s} / R_{c}$ , and $R_{T}$ is constant. Figure 3(c) shows that the system distortion curve is influenced by $R_{s}$ and $R_{c}$ , which indicates that the restored image distortion rate ( $D$ ) and the distortion rate caused by $R_{s}$ ( $D_{s}$ ) follow the law of $D > D_{s}$ . According to the point $(R_{s 1}, D_{1})$ in Figure 3(c), at first, $D_{s}$ is quite large due to the small value of $R_{s}$ . Even though the channel coding could suppress the channel noise largely, which means that $D$ equals $D_{s}$ , $D$ is still very large. At this time, the source compression coding distortion is the main reason for the restored image distortion. Then, as $R_{s}$ increases, $D_{s}$ will decrease and at the same time, $R_{c}$ will increase. Once $R_{c}$ increases to the extent, the receiver would generate a large amount of channel decoding errors for lack of sufficient protection from the channel coding. As $R_{s}$ increases, the distortion caused by the channel decoding errors is greater than the gain of the image quality, which is $D > > D_{s}$ , as the point $(R_{s 2}, D_{2})$ shown in Figure 3(c). There is a critical point $(R_{s 0}, D_{0})$ , where the distortion of restored image is the minimum. Thus, how to find the critical point $(R_{s 0}, D_{0})$ accurately is the main purpose of the joint rate allocation scheme.

Joint source–channel coding rate allocation by selection from discrete rate sets

In practical system design, for implementation simplicity, both the source coding rates and channel coding rates are selected from discrete rate sets. Let $ℝ_{s}$ and $ℝ_{c}$ denote the source coding rate set and channel coding rate set, respectively, that is

$\begin{matrix} ℝ_{s} & = {R_{s 1}, R_{s 2}, \dots, R_{sm}, \dots, R_{sM}}, R_{s} \in ℝ_{s} \\ ℝ_{c} & = {R_{c 1}, R_{c 2}, \dots, R_{cm}, \dots, R_{cM}}, R_{c} \in ℝ_{c} \end{matrix}$ (1)

where $M$ is total number of source or channel coding rates and $m$ denotes the rate index. To perform joint source–channel rate allocation, any rate pair $(R_{sm}, R_{cm})$ could be selected, and the system coding rate $R_{T}$ is fixed as

$R_{T} = \frac{R_{s 1}}{R_{c 1}} = \frac{R_{s 2}}{R_{c 2}} = \dots = \frac{R_{sm}}{R_{cm}} = \dots = \frac{R_{sM}}{R_{cM}}$ (2)

In this article, we select the “Mars Rock” and the “Moon Surface” images as the test images, which both have a standard size of 512 $\times$ 512 and a gray scale of 8 bits. Figure 4(a) shows the “Mars Rock” standard test image, and Figure 4(b) shows the “Moon Surface” standard test image.

Figure 4.

The standard test images used in this article: (a) the photo of Mars Rock and (b) the photo of Moon Surface.

Select the “Mars Rock” image as the test object. Using the SPIHT as the source compression algorithm and Polar codes as the channel code transmitting over an AWGN channel whose SNR is 2.5 dB, fix $R_{T}$ to be 2.0 bit per pixel (bpp). The source coding rate set is set to be $ℝ_{s} = {0.25, 0.35, 0.4, 0.5, 2 / 3, 8 / 11, 8 / 10, 8 / 9, 1.0}$ , and the channel coding rate set is set to be $ℝ_{c} = {0.125, 0.15, 0.175, 0.2, 0.25, 1 / 3, 4 / 11, 4 / 10, 4 / 9, 0.5}$ . Then, we can get the peak signal-to-noise ratio (PSNR) simulated under different rate pairs by varying the value of $R_{s}$ , as is shown in Figure 5.

Figure 5.

The effect of source–channel rate on image PSNR.

In Figure 5, the curve has a peak point, indicating that there is a set of $R_{s}$ and $R_{c}$ that can get the optimal performance of the restored image. Moreover, the closer the values of $R_{s}$ and $R_{c}$ to the best combination, the better the image restoration quality.

The UEP

In many practical communication systems such as wireless networks, data can be partitioned into several parts that have different degrees of significance. Traditional EEP approach is usually not the optimal way to guarantee the quality of the important data. Hence, UEP is proposed to make the best use of the bandwidth.

UEP is one of the joint source–channel coding methods, which is proposed relatively to EEP. When the channel condition is poor, EEP uses the same degree of error protection for all bitstreams, thus the important bitstreams are not sufficiently protected, resulting in the degradation of decoding quality. In contrast, UEP applies different degrees of channel protection to bitstreams with different levels of significance. More specifically, those more important bitstreams are protected in a higher degree and the less important bitstreams are protected in a lower degree.

It is a common method to implement UEP through channel coding technology. For the traditional channel coding method, the lower the bit rate, the better the error correction and detection performance. According to this characteristic, in the process of channel coding, the source coding output bitstreams with higher importance level are protected by codewords with lower channel coding rate, while the bitstreams with lower importance level are protected by codewords with higher channel coding rate so that different levels of fault tolerance protection are achieved.

As is described in the system model part, each packet is divided into $N$ sub-packets in our design. According to the progressive scalability feature of image compression results, the significance of the $N$ sub-packets decreases one by one. Therefore, in order to perform UEP, the channel coding rates for different sub-packets can be varied from lower than $R_{c}$ to higher than $R_{c}$ , by making the effective coding rate for the whole packet equal to $R_{c}$ . Specifically, corresponding to each channel code rate $R_{cm} \in ℝ_{c}$ , there exists an UEP code rate set ${r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}}$ , the values of which can be calculated according to the following rules²⁰

$R_{cm} = r (r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N})$ (3)

$r_{cm}^{1} < r_{cm}^{2} < \dots < r_{cm}^{N}$ (4)

$f (r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}) = A$ (5)

where $r (\cdot)$ in equation (3) denotes the function that calculates the coding rate for the entire packet using the coding rates of the sub-packets. Since all the sub-packets are of equal length in this work, the form of $r (\cdot)$ is as follows

$r (r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}) = \frac{N}{\frac{1}{r_{cm}^{1}} + \frac{1}{r_{cm}^{2}} + \dots + \frac{1}{r_{cm}^{N}}}$ (6)

Equation (4) gives the rule that lower code rates should be assigned to those earlier sub-packets due to higher degree of significance. Equation (5) means that certain relationship which is described by $f (\cdot) = A$ (where $A$ is just a trivial constant) among ${r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}}$ could be further applied in addition to equation (4). For example, we can explicitly force that each sub-packet should be more strongly protected than its following packet with a two times lower coding rate. That is, the rate relationship described by $f (\cdot) = A$ in equation (5) can now be clearly expressed as

$r_{cm}^{n + 1} - 2 r_{cm}^{n} = 0$ (7)

where $n \in {1, 2, \dots, N}$ denotes the sub-packet index.

Therefore, the source coding and channel coding rate pair of the image transmission system is $(R_{sm}, r (r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}))$ . The selection of which rate pair $(R_{sm}, R_{cm})$ is used for joint rate allocation, and the $N$ channel coding rates $(r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N})$ for sub-packets to composite a particular channel code rate $R_{cm}$ is for UEP. Therefore, we have combined the joint source–channel code allocation technique and the UEP technique in this article.

The algorithm for optimal allocation of the source–channel rate

In this article, the proposed joint source–channel rate allocation method combines the rate allocation with the UEP technique to achieve the optimal allocation of source–channel rate. Next, we will present the details of the proposed scheme. The scheme is composed of two phases, corresponding to two algorithms, including Algorithm 1 for initialization and Algorithm 2 for rate pair selection.

Algorithm 1

Initialization.

1: The system transmission rate

\leftarrow R_{T}

;2: The source coding rate set

\leftarrow ℝ_{s} = {R_{s 1},

R_{s 2}, \dots, R_{sM}}

;3: The channel coding rate set

\leftarrow ℝ_{c} = {R_{c 1}, R_{c 2}, \dots, R_{cM}}

;4: The number of sub-packets for UEP

\leftarrow N

;5: Calculate the channel code rate set for UEP, by equations (3)–(5);6: for

m = 1 : M

do7: Substitute

R_{cm}

in equation (3), and then using the constraints expressed by equations (4) and (5) to solve the values of

N

UEP code rates

(r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N})

8: end for9: Determine the initial search index

m

by channel state prediction or simply start from the middle index, that is,

m = M / 2

.10: return The starting search rate pair

(R_{sm}, r (r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}))

Algorithm 2

The optimal rate pair selection.

1: Initialize the starting search rate pair

(R_{sm}, r (r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}))

by Algorithm 1;2: Calculate the packet loss rate

g_{m}

;3: Regard the code rate pair

(R_{s (m + 1)}, r (r_{c (m + 1)}^{1}, r_{c (m + 1)}^{2}, \dots, r_{c (m + 1)}^{N}))

as the transmission combination and

R_{sm} < R_{s (m + 1)}

, then calculate

g_{m + 1}

;4: Regard the code rate pair

(R_{s (m - 1)}, r (r_{c (m - 1)}^{1}, r_{c (m - 1)}^{2}, \dots, r_{c (m - 1)}^{N}))

as the transmission combination and

R_{s (m - 1)} < R_{sm}

, then calculate

g_{m - 1}

;5: Compare

g_{m + 1}

g_{m - 1}

with

g_{m}

, there are three cases:6: Case 1:7: if

g_{m + 1} > g_{m}

g_{m - 1} > g_{m}

then8: return

(R_{sm}, r (r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}))

as the optimal rate pair;9: end if10: Case 2:11: if

g_{m - 1} > g_{m} > g_{m + 1}

then12: for

i = 1 : (M - m - 1)

do13: search

(R_{s (m + i)}, r (r_{c (m + i)}^{1}, r_{c (m + i)}^{2}, \dots, r_{c (m + i)}^{N}))

14: until

g_{m + i} < g_{m + i + 1}

15: return

(R_{sm}, r (r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}))

as the optimal rate pair;16: end for17: end if18: Case 3:19: if

g_{m - 1} < g_{m} < g_{m + 1}

then20: for

i = 1 : (m - 2)

do21: search

(R_{s (m - i)}, r (r_{c (m - i)}^{1}, r_{c (m - i)}^{2}, \dots, r_{c (m - i)}^{N}))

22: until

g_{m - i} < g_{m - i - 1}

23: return

(R_{sm}, r (r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}))

as the optimal rate pair;24: end for25: end if

By Algorithm 1, the main settings of the system are configured, including the system transmission rate, the source coding rate set, the channel coding rate set, and the UEP rate set that assembles each individual element of the channel coding set. Based on these basic settings, the starting search rate pair is determined and returned by Algorithm 1 for later use in Algorithm 2. It should be noted that the channel state prediction method for the initial search index determination in Algorithm 1 is based on the fact that space channels are usually memory channels, whose dynamic natures such as burst errors could be modeled by the Markov process. Therefore, the Markov decision process–based channel state prediction strategy could be developed. We leave this issue to the future work, while in this article, we simply choose the middle index as the initial search index.

By Algorithm 2, a searching procedure is carried out from the starting search rate pair generated by Algorithm 1 to find out the optimal rate pair for transmission. The basic idea is to use a “sliding window” to locate the optimal rate pair based on the loss rates of the rate pairs within the sliding window. The window is initialized as the three rate pairs including the starting search rate pair and its two neighbors. The sliding direction is guided by the rate pair with the minimum loss rate. If the center rate pair in the window has the minimum loss rate, then the sliding search process ends, and the center rate pair is returned as the final result. As described in Algorithm 2, when comparing the packet loss rate $g_{m}$ with its two neighbors, there are three cases in the searching procedure. If $g_{m + 1} > g_{m}$ and $g_{m - 1} > g_{m}$ , which means $g_{m}$ is the minimum loss rate, then output $(R_{sm}, r (r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N}))$ is the optimal rate pair. If $g_{m - 1} > g_{m} > g_{m + 1}$ , keep search in the direction of $(R_{s (m + i)}, r (r_{c (m + i)}^{1}, r_{c (m + i)}^{2}, \dots, r_{c (m + i)}^{N}))$ until the code rate pair that satisfies $g_{m + i} < g_{m + i + 1}$ is found. If $g_{m - 1} < g_{m} < g_{m + 1}$ , keep search in the direction of $(R_{s (m - i)}, r (r_{c (m - i)}^{1}, r_{c (m - i)}^{2}, \dots, r_{c (m - i)}^{N}))$ until the code rate pair that satisfies $g_{m - i} < g_{m - i - 1}$ is found.

Simulation results

In this part, we give some simulation results to demonstrate the advantages of the proposed joint source–channel rate allocation–based transmission framework as well as the proposed rate allocation algorithm. The images used for simulations are “Mars Rock” and “Moon Surface.” We use the SPIHT as the source compression algorithm and use Polar codes as the channel code. The simulations are carried out over AWGN channel with $E_{b} / N_{0}$ ranging from 0 to 4 dB, which is the typical SNR range for space communication scenarios.²⁰ The system transmission rate $R_{T}$ is fixed to be 2.0 bpp, and the source–channel coding rate pair of the traditional separate coding system is set as $(0.5, 0.25)$ . The number of sub-packets for UEP is $N = 2$ and each sub-packet has 500 bits. The discrete source coding and channel coding rate sets of the proposed joint source–channel code allocation scheme are as follows:

$\begin{matrix} ℝ_{s} = {0.25, 0.3, 0.35, 0.4, 0.5, 2 / 3, 8 / 11, 8 / 10, 8 / 9, 1.0} \\ ℝ_{c} = {0.125, 0.15, 0.175, 0.2, 0.25, 1 / 3, 4 / 11, 4 / 10, 4 / 9, 0.5} \end{matrix}$

Equation (7) is used together with equations (4) and (6) to calculate the channel code rate set for UEP, that is, $(r_{cm}^{1}, r_{cm}^{2}, \dots, r_{cm}^{N})$ .

First, the rationality of the pre-configured source coding rate set is verified. The minimum source coding rate in the set is 0.25 bpp and the corresponding compression ratio is 32:1, while the maximum source coding rate in the set is 1 bpp and the corresponding compression ratio is 8:1. Figure 6(a) and (b) shows the reconstructed images of “Mars Rock” and “Moon Surface,” with the compression ratio being 8:1. And Figure 6(c) and (d) shows the reconstructed images with the compression ratio being 32:1. It can be seen that the recovery results of “Mars Rock” and “Moon Surface” under different compression ratios all have acceptable reconstruction quality, proving that the pre-configured set of source coding rate is appropriate.

Figure 6.

Recovery results of the Mars Rock and Moon Surface images under different compression ratio: (a) compression ratio is 8:1 (PSNR = 33.07 dB), (b) compression ratio is 8:1 (PSNR = 35.46 dB), (c) compression ratio is 32:1 (PSNR = 25.80 dB), and (d) compression ratio is 32:1 (PSNR = 28.09 dB).

Then, we verified the rationality of the pre-configured channel coding rate set by observing the corresponding bit error rate (BER) performance of each channel code rate. The AWGN channel is used for test, and the results are shown in Figure 7. The lowest rate of the Polar codes is 0.125, and the highest is 0.5. It can be seen that with the pre-set channel code rate, the performance of Polar codes is in a rational range for image transmission, for example, BER ranges between $10^{- 4}$ and $10^{- 2}$ when the $E_{b} / N_{0}$ is 2.5 dB. It can also be seen that the lower the code rate, the better the decoding performance, which verifies that the performance of Polar codes is consistent with the performance of classical channel coding.

Figure 7.

The BER performance of Polar codes with different code rates.

Finally, we verified the performance of the proposed joint source–channel rate allocation–based transmission system. In Figures 8 and 9, the simulation results of the traditional separate source–channel coding–based transmission system are compared among that of the joint rate allocation without UEP technique and the proposed joint design system in this article. It can be seen that under different channel conditions, that is, when $E_{b} / N_{0}$ varies, the proposed transmission system is stably better than the joint rate allocation without UEP technique and the traditional separate transmission system. In the simulation, the image reconstruction quality is measured by PSNR. Compared with the traditional separate source–channel coding–based transmission system, the joint rate allocation without UEP technique transmission system has an average improvement of 2–3 dB in terms of PSNR, while the proposed transmission scheme can achieve 3–5 dB performance gain in image reconstruction quality. As has been described in previous sections, the performance gain comes from the joint rate configure of the two coding modules and the UEP processing, which can tune the system to best match the current channel condition and meanwhile give more protection for source coding packets that have stronger significance.

Figure 8.

The PSNR performance of Mars Rock transmitted over AWGN channel.

Figure 9.

The PSNR performance of Moon Surface transmitted over AWGN channel.

Conclusion and future work

In this article, we proposed a high reliable and efficient space image transmission framework that combines the joint rate allocation and UEP technology. The SPIHT algorithm and the Polar codes are adopted as the source coding and channel coding techniques. An algorithm for selection of the optimal source and channel rate pair based on sliding comparison of the loss rates is proposed. Meanwhile, the progressive scalability of the image compression is considered by applying UEP coding on the source coding output. Results show that compared with the traditional separate source–channel coding–based transmission system, the proposed scheme can provide an image reconstruction quality improvement of 3–5 dB in terms of PSNR.

For the future work, we plan to take investigations on the impact of number of UEP levels and the varying of UEP code rate sets on the transmission performance. In addition, the dynamic nature of space channels will also be considered. Performance-enhancing methods such as the channel state prediction–based rate pair initialization will be investigated.

Footnotes

Academic Editor: Katsuya Suto

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This research was sponsored in part by the National Natural Science Foundation of China (Grant Nos 61371102,91638204,61001092,and 61201144),the Shenzhen Fundamental Research Project (Grant No. JCYJ2016032816 3327348),and the Natural Science Foundation of Guangdong Province (Grant No. 2015A030310343).

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