Abstract — This paper presents sub-block design of low-density parity-check (LDPC) code as the efficient channel coding technique for JPEG image transmission over Rayleigh fading channel. The code is used as forward error correction (FEC) technique to protect transmitted source data over the channel. The sub-block encoder is designed with two different code rates of 0.769 and 0.935, and two different block sizes of 1057 and 4376. The performance of sub-block encoder design is evaluated by bit error rate (BER) improvement 50% and peak signal-to-noise ratio (PSNR) more than 30 at 8 dB SNR.

I. INTRODUCTION

Wireless multimedia service is an important and high efficient transmission is needed for digital communication. Communication reliability and spectrum efficiency are two aspects in part of communication system. Consequently, both efficiency and reliability are considered in this paper by designing of sub block encoder of high rate LDPC code over Rayleigh fading channel to improve the performance and quality of received images.

Forward error correction (FEC) techniques are one of many available tools made for achieving consistent data transmission, which is used in many applications such as DVB2 (Digital Video Broadcast 2), magnetic recorder system, optical storage system, etc. Low-density parity-check (LDPC) codes was introduced by Gallager [1] in 1962 and it was rediscovered by Mackay and Neal [2] as one of many kinds of linear block codes that have been vastly studied in communication system. In [3], Mackey and Davey explored whether Gallager codes are useful for high rates (R>2/3) and small block lengths (N<5000) and showed that they could outperform Reed Solomon code. Ryan and Yongqing [4,5] proved high rate LDPC codes have a good performance. After that, sub-block

encoder is designed for high rate LDPC that can keep the quality and improve the performance [6]. The accuracy for sub block encoder of LDPC is improved to enhance the performance for image transmission when code length increases [7]. In this paper, sub block design of high rate LDPC code is used to get high performance via fading channel for JPEG image transmission.

This paper is organized as follows. In Section II, LDPC code algorithm is introduced. Section III presents the methodology. The simulation results are in Section IV. Finally, the conclusion is made in Section V.

II. LDPC CODE

A. LDPC Encoding

The LDPC encoding has a linear complexity. The encoding transforms a message into a codeword. For systematic code, this means adding parity bits. A simple scheme is to exploit the relationship between codeword and the parity-check matrix H . We define a codeword with c dimension of 1 n× and the corresponding matrix parity check H with dimension of ( )n k n− × and 0 are a vector

with dimension of ( )n k n− × . The encoding process uses modulo-2 addition or exclusive-or (XOR) operation. The relationship between the party matrix H and codeword c can be written as equation (3).

TcH = 0 (3)

Equation (4) is to transpose both sides of equation (3).

T THc = 0 (4)

We define a systematic codeword c as the follows,

Sub-block Encoder of High-Rate LDPC Code over

Fading Channel for Image Transmission

Tanaporn Payommai, Werapon Chiracharit and Kosin Chamnongthai Department of Electronic and Telecommunication Engineering

Faculty of Engineering King Mongkut’s University of Technology Thonburi

126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand E-mail: 52530019@ st.kmutt.ac.th

978-1-4673-2025-2/12/$31.00 ©2012 IEEE

1 2 1 2.... | .... [ ]n k kp p p m m m−⎡ ⎤= =⎣ ⎦c p m (5)

where the parity bits are positioned at the front part

and the message bits are at the back part. In this scheme, the encoding can be done efficiently.

The transpose of codeword c in equation (6) can be

written as

⎡ ⎤⎢ ⎥⎣ ⎦

T pc =

m (6)

Substituting equation (6) into equation (2), the parity-

check equation can be derived, for example, given that a parity-check matrix H of a (3, 7) code is

1 0 0 0 1 1 10 1 0 1 1 0 10 0 1 1 0 1 1

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

H . (7)

Equation (8) is rewritten as

1

2

3

1

2

3

4

001 0 0 0 1 1 100 1 0 1 1 0 10

0 0 1 1 0 1 1000

pppmmmm

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎡ ⎤ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥= =⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦⎣ ⎦

T THc = 0. (8)

Then the parity-check equations are

1 2 3 4

2 1 2 4

3 1 3 4

000

p m m mp m m mp m m m

+ + + =+ + + =+ + + =

, (9)

where ‘+’ is a modulo-2 addition or an XOR operation. The parity bits can be then found from

1 2 3 4

2 1 2 4

3 1 3 4

p m m mp m m mp m m m

= + += + += + +

, (10)

B. LDPC Decoding The decoding algorithm used for LDPC codes was

discovered independently and comes under different names.

The most common is the belief propagation algorithm, the message passing algorithm and the sum-product algorithm. In the log-domain sum-product algorithm, the message passes between check nodes and variable nodes. In each pass the log likelihood ratio is recorded for its probability of its likely symbol.

Tanner graph is an intuitive way in understanding the LDPC decoder. The graph can be drawn directly from the H matrix as shown in Fig. 1

1 0 0 0 1 1 10 1 0 1 1 0 10 0 1 1 0 1 1

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

H .

Figure 1. Parity-check matrix and its Tanner graph.

C. Sub-block Encoder Designed

The encoder complexity can be reduced by encoding systematic codeword c sub-block. It is defined by using the parity bits positioned at the front part, the back part and the middle part which is between the message bits [6] as the follows,

1 1 2 2 3 4 3p m m p m m p⎡ ⎤= ⎣ ⎦c (11)

In this scheme, the encoding can protect and keep quality of the received image.

III. METHODOLOGY

A. LDPC Encoder for Image Transmission The configuration of image transmission system is shown

in Fig. 2. The RGB color image data is compressed by using JPEG compression. After compression, the compressed

Figure 2. Block diagram for image transmission system.

image is encoded by sub block design of LDPC encoder and passed into binary phase shift keying (BPSK) modulation over Rayleigh fading channel. The reverse process is shown by the receiver part.

B. Rayleigh fading channel The system is used by fading model in Fig. 3, which is

widely used for the performance evaluation of the error correcting code.

Fig. 3 Fading channel model.

Correspondingly, k k k ky a x n= + where the coefficient

variable ka is a random variable which obeys Rayleigh fading channel which known as channel state information (SI). kn is additive white Gaussian noise (AWGN) noise.

IV. SIMULATION RESULTS AND DISCUSSIONS

In this section, the simulation results of the image transmission using the proposed LDPC code as channel coding with BPSK modulation via fading channel at various noise levels are shown.

We examine the system performance with subjective received images visualization, bit-error-rate (BER) and peak-signal-noise-ratio (PSNR), respectively. In the simulation, Baboon and Lena jpeg images are tested with various levels of noises at high rate of 0.769 and 0.935, with block size of 1057 and 4376 in order to evaluate the performance of the proposed channel coding. The parameters of the simulation are listed in Table I. To select the best codes among designed code, Parity Position of sub block encoder at the front part, the middle part and the back part with rate 1: 1: 1. We simulate the performance and compare result in fading channel.

TABLE I CODE PARAMETERS WITH BOTH BLOCK SIZE

Code 1 Code 2 Code 3

Block size (N) 1057 1057 4376 Parity (P) 244 69 282

Message (M) 813 988 4094 Code rate (R) 0.769 0.935 0.935

Parity Position of sub block encoder

1 : 0 : 1

1 : 1 : 1

1 : 1 : 1

Iterations 20

As the result of the bit error rate curves in Fig 3, we can see that sub-block design of high rate LDPC can achieve good performance for image transmission. The peak signal-

to-noise ratios of the received images are show in Fig. 4. Fig. 5 shows the comparison of the received images.

The objective measured quality of the received images can be evaluated by PSNR calculated from the following equation (12).

21 ( , ) ( , )

y x

PSNR g x y g x yL P

∧⎡ ⎤= −⎢ ⎥× ⎣ ⎦∑∑ (12)

where ( , ), ( , )g x y g x y∧

represent the grayscale values of any pixels in an original image and a recovered image, respectively. ,L P represent the width and height of the image, respectively.

Figure 3. Image transmission BER of sub-block encoder design of LDPC

Code using 20 iterations.

From the simulation results, it shows that the sub-block encoder of high rate LDPC codes perform well with iterative decoding and achieves a good performance in image transmission over fading channel. The BER curves of the sub-block design are shown in Fig. 3, Code 1 and Code 2 have the same code length is 1057. We can see that when BER 10-4, the performance of coding gain Code 1 is 2.5 dB better than Code 2. We also found that the same code rate of Code 2 and Code 3 is 0.935. The performance of coding gain Code 3 is 0.5 dB better than Code 2. From the results, we also compare our result to an existing published works proposed by Yongqing et al. [5]. Yongqing’ s LDPC has Code 1 (N = 1057 , R =0.769), Code 2 (N = 1057 , R =0.935) and Code 3 (N = 4376 , R =0.935). From Yongqing’ s LDPC result, when BER 10-4, Code 1 and Code 2 have the same code length is 1057. Coding gain of Code 1 is 5 dB better than Code2. Code 1 and Code 2 have the same code rate is 0.935. Coding gain of Code 3 is 1dB better than Code2. However, the performance sub-block encoder of high rate LDPC code is better than Yongqing’ s LDPC code. At the same code length (N=1057), we can see that the sub-block encoder of LDPC code can improve the performance 50% while the same code rate is 0.935 with 50% improvement. The PSNR curves of the recovered images at three kinds are shown in Fig. 4.

Figure 4. PSNR of three kinds of sub-block encoder design of LDPC code.

(a) N= 1057, R = 0.769 (b) N= 1057, R = 0.769

(c) N= 1057, R = 0.935 (d) N= 1057, R = 0.935

(e) N= 4376, R = 0.935 (f) N= 4376, R = 0.935

Figure 5. Comparison of the transmitted images for three rates at the SNR equal 8 dB.

The Comparison of the transmission images at 8b oE N dB= , The PSNR of code 1, Code 2 and Code 3 are about 31, 35 and 44, respectively. The images are shown in Fig. 5. The proposed sub-block encoder designs of high rate LDPC code can achieve satisfied performance to keep a good quality of the transmitted image

V. CONCLUSIONS

The sub-block encoder design of high rate LDPC code, a channel coding applied to jpeg image transmission via fading channel has been presented in this paper. The simulation results show a good performance for correcting data error. The proposed sub-block encoder design of high rate LDPC code can reduces bit error when code length increasing and keeps sufficiently quality of the received image for image communication. The objective performance is evaluated by BER and PSNR.

ACKNOWLEDGMENT

This paper is finished finely. Thanks to friends and seniors who help and give me all supports. Finally, thanks to everyone who took part in this manuscript.

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