ERROR RESILIENT CODING FOR JPEG IMAGE ... - Semantic Scholar

ERROR RESILIENT CODING FOR JPEG IMAGE TRANSMISSION OVER WIRELESS FADING CHANNELS R. Chandramouli, N. Ranganathan

Shivaraman J. Ramadoss

Center for Microelectronics Research Dept. of Computer Science and Engg. University of South Florida, Tampa

Digital Video Express Herndon Parkway Herndon, VA

ABSTRACT In this paper, a new fast error resilient entropy coder (FEREC) for robust image transmission over wireless fading channels is proposed. A slow, frequency non-selective Rayleigh fading channel model is used. The proposed FEREC algorithm is observed to be almost twice as fast as EREC [3] in encoding the data and hence the error resilience capability is also signi cantly better. Upto 2 dB improvement in the peak signal to noise ratio of the received image is achieved when compared to EREC. 1. INTRODUCTION Image transmission through band limited and high bit error rate fading wireless communication channels, like the wireless mobile channels, requires good compression algorithms and error resilient coding techniques. Recently, error protection schemes for image and video transmission over noisy fading channels have been proposed in [1]-[3]. Video transmission over Rayleigh fading channels using low-complexity BCH codes is given in [1]. An ARQ error control technique is employed for video signals over wireless channels at 64 kb/s in [2]. The erroneous data frames are retransmitted. Error resilient entropy coding reduces the redundancy due to channel coding and yet pro-

tects against error propagation. Such a coder is proposed in [3] using a bit reorganization algorithm. The variable lengths of data blocks due to variable length encoding are placed into a xed number of slots of equal size using an error resilient entropy coder (EREC) before transmission. This results in a graceful degradation with increasing channel bit error rate is obtained. It also produces data that is corrupted only as long as the burst length with little or no additional delay and redundancy. In this paper, we propose a fast error resilient entropy encoder (FEREC) for JPEG image transmission over a slow, frequency nonselective Rayleigh fading channel. The encoder is shown to be twice as fast as EREC in packing the blocks of data into available slots through extensive simulations. Therefore, FEREC possesses superior error containment capabilities. A total number of fty 8 bit 256256 gray level images were tested. The peak signal to noise ratio of the received image using FEREC was observed to be higher than that with EREC for channel bit error rates (pe ) between 10? to 10? . 4

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2. THE BASELINE JPEG The JPEG compression standard is widely used for still image compression. The input image,

X , is partitioned into N  N blocks followed by the 2-D discrete cosine transform (DCT) for each block. DCT reduces the inherent redundancy in the signal. Then, each DCT coecient is quantized using a quantization table. The quantized coecients are zig-zag scanned, run-length and Human encoded to obtain the nal JPEG compressed image. Decompression is the exact reverse process. 3. FAST ERROR RESILIENT ENTROPY CODER The outputs of the JPEG encoder are the quantized and variable length coded DCT coecients. The error resilient entropy coder rearranges the variable length data blocks (bits), bi; i = 1; 2;


; N of average length L into slots sj , j = 1; 2;


; N each of length L. The reorganization is done such that the beginning of the next block in the sequence is exactly known. This means that the decoder is synchronized automatically to the start of each block in the absence of channel errors. This builds an error resilient structure, so that the propagation of errors during noisy transmission does not aect the most signi cant bits of the other blocks. The encoding algorithm is said to converge when all the blocks have been placed completely in the available slots. The speed of convergence of the algorithm is the number of iterations or stages for convergence. Though the search method used in EREC is intuitively appealing and simple, it fails to use the statistics of the data to the fullest extent. Various compression methods produce data with different statistical properties. By using this information we can design better and faster error resilient entropy coders (FEREC). We introduce some terminology that will be used to describe the proposed encoding algorithm. Let l(sni) denote the number of bits in slot si; i = 1; 2;


; N at iteration n of the algorithm. The indicator function is denoted by 1

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I . In the de nitions given below we drop n for convenience. De nition 1 The set F=fsi; si ;


; sk g is a full cluster if Ifl s Lg = 1, j = i; i + 1;


; k, Ifl s ?1 Lg = 0 and Ifl s +1 Lg = 0. De nition 2 The set E=fsi; si ;


; sk g is a partially full cluster if Ifl s Lg = 0, j = i; i + 1;


; k, Ifl s ?1 Lg = 1 and Ifl s +1 Lg = 1. The output blocks of the JPEG source coder whose length exceeds L are more likely to be followed by similar blocks. Likewise, blocks of size less than the average length will precede blocks of the same nature. This statistical property is due to the run length and Human encoders in JPEG. In the rst stage, the blocks are placed in the corresponding slots. Since consecutive blocks have similar lengths, the probability of an over owing block bi nding a partially full slot, sj , is high for j > i +1. Therefore, the block has to cross the full cluster and reach the empty cluster in the successive stages to be placed in a slot. If F ; F ;


; Fm denotes the m full clusters, then the average length of a full cluster is given by   1 Lf = m [C (F ) + C (F );


; C (Fm)] (1) and for the partially full cluster it is   1 Le = m [C (E ) + C (E );


; C (Em )] (2) C denotes the cardinality of a set and d:e is the ceiling function. On an average a block crosses (Lf + Le )=2 slots to nd a free slot. This suggests that a better initial oset,  , for the search starting from si, i = 1; 2;


; N is equal to d(Lf + Le )=2e. The oset for the successive stages is given by 8 > < ? ; n = 2 n = >  + (2k ? 1)(mod N ); n = 2k + 1 :  ? (2k ? 1)(mod N ); n = 2k + 2 for k = 1; 2;


. The algorithm can be described as follows : +1

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for i=1 to N /* Initialize lengths of slots */ length(si )=dLe endfor n=1 for i= 1 to N /* Compute number of bits in si */ ki =min(l(bi),dLe) /* Place bi in si at stage n */ sni (1 : ki ) = bi(1 : ki) endfor for i= 1 to N /* No. of bits in bi remaining to be placed */ ri=l(bi)-dLe endfor repeat /* Increment stage number */ n = n+1 for i= 1 to N if ri > 0 if (dLe ? ki  ) > 0 temp = min(dLe ? ki  ; ri) n si  (ki  + 1 : ki  +temp)= bi(l(bi) ? ri+1:l(bi)-ri+temp) /* Update the number of bits in bi remaining to be placed */ ri=ri-temp /* Update the number of bits in si  */ ki  =ki  +temp endif endif endfor until ri  0,8i = 1; 2;


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FEREC limits the error propagation due to channel errors to the least signi cant bits of the other blocks. 4. SIMULATION RESULTS Extensive simulations were done on fty 8 bit, 256  256 gray level images that were compressed using JPEG. A slow, frequency nonselective Rayleigh fading channel model was

used in the simulations. Channel bit error rates ranging from 10? to 10? were considered. 4

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4.1. Speed-up of FEREC over EREC The speed-up of FEREC over EREC is de ned as the ratio of the number of iterations for EREC to converge to the that of FEREC. The speed-up of FEREC for fty images is shown in Figure 1(a). FEREC is observed to converge in nearly half the number of iterations when compared to EREC on an average. The images corresponding to the numbers are given in [4]. This speed-up is achieved due to the search strategy that avoids searching the slots which are more likely to have been lled by other blocks in the previous iterations. 4.2. Peak SNR and Bit Error Rate The peak SNR of the received "House" image using EREC and FEREC is shown in Figure 1(b). Both the algorithms exhibit similar trend. But FEREC consistently gives a higher PSNR than EREC. There is upto a 2 dB improvement in the PSNR using FEREC. Figure 2 shows the reconstructed images for pe equal to 10? . Clearly, FEREC performs better. 2

5. CONCLUSIONS A fast error resilient coding technique that exploits the source statistics is proposed. It is shown that it performs better than the EREC algorithm in terms of the speed of convergence and error resilience. The average speed-up of FEREC is nearly two over a set of fty images. The improvement in the peak SNR of the received image is upto 2 dB when compared to EREC. Modi cations of the method that take into account the characteristics of compressed video is an interesting problem to study.

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Figure 1: (a) Speed-up of FEREC over EREC for fty images, (b) PSNR vs. bit error rate 6. REFERENCES

Figure 2: Reconstructed images for pe = 10? using EREC and FEREC

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[1] R. Stedman, H. Gharavi, L. Hanzo and R. Steele, "Transmission of subband-coded images via mobile channels", IEEE Trans. of Circuits and Systems for Video Tech., pp. 1526, Feb.1993. [2] M. Khansari, A. Jalali, E. Dubois and P. Mermelstein, "Low bit-rate video transmission over fading channels for wireless microcellular systems", IEEE Trans. on Video Tech., vol. 6, pp. 1-11, Feb. 1996. [3] D.W. Redmill and N.G. Kingsbury, "The EREC: An error resilient technique for coding variable-length blocks of data", IEEE Trans. on Image Processing, vol. 5, pp. 565574, April 1996. [4] S.J. Ramadoss, Adaptive quantization and fast error resilient entropy coding for using JPEG in wireless communication, M.S. Thesis, University of South Florida, 1996.