COMBINED ERROR PROTECTION AND COMPRESSION WITH TURBO CODES FOR IMAGE TRANSMISSION USING A JPEG2000-LIKE ARCHITECTURE Maria Fresia University of Genova-DIST Genova, Italy maria.fresia@dist.unige.it Giuseppe Caire University of Southern California Los Angeles, CA caire@usc.edu ABSTRACT In this paper, a joint source channel coding scheme for error resilient image transmission is proposed. Instead of compressing the image using the classical entropy coder, the redundancy of the image is ex- ploited by using turbo codes for both data compression and error pro- tection. At the decoder, the bit-planes are reconstructed in sequence by a multistage decoder. By properly choosing rate and puncturing, the system is able to approach the limit theoretically attainable and to outperform the separated approach of a JPEG2000 compressed image and the best turbo codes for the same overall length. Index Terms— Joint source-channel coding, linear codes 1. INTRODUCTION A stationary ergodic source can be transmitted over an information- stable channel with end-to-end average distortion D with efficiency η not larger than C/R(D) source samples per channel use, where D is defined according to some suitable distortion measure, R(D) is the source rate distortion function and C is the channel capacity. Furthermore, according to Shannon’s separation theorem, this limit can be approached arbitrarily closely by concatenating an optimal source coder, designed independently of the channel, with an opti- mal channel code, designed independently of the source [1]. While Separated Source-Channel Coding (SSCC) allows for a great deal of flexibility, in some applications it might impose un- needed constraints on the performance of either the source or the channel code. In these cases, Joint Source-Channel Coding (JSCC) may lead to a lower overall complexity for the same performance (i.e., same (η,D) operating point), or to a performance improve- ment (better (η,D) operating point) for the same complexity. As a matter of fact, most practical source coding schemes are based on some linear transformation (e.g., Wavelet transform, DCT, etc.), followed by decimation and quantization. The resulting sequence of quantization indices is treated as a redundant discrete Finite-Memory Source (FMS), and it is losslessly compressed by an entropy coding stage. This stage is typically implemented by some form of arith- metic coding with adaptive estimation of the probability distribution of the FMS sequence. Classical lossless compression is typically catastrophic, in the well-known coding theory sense: its inverse function is ill-conditioned. A small Hamming distortion (number of bits in error) in the entropy-coded sequence is mapped into a re- constructed sequence of symbols that yields a very large distortion of the reconstructed source. This feature imposes a very strict target error probability constraint on the channel coding stage, thus involv- ing both complex channel coding schemes and operating points that are quite far from the theoretical limits, in order to guarantee some margin in the performance of the channel code. Several works focused on methods to exploit residual source re- dundancy [2, 3] in order to help the channel decoding stage. Other works have focused on finding optimal rate allocation algorithms, in order to distribute the available redundancy between the source and the channel coders [4]. In this paper, we propose a new JSCC scheme targeted to the transmission of digital images over a noisy channel. Our approach consists of preserving the linear transforma- tion, decimation and quantization stages of state-of-the-art source coders for image compression, but replacing the classical entropy coding stage with a linear coding stage. It was shown in [5] that fixed-to-fixed length data compression of a FMS with linear codes is asymptotically optimal, in the sense that compression up to the source entropy rate can be achieved. This is strongly related to the transmission using the same linear code on a discrete additive noise channel where the noise has the same statistic of the source. This analogy can be exploited in order to design the coding stage. De- signs based on Low-Density Parity-Check codes [5] or turbo codes [6] have been proposed. The rationale behind our design is that the linear code combines in a single linear transformation the two map- pings FMS → entropy-coded bits → channel-encoded symbols. The advantage of this approach is that linear maps are easily de- signed in order to have a non-catastrophic decoder (in fact, the de- sign of non-catastrophic encoding/decoding pairs is a well-known problem in channel coding theory). The purpose of the proposed scheme is to preserve the distortion performance of state-of-the-art image coders, while achieving better robustness to channel errors. Although the approach philosophy is fully general, in this work we shall consider a particular case where the first stage is taken from JPEG2000 [7], and the linear coding stage consists of multi-level turbo coding. The details of the proposed scheme and its perfor- mance will be given in the following. 2. JOINT DATA COMPRESSION AND CHANNEL CODING WITH LINEAR CODES In this paper we propose a JSCC approach: instead of mitigating the catastrophic behavior of the entropy coding stage, we avoid it by replacing the entropy coding and channel coding stages with a single non-catastropic encoding operation. The goodness of our scheme is supported by the following result, that is an immediate corollary of the optimality of linear codes for both lossless compression [5] and for achieving capacity of Binary Input Symmetric Output (BIOS) channels. Theorem 1. Consider a binary source U defined by the sequence of K-dimensional joint probability distributions {P (K) (u): K =