Soft Multilevel Slepian-Wolf Decoding in Systems Using Turbo Joint Decoding and Decompressing Yinan Qi Centre for Communication Systems Research University of Surrey Guildford, UK eep1yq@surrey.ac.uk Reza Hoshyar, Rahim Tafazolli Centre for Communication Systems Research University of Surrey Guildford, UK Abstract— It has been pointed out that Slepian-Wolf (SW) coding is efficient to compress data with side information available at the receiver. However, most papers assume that the compressed information is perfectly known to the receiver. In this paper, we consider more practical assumptions that the channel between the relay and the destination is not perfect and error protection need to be implemented. Accordingly, a soft Slepian-Wolf decoding structure is proposed. The new structure not only supports soft Slepian-Wolf decoding within one level, but it also allows soft information passing between different levels. We also consider the relationship between the codes for error protection and the codes for compression and propose a joint decoding and decompressing algorithm to further improve the performance. Keywords- Compress-and-forward (CF); log-likelihood ratio (LLR); Wyner-Ziv coding; Slepian-Wolf (SW) coding; Joint decoding and decompressing I. INTRODUCTION Relay technique has drawn more and more attentions in recent years because when multiple antennas are not able to be supported, path diversity is still achieved to improve the effective SNR of a fading channel. The relay model was first introduced by van der Meluen in [1] and substantially developed by Cover and El Gamal in [2]. One of the schemes called compress-and-forward (CF) has drawn more and more attentions, where the relay quantizes, compresses and transmits the compressed version of its received signal to the destination. It has been pointed out that Wyner-Ziv coding (WZC) [3] is an efficient way to compress the signal. A structure consists of a quantizer followed by multilevel SW coding [4] has been proposed for Wyner-Ziv problem [5], [6]. In those papers, Gaussian distributed information X is quantized into binary index and the index are compressed with SW coding. Compressed data are decompressed with the help of Gaussian distributed side information Y. X and Y are correlated in a way that Y is equal to X+Z, where X and Z are independent. And another assumption is that the compressed data are perfectly known to the receiver. However, in CF relay system, the relay signal and the destination signal are correlated in a different way. Besides, the channel between the relay and the destination is not perfect and the compressed data should be protected by some codes. Based on these changed conditions, we first extend multilevel SW coding into half-duplex CF scenario and provide a soft multilevel SW decoding algorithm. Throughout this paper the terms compressing/decompressing has the same meaning with SW coding/decoding in CF systems. We might use any group of the terms without explanation. Secondly, we incorporate soft processing concept into multilevel SW coding. At last, a joint Turbo decoding and decompressing structure is proposed. It has been pointed out that LDPC codes are suitable for SW coding for their near-capacity[5]. We use systematic LDPC codes to implement SW codes. The rest of this paper is organized as follow. Section II gives the system model and section III investigates soft SW decoding which is also called soft decompressing algorithm within one level. Soft information passing for multilevel Slepian-Wolf decoding is introduced in section IV. Section V proposes joint Turbo decoding and decompressing structure. Simulation results are given in section VI and the final section summarizes. II. SYSTEM MODEL We extend the work in [5] to CF relay scenario. In this work, we use bold letters to denote matrix. We use upper-case letters to represent random variables, e.g. X. We use the corresponding lower-case letters to represent realizations, e.g. x and a subscript within bracket to denote time phase 1 and 2 in half-duplex relay system, e.g. . We use a superscript to denote a sequence, e.g. x n = . In phase 1, the source broadcasts to both the relay and the destination. (1) where and are relay signal and destination signal, and and are relay noise and destination noise. is quantized into binary represented bin index matrix [ ] { } n i N l B B B B B B B B li l n l n N n N n n ≤ ≤ ≤ ≤ ∈ = = - 1 , 1 1 , 0 , , , , ln 1 1 2 1 B (2) 978-1-4244-1645-5/08/$25.00 ©2008 IEEE 1514