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Unformatted text preview: The 17th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC’06) THE DESIGN AND DECODING SCHEMES FOR SHORTENED TURBO PRODUCT CODES Changlong Xu, Ying-Chang Liang and Wing Seng Leon Institute for Infocomm Research 21 Heng Mui Keng Terrace, Singapore 119613 [email protected] ABSTRACT In this paper, we study the design and decoding schemes for shortened turbo product codes adopted in IEEE 802.16 stan- dard. To design a good structure for shortened turbo product code, we compute the undetected error probability of the com- ponent codes and select the optimal generator polynomials in terms of their undetected error probability. For the decoding algorithm, we present an efficient Chase decoding algorithm for shortened turbo product codes in which the reliability fac- tor used in Pyndiah’s scheme is not needed. Thus the decoding complexity is reduced greatly by avoiding the normalization operation of the whole codeword at each iteration. Simulation results are presented to verify the performance of the proposed algorithm. I. INTRODUCTION After Berrou introduced parallel concatenated convolutional turbo codes (CTC) , Pyndiah proposed a soft in / soft out iterative decoding algorithm for product codes in 1994 [2, 3]. Thus, product codes are called turbo product codes (TPC) or block turbo codes (BTC) accordingly. Compared with CTC, TPC can achieve a performance closer to the Shannon capacity limit with low decoding complexity and high code rate . Be- cause of that, TPC has been adopted in many standards, such as IEEE 802.16 , satellite communication systems and digital storage systems. Considering the decoding complexity, extended Hamming codes are usually chosen as the component codes for TPC and shortened extended Hamming codes for shortened TPC as well. In general there exist several code definitions that gen- erate equivalent Hamming codes with same codeword length . The TPC codes constructed by these equivalent Hamming codes have the equal weight distributions as well as equal unde- tected error probabilities. However, the undetected error char- acteristics of shorten TPC may differ significantly from each other. Among the equivalent TPC codes of a given block size, the best shortened codes are the codes that have minimum un- detected error probability. Unfortunately, it is impossible to obtain the undetected error probabilities of TPC codes because there are no existing algorithm to calculate the weight distribu- tions of TPC and shortened TPC codes so far. In this paper, we will utilize another criteria to decide the best design for short- ened TPC codes. Recently, several algorithms have been proposed to reduce the complexity of the TPC decoder proposed by Pynadiah [6, 7]. However, none of them have discussed the decoding algorithm for shortened TPC. In this paper, we propose an ef- ficient Chase decoding algorithm for shortened TPC over flat fading channels. The proposed algorithm does not require thefading channels....
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This note was uploaded on 01/25/2011 for the course SCE 5441 taught by Professor Lung during the Spring '10 term at Carleton CA.
- Spring '10