Shortened Turbo Product Codes: Encoding Design and Decoding Algorithm

Shortened turbo product codes (TPCs) have already been adopted in many standards. In this paper, we study shortened TPCs from two aspects, namely encoding design and decoding algorithm. To obtain different encoding block sizes, shortened-extended Hamming codes are used as the component codes of product codes in the IEEE 802.16 standard. To design a good structure for the shortened TPC, we compute the undetected error probability of its corresponding component codes. The component codes are shortened-extended Hamming codes, and their optimal generator polynomials are selected in terms of their undetected error probability. For the decoding algorithm, we present an efficient Chase decoding algorithm for shortened TPCs in flat fading channels. In the proposed scheme, the reliability factor used in Pyndiah´s scheme is not needed; thus, the decoding complexity is greatly reduced by avoiding the normalization operation of the whole code word at each iteration. Simulation results are also presented to verify the performance of the proposed algorithm.