Single parity check product codes

This paper considers the performance of single parity check (SPC) multidimensional product codes in an Additive White Gaussian Noise channel. Asymptotic performance bounds are derived and compared to simulation results. A new code structure based on SPC product codes is introduced. This structure involves interleaving between the encoding of each dimension. Weight distribution analysis is used to explain the extremely good performance results for this class of codes. 1 Background Product codes, or iterated codes, were introduced by Elias 1] in 1954 and represent the rst method capable of achieving error free coding with a non-zero code rate (as the number of dimensions increases to innnity). A product code can be constructed in the following way 6]. The data to be transmitted is arranged in a hypercube of dimension d with the length in each dimension deened by