Successive Cancellation Decoding of Z_2S Splitting Codes

In this paper, we introduce an improved suboptimal SISO decoding algorithm for splitting codes - a class of linear codes over the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z_2S</tex> ring (the ring of integers modulo <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2S)</tex> , based on the lifting decoder technique. This algorithm is demonstrated for generalized Kerdock codes, and it is compared to the MAP decoding algorithm in terms of its error correction performance. Simulations show that our novel algorithm has a comparable error correction performance to the optimal decoder with significantly lower decoding complexity. In the case of the generalized Kerdock codes, our algorithm has the complexity of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O(SNlog₂N)</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> is the code length in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z_2S</tex> , i.e. the number of ring elements in a codeword.