A Simple Design of Puncturing Pattern for Symbol-wise Viterbi Decoding

Abstract

A symbol-wise decoder which employs a modified trellis diagram is suitable for decoding a convolutionally encoded bit sequence with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> -ary frequency shift keying (FSK) modulation. Because performances of the symbol-wise decoder degrade due to a branch with a large likelihood value, we have proposed an optimized puncturing pattern which minimizes the number of branches with large likelihood value in a shortest merged path. However, we need to search all candidate patterns to optimize the puncturing pattern for each parameter because the examined optimization is only for the specific parameter. Therefore, in order to improve efficiency of puncturing pattern optimization, we propose a simple design method of puncturing pattern for symbol-wise viterbi decoding. The proposed method extracts only puncturing patterns having few branches with large likelihood value by utilizing a table which indicates correspondence between an information bit and a coded bit in the shortest merged path. We show that the proposed method reduces the number of search patterns by about 75 % compared to the conventional full search method. Furthermore, the performance evaluation by computer simulation shows that the puncturing pattern designed by the proposed method achieves the performance improvement.