A new M-PSK code construction with good minimum Euclidean distance for AWGN channels
An important goal in communication theory is to construct good minimum squared Euclidean distance (MSED) codes for transmission over additive white Gaussian noise (AWGN) channels. In this paper, a new construction method for the M-ary phase-shift-keyed (M-PSK) codes over the ring structure Z(M) the ring of integers module M, with a good minimum Euclidean distance, is proposed. The proposed codes are linear when multiple coset leaders are considered. The characteristics and performance levels of the newly constructed codes are analyzed for code length up to n less than or equal to 8. It is found that the proposed codes compare favorably with Piret's codes and Graeffe's method codes on Gaussian channels in terms of decoding complexity, coding gain, and error performance.
ring structure decoding complexity coset codes ideal idempotents