Design of Irregular Weighted Nonbinary Repeat-Accumulate Codes over GF(q) with q-ary Orthogonal Modulation Using a Gaussian Approximation

Using a Gaussian approximation to the distribution of the message vectors under density evolution, we design irregular weighted nonbinary repeat-accumulate codes over GF(q) with q-ary orthogonal modulation. The resulting codes achieve a frame error rate of 10
^-1
within 0.56 to 0.91 dB of channel capacity under the AWGN channel.