An efficient algorithm to calculate BICM capacity

Bit-interleaved coded modulation (BICM) is a practical approach for reliable communication over the AWGN channel in the bandwidth limited regime. For a signal point constellation with 2m points, BICM labels the signal points with bit strings of length m and then treats these m bits separately both at the transmitter and the receiver. BICM capacity is defined as the maximum of a certain achievable rate. Maximization has to be done over the probability mass functions (pmf) of the bits. This is a non-convex optimization problem. So far, the optimal bit pmfs were determined via exhaustive search, which is of exponential complexity in m. In this work, an algorithm called bit-alternating convex concave method (Bacm) is developed. This algorithm calculates BICM capacity with a complexity that scales approximately as m3. The algorithm iteratively applies convex optimization techniques. Bacm is used to calculate BICM capacity of 4,8, 16, 32, and 64-PAM in AWGN. For PAM constellations with more than 8 points, the presented values are the first results known in the literature.