An Efficient Algorithm to Calculate BICM Capacity

Paper in proceeding, 2012

Abstract 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 2^m points, BICM labels the signal points with bit strings of length m and then treats these m bits separately both at transmitter and receiver. To determine the capacity of BICM, the mutual information between input and output has to be maximized over the bit pmfs. This is a non-convex optimization problem. So far, the optimal 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 m^3. 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 constellations with more than 8 points, the presented values are the first results known in literature.