An Efficient Algorithm to Calculate BICM Capacity

TL;DR

This paper introduces Bacm, an efficient algorithm that calculates BICM capacity with significantly reduced complexity, enabling capacity analysis for larger PAM constellations in AWGN channels.

Contribution

The paper presents Bacm, a novel iterative convex optimization algorithm that efficiently computes BICM capacity, overcoming the exponential complexity of exhaustive search methods.

Findings

Bacm computes BICM capacity for large PAM constellations efficiently.

First known BICM capacity results for PAM with more than 8 points.

Bacm scales approximately as m^3 in complexity.

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 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 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 PAM constellations with more than 8 points, the presented values are the first results known in the literature.