Concatenated Polar codes

Polar codes have attracted much recent attention as one of the first codes with low computational complexity that provably achieve optimal rate-regions for a large class of information-theoretic problems. One significant drawback, however, is that for current constructions the probability of error decays sub-exponentially in the block-length more detailed designs improve the probability of error at the cost of significantly increased computational complexity. In this work we show how the the classical idea of code concatenation - using "short" polar codes as inner codes and a "high-rate" Reed-Solomon code as the outer code - results in substantially improved performance. In particular, code concatenation with a careful choice of parameters boosts the rate of decay of the probability of error to almost exponential in the block-length with essentially no loss in computational complexity. We demonstrate such performance improvements for three sets of information-theoretic problems - a classical point-to-point channel coding problem, a class of multiple-input multiple output channel coding problems, and some network source coding problems.