Optimized Polar Codes via Mutual Information Maximization With Neural Polar Decoders

This paper proposes a method to maximize the rate of reliable communication for polar codes operating on channels with memory. The channel is learned implicitly from data by optimizing a neural polar decoder (NPD). This approach enables simultaneous optimization of the code rate over the input distribution and the design of a practical coding scheme within the framework of polar codes. The proposed approach applies to scenarios where the channel model is unknown and treated as a black-box that produces output samples from input samples. We use NPDs to estimate the mutual information (MI) between the channel inputs and outputs, and optimize a parametric model of the input distribution. The methodology involves a two-phase process: a training phase and an inference phase. In the training phase, two steps are repeated iteratively. The first step optimizes the NPD to estimate the MI of the channel inputs and outputs. The second step improves the input distribution parameters by maximizing the MI estimate obtained with the NPD. In the inference phase, the optimized model is used to construct polar codes. This approach uses the Honda-Yamamoto (HY) scheme, which implements polar codes with optimized input distributions, together with list decoding. Experimental results on memoryless and finite state channels (FSCs) demonstrate the effectiveness of this approach, particularly in cases where the channel’s capacity-achieving input distribution is non-uniform. For these cases, significant improvements in MI and bit error rates (BERs) are shown over those achieved by uniform and independent and identically distributed (i.i.d.) input distributions, validating our method for block lengths up to 1024. This data-driven approach can be utilized in real-world communication systems, bridging theoretical capacity estimation and practical coding performance.