The Compound Capacity of Polar Codes

TL;DR

This paper investigates the limits of polar codes' performance across multiple channels, revealing that their success under successive decoding is generally less than the ideal capacity for all channels combined.

Contribution

The paper introduces bounds on the compound capacity of polar codes under successive decoding, demonstrating it is typically smaller than the unrestricted capacity.

Findings

Compound capacity under successive decoding is strictly less than the unrestricted capacity.

Derived bounds provide insights into polar codes' performance across channels.

Results highlight limitations of polar codes in compound channel scenarios.

Abstract

We consider the compound capacity of polar codes under successive cancellation decoding for a collection of binary-input memoryless output-symmetric channels. By deriving a sequence of upper and lower bounds, we show that in general the compound capacity under successive decoding is strictly smaller than the unrestricted compound capacity.