Design of Generalized Concatenated Codes Based on Polar Codes With Very Short Outer Codes

We present a new design approach to construct generalized concatenated codes (GCCs) based on polar codes (PCs). It is already known that PCs can be considered as a special class of the GCCs with polar outer and inner codes. We show how density evolution (DE) can be used to develop a channel-specific method to design outer codes of length $L$ under maximum-likelihood (ML) decoding. Once a bank of outer codes of length $L$ and different rates have been designed, we develop a rate-allocation algorithm to allocate rates to the outer codes of the GCC with the goal of minimizing the overall block error rate for a given overall rate of $K/N$ . To maintain the low complexity of the SC decoder, we only design very short outer codes $(L\le\text{8})$ . We show that, at this outer code length, it is possible to design GCC-PCs that can result in up to 0.5-dB coding gain while reducing decoding complexity.