Hybrid Polar Encoding with Applications in Non-Coherent Channels

TL;DR

This paper introduces a hybrid polar encoding scheme combining systematic and non-systematic bits, enabling effective channel estimation and decoding, with performance nearing that of ideal schemes at high SNR.

Contribution

It proposes a novel hybrid encoding method for polar codes and a joint channel estimation and decoding scheme utilizing systematic bits as pilots.

Findings

Performance approaches that of non-systematic polar codes with perfect CSI at high SNR

Dynamic pilot design mitigates rate loss and enhances error detection

Simulation confirms effectiveness of the hybrid scheme in practical scenarios

Abstract

In coding theory, an error-correcting code can be encoded either systematically or non-systematically. In a systematic encode, the input data is embedded in the encoded output. Conversely, in a non-systematic code, the output does not contain the input symbols. In this paper, we propose a hybrid encoding scheme for polar codes, in which some data bits are systematically encoded while the rest are non-systematically encoded. Based on the proposed scheme, we design a joint channel estimation and data decoding scheme. We use the systematic bits in the hybrid encoding scheme as pilots for channel estimation. To mitigate the code rate loss caused by the pilots and to provide additional error detecting capability, we propose a dynamic pilot design by building connections between the systematic bits and non-systematic bits. Simulation results show that the performance of the proposed scheme approaches that of the traditional non-systematic polar coding scheme with perfect channel state information (CSI) with the increase of SNR.