Successive Syndrome-Check Decoding of Polar Codes

TL;DR

This paper introduces a two-part successive syndrome-check decoding method for polar codes that refines received codewords and checks their syndromes, reducing decoding time especially at high SNRs.

Contribution

It presents a novel successive syndrome-check decoding approach that improves efficiency of SC and SCL decoders by early error detection and refinement.

Findings

Reduces time-complexity of SC and SCL decoders

Effective at high signal-to-noise ratios

Extends to SC list decoding with syndrome checks

Abstract

A two-part successive syndrome-check decoding of polar codes is proposed with the first part successively refining the received codeword and the second part checking its syndrome. A new formulation of the successive-cancellation (SC) decoding algorithm is presented that allows for successively refining the received codeword by comparing the log-likelihood ratio value of a frozen bit with its predefined value. The syndrome of the refined received codeword is then checked for possible errors. In case there are no errors, the decoding process is terminated. Otherwise, the decoder continues to refine the received codeword. The proposed method is extended to the case of SC list (SCL) decoding by terminating the decoding process when the syndrome of the best candidate in the list indicates no errors. Simulation results show that the proposed method reduces the time-complexity of SC and SCL decoders and their fast variants, especially at high signal-to-noise ratios.