Mitigating Clipping Effects on Error Floors under Belief Propagation Decoding of Polar Codes

TL;DR

This paper investigates the cause of error floors in polar belief propagation decoding, identifying clipping of LLRs as a key factor, and proposes modifications to mitigate this issue, confirming that error floors are decoder-dependent.

Contribution

It introduces a measure for the error floor caused by LLR clipping and proposes four modifications to reduce this effect in BP decoding of polar codes.

Findings

Error floors are mainly due to LLR clipping values.

Proposed modifications effectively mitigate the error floor.

Error floors are a property of the decoder, not the code.

Abstract

In this work, we show that polar belief propagation (BP) decoding exhibits an error floor behavior which is caused by clipping of the log-likelihood ratios (LLR). The error floor becomes more pronounced for clipping to smaller LLR-values. We introduce a single-value measure quantifying a "relative error floor", showing, by exhaustive simulations for different lengths, that the error floor is mainly caused by inadequate clipping values. We propose four modifications to the conventional BP decoding algorithm to mitigate this error floor behavior, demonstrating that the error floor is a decoder property, and not a code property. The results agree with the fact that polar codes are theoretically proven to not suffer from error floors. Finally, we show that another cause of error floors can be an improper selection of frozen bit positions.