Faulty Successive Cancellation Decoding of Polar Codes for the Binary Erasure Channel

TL;DR

This paper investigates the impact of faults on successive cancellation decoding of polar codes over the binary erasure channel, showing that faultiness prevents polarization and proposing a protection scheme to mitigate errors.

Contribution

It introduces a fault model for polar code decoders, analyzes the effects on polarization, and proposes an unequal error protection scheme to improve fault tolerance.

Findings

Polarization does not occur under faulty decoding.

A lower bound on frame error rate is derived.

Protecting a small fraction of the decoder improves performance.

Abstract

In this paper, faulty successive cancellation decoding of polar codes for the binary erasure channel is studied. To this end, a simple erasure-based fault model is introduced to represent errors in the decoder and it is shown that, under this model, polarization does not happen, meaning that fully reliable communication is not possible at any rate. Furthermore, a lower bound on the frame error rate of polar codes under faulty SC decoding is provided, which is then used, along with a well-known upper bound, in order to choose a blocklength that minimizes the erasure probability under faulty decoding. Finally, an unequal error protection scheme that can re-enable asymptotically erasure-free transmission at a small rate loss and by protecting only a constant fraction of the decoder is proposed. The same scheme is also shown to significantly improve the finite-length performance of the faulty successive cancellation decoder by protecting as little as 1.5% of the decoder.