On Generalized Minimum Distance Decoding Thresholds for the AWGN Channel

TL;DR

This paper develops a method to optimize threshold-based erasure decoding for the AWGN channel with BPSK, improving the exploitation of soft information to enhance decoding performance.

Contribution

It provides an explicit approach to determine optimal thresholds for generalized minimum distance decoding, extending previous work to multiple thresholds with a geometric interpretation.

Findings

Optimal thresholds minimize decoding error probability

Extension from one to multiple thresholds improves decoding performance

Explicit threshold determination method based on geometric analysis

Abstract

We consider the Additive White Gaussian Noise channel with Binary Phase Shift Keying modulation. Our aim is to enable an algebraic hard decision Bounded Minimum Distance decoder for a binary block code to exploit soft information obtained from the demodulator. This idea goes back to Forney and is based on treating received symbols with low reliability as erasures. This erasing at the decoder is done using a threshold, each received symbol with reliability falling below the threshold is erased. Depending on the target overall complexity of the decoder this pseudo-soft decision decoding can be extended from one threshold T to z>1 thresholds T_1<...<T_z for erasing received symbols with lowest reliability. The resulting technique is widely known as Generalized Minimum Distance decoding. In this paper we provide a means for explicit determination of the optimal threshold locations in terms of minimal decoding error probability. We do this for the one and the general z>1 thresholds case, starting with a geometric interpretation of the optimal threshold location problem and using an approach from Zyablov.