The Trapping Redundancy of Linear Block Codes

TL;DR

This paper introduces the concept of trapping redundancy for linear block codes, providing bounds and analysis on the smallest trapping sets that affect decoder performance, with applications to specific codes.

Contribution

It generalizes stopping redundancy to trapping redundancy, offering bounds and methods to identify trapping sets that impact decoding error floors.

Findings

Bounds on trapping redundancy are established.

Numerical bounds are computed for specific codes.

Analysis covers both general and elementary trapping sets.

Abstract

We generalize the notion of the stopping redundancy in order to study the smallest size of a trapping set in Tanner graphs of linear block codes. In this context, we introduce the notion of the trapping redundancy of a code, which quantifies the relationship between the number of redundant rows in any parity-check matrix of a given code and the size of its smallest trapping set. Trapping sets with certain parameter sizes are known to cause error-floors in the performance curves of iterative belief propagation decoders, and it is therefore important to identify decoding matrices that avoid such sets. Bounds on the trapping redundancy are obtained using probabilistic and constructive methods, and the analysis covers both general and elementary trapping sets. Numerical values for these bounds are computed for the [2640,1320] Margulis code and the class of projective geometry codes, and compared with some new code-specific trapping set size estimates.