New Geometrical Spectra of Linear Codes with Applications to Performance Analysis

TL;DR

This paper introduces new geometrical enumerating functions for linear codes, computed via trellis algorithms, which enhance performance bounds on maximum likelihood decoding.

Contribution

The paper defines novel triangle and tetrahedron enumerating functions for linear codes, providing a new approach to analyze code performance.

Findings

New enumerating functions can be computed efficiently using trellis-based algorithms.

These functions improve existing bounds on maximum likelihood decoding performance.

The complexity is primarily determined by the trellis complexity.

Abstract

In this paper, new enumerating functions for linear codes are defined, including the triangle enumerating function and the tetrahedron enumerating function, both of which can be computed using a trellis-based algorithm over polynomial rings. The computational complexity is dominated by the complexity of the trellis. In addition, we show that these new enumerating functions can be used to improve existing performance bounds on the maximum likelihood decoding.