An Expurgated Union Bound of Punctured Space-Time Turbo Codes

Luiz Caldeira,Daniel Chaves,Cecilio Pimentel

doi:10.14209/jcis.2018.6

Abstract

This paper presents a new technique to obtain an expurgated union bound on the frame error rate of punctured space-time turbo codes (STTuC) in quasi-static Rayleigh fading channels. The STTuC scheme is composed of two component space-time trellis encoders connected in parallel via an interleaver. An adjacent matrix of an augmented state diagram is defined which allows the enumeration of each punctured component encoder. The distance spectrum of the STTuC is then obtained using the concept of uniform interleaver. A method to identify the dominant error events is proposed and an expurgated union bound on the frame error rate of STTuC schemes is computed using these dominant error events. Comparisons with simulated results reveal that the expurgated union bound is tight for codes with different construction criteria for a wide range of signal to noise ratio.

Highlights

T He parallel concatenation of two component space-time trellis codes (STTCs) [1] combines the coding gain of turbo coding schemes [2] with the diversity gain of multiple transmit and receive antennas, resulting in a transmission scheme known as space-time turbo codes (STTuCs) [3]- [8]
A matrix-based technique to evaluate the distance spectrum of punctured STTuCs was presented in this work
We defined an adjacency matrix of an augmented state diagram which allows the enumeration of each component STTC encoder

Summary

INTRODUCTION

T He parallel concatenation of two component space-time trellis codes (STTCs) [1] combines the coding gain of turbo coding schemes [2] with the diversity gain of multiple transmit and receive antennas, resulting in a transmission scheme known as space-time turbo codes (STTuCs) [3]- [8]. Tight frame error rate (FER) bounds for STTCs over quasistatic Rayleigh fading channels have been obtained in [17]– [19] using a combination of three techniques: the enumeration of the signal matrix of error events (SMEE) together with its multiplicities (the so called distance spectrum), the derivation of the expurgated union-bound on the first error event using. The objective of this paper is to generalize these techniques (developed for STTCs) in order to evaluate accurate expurgated FER bounds for STTuC schemes. Previous works on this subject include [11], [20], [21].

PAIRWISE ERROR PROBABILITY OF AN STTC OVER x input

The Puncturing Effect

DETERMINATION OF THE SET OF DOMINANT SMEE

W w0 X x0 Y y0 Zz0 0

CONCLUSIONS