THE RELATIONSHIP BETWEEN G.826 ERROR PERFORMANCE OBJECTIVES AND EQUIVALENT BER

Journal of Information, Control and Management Systems, Vol. 2, (2007), No. 1 39

THE RELATIONSHIP BETWEEN G.826 ERROR

PERFORMANCE OBJECTIVES AND EQUIVALENT BER

Petr IVANIGA, Ľudovít MIKUŠ

University of Žilina, Faculty of Management Science and Informatics, Slovak Republic

e-mail: [email protected], [email protected]

Abstract

Error performance at the physical layer of digital communications equipment is a major

factor in determining transmission quality. In this paper, we discuss the impact of the

block-based error performance of transport systems. However, the impact of G.826 is

difficult to evaluate directly since the performance recommendations are not given in

terms of bit-error rate (BER) values. Hence, we present a procedure to covert block

error rates to BER. This conversion is based on statistical modeling of the error process

and includes an analysis of burst errors as well as random errors

Keywords: digital networks, block error, random errors, burst errors

1 INTRODUCTION

The recommendation ITU G.826 [ ]1 , [ ]4 defines qualitative parameters and final values for high-speed error transmission evaluation. The specifications in G.826 apply end-to-end hypothetical reference path or connection having a length of 27000 km. There are no specific provisions for different transmission media (for example optical fiber, digital radio relay, and metallic cable and satellite transmission systems).

2 ERROR UNITS AND ERROR PARAMETERS DEFINITION

ITU G.826 recommendation follows four basic parameters for the block error rate valuation:

Errored Block (EB) – block, which contains one, or more error bits;

Errored Second (ES) – limited period of one second, which contains one, or more error blocks;

Severely Errored Second (SES) – length interval of one second, which contains at least 30% of error blocks, or severely error limit period;

40 The Relationship between G.826 Error Performance Objectives and Equivalent BER

We acquire absolute values of these quantities by error units measured as started above. It is naturally more effectual to use relative values. G.826 recommendation defines three relative error parameters.

Errored Second Ratio (ESR) – the ratio of ES to total seconds in available time during a fixed measurement interval;

Severely Errored Second Ratio (SESR) – the ratio of SES to total seconds in available time during a fixed measurement interval;

Background Block Error Ratio (BBER) – is the ratio of error blocks to total blocks during a fixed measurement interval, excluding all blocks during SES and unavailable time

These error parameters are valid, assuming that the system is serviceable. According to ITU G.826 recommendation, in case at least 10 seconds with error rate

bigger than 310− follow one after another, the transmission system is not serviceable [ ]3 .

3 THE RELATIONSHIP BETWEEN G. 826 EPO AND BER

It is useful to express the G.826 EPO in terms of BER values. The relationship between G.826 EPO and BER is dependent on the choice of models to describe the occurrence of errors. The errors can occur randomly or in bursts. Systems using forward error correction (e.g., satellite systems and digital radio systems) and adaptive equalization (e.g., digital radio systems) are particularly susceptible to burst errors [ ]2 .

3.1 RANDOM ERRORS

Here, we assume bits are independent with constant probability, p, of error. ESR:

( ) ( ) ( )RpEFSPESPESR −−=−== 111 (1)

EFS - Error free second

BBER:

)(BBEPBBER = (2) =P(EB not occurring in SES or unavailable time) =P(EB and the second is not an SES) neglecting the unavailability condition which has a negligible effect on the probability. Hence

( )21 EEEBPBBER ∩∩= (3)

1E - Event that 30≥ % of the blocks in the second are error

2E - Event that an SDP occurs in the second


SESR:

( )SESPSESR = (4)

( )21 EEPSESR ∪= neglecting the unavailability condition

( )211 EEPSES ∩−=

3.2 Burst Errors

Model discussed by Pullmum where the occurrence and length of bursts are modeled by independent Poisson distributions. The resulting compound Posson distribution is often described Neyman Type A distribution. This model also overcounts since error bursts can overlap [ ] [ ]3,9 .

Each bit has a constant probability bp of starting a burst of errors. In this paper

we say the leng of each burst is Y+1, where Y has a Poisson distribution with parameter 1−µ . This slight alternation to Neyman distribution is to avoid the occurence of

bursts of lengh zero. The burst error probability, bp , can by to the BER by the

aproximation µ

ppb = or by the exact result derived below which adjusts for

overcounting.

A bit is error free if it does not start a bursts of errors and no previous bits start a burst of errors which include it. Since the jth previous bit has probability

( )jYPpb ≥ ,of starting a burst which covers the bit in question we can write:

( )[ ]∏∞

=

≥−−=0

11j

b jYPpp (5)

ESR:

( )R

bpESR −−= 11 (6)

R – Number of bits per second

P – BER

4 G.826 ERROR OBJECTIVES

G.826 specifies the bit error performance objectives for TDM networks. Table 1 of G.826 specifies that an Errored Second Ratio (ESR) of for percent is allowable for both E1 and T1 connections. This assumes the G.826 Hypothetical Reference Path (HPR) that is typical of end-to-end international connections [ ]8 .

For the Y. tdmpls case, assuming the worst case of isolated packet loss, this ESR translates to a loss event every 25 seconds. For simplicity we will herein assume an


integer number of TDM frames per MPLS packet, and hence the number of packets per second is given by: Packet per second = 8000 / (frames per packet) (7) Where prevalent cases would be 1, 2, 4 and 8 frames per packet. The following table shows the maximum packet loss rate that enables full conformance with G.826

Table 1 Maximum packet loss rate

Frames per packet Packet per second Permitted packet loss rate

1 8000 0,0005% 2 4000 0,001% 3 2000 0,002% 4 1000 0,004%

In reality when packet loss is above 0,001%, it is due micro- congestion events, which incur multiple lost packets. If the lost packets belong to a single measurement block then the permitted packet loss rate increases by the appropriate factor, without G.826 being cognizant of any change. Even were the lost packets to occupy more than a single measurement block, as long as they are within a second of each other the ESR is unaffected, although in extreme cases the severely errored second ration (SESR) may increase.

Next we will go to the opposite extreme and assume that all packet loss events are in periodic loss bursts. In order to minimize the ESR we will assume that the burst lasts no more than one second, and so we can afford to lose no more than packet per second packets in each burst. As long as such one-second bursts do not exceed four percent of time, we still maintain the allowable ESR. Hence the maximum permissible packet loss rate is 4%. In order to withstand the SESR criteria we need to restrict the length of the burst to 30% of this length, meaning that 1,2% packet loss may still not surpass G.826 limits.

5 CONCLUSION

Draft recommendation G.826 does not define apportionment rules for the originating and terminating country block allowances. The stringency of G.826 can only be assessed after an apportionment methodology for the block allowances is clarified. In this section, we discuss various scenarios for the apportionment and comment on the equivalent BER requrements for the scenarios in terms of BER masks and simple BER thesholds. In reality for true networks the values will be intermediate between the extremely low estimates of the table 1, and the 1,2 % of maximal calculation. In ordher to numerically gauge the simulation, we performed a computer simulatin in packet loss, ESR, and SESR were measured.


Acknowledgement

This work has been supported by research VEGA 1/4061/07

REFERENCES

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THE RELATIONSHIP BETWEEN G.826 ERROR PERFORMANCE OBJECTIVES AND EQUIVALENT BER