Bandwidth efficient coding for satellite communications

N92-22018 Bandwidth Satellite

Efficient Coding Communications*

for

Shu Lin University of Hawaii Honolulu, Hawaii 96822 Daniel J. Costello, Jr. University of Notre Dame Notre Dame, Indiana 46556 Warner H. Miller James C. Morakis William B. Poland, Jr. Goddard Space Flight Center Greenbelt, Maryland 20771

RESEARCH

The trol

purpose

coding

reliability coding

*

of this

scheme by

PURPOSE

research

to achieve

using

coded

is to devise

large

coding

modulation

an error gain

with

reduced

complexity.

Supported

by NASA

Grants

PRECEDING

NAG 5-931

PAGE

BLANK 269

NOT

and NAG 5-557.

FILMED

and

conhigh de-

CODED

•

To achieve bility,

•

In

a 3 to 5 dB

the

fact,

decoding

to

complexity

•

MODULATION

complexity

is quite

simple,

no

(BCM)

(TCM)

of the

gain,

moderate

relia-

modest.

the

matter

whether

or block

coded

decoding trellis modu-

is used.

to achieve complexity

and

is quite

coding

lation

mentation

gain

a 3 dB

modulation

coding

coding

achieve

coded

However,

ALONE

coding

gains

increases

exceeding

drastically,

decoder

becomes

unpractical.

270

5 dB, and

very

the

expensive

the

de-

impleand

A BASIC

•

How ity

can by

we achieve

using

complexity

coded

QUESTION

large

coding

modulation

?

271

gains with

and

high

reduced

reliabildecoding

AN

•

Use

coded

nated

•

A

in

cascaded)

short

(trellis

•

modulation

(or

good

ANSWER

or

bandwidth

block)

efficient

is used

powerful

outer

code.

With

properly

chosen

nated

coded

modulation

large

coding

as the

Reed-Solomon

gains

width

efficiency

This

combination coding

of three

worlds,

efficiency

and

concate-

outer

scheme

not

decoding

and

complexity.

272

relaas the

a concate-

only

can

with

good

achieve band-

implemented

and

of achieving coding

and

codes,

modulation

a way

code

is used

can be practically

offers

reliability

code

code

reliability

of coded really

inner

and

high

also

modulation

(RS)

inner

and

but

with

coding.

tively

nated

conjunction

gain,

concatethe

best

bandwidth

PROPOSED

•

A concatenated

SCHEME

( or cascaded

) coded

modulation

scheme.

For NASA

high-speed

large data file transfer

satellite where

communications

for

very high reliability

is

required.

The

outer

symbols

code from

C2 is an

GF

(n2,

The outer

code

•

The inner

code is a bandwidth

PSK

RS

code

with

(2b).

•

M-ary

k2)

is interleaved

code of length

to a depth

efficient r_l

of rn.

block

and dimension

kl = tab. •

Under

the same

gated

concatenated

research

project,

coding

273

we have

with TCM

inner

investicodes.

THE CONCATENATED

• The

with

The

CODED

outer

which

OVERALL

code

C,

is an

is designed 0 _< t,

inner

MODULATION

(n,,

to

correct

< [(n_-k_

)/2J.

code

C,

k_ ) RS t,

is a 2'-PSK

SCHEME

code

or fewer

code

over

GF(T),

symbol

of length

errors

n,

and

dimension

iffil

where

k, = mb.

•

The

outer

code

•

The

encoding

C_ is interleaved

to a depth

of m.

consists

of two stages,

the

outer

and

inner

consists

of two

the

inner

and

outer

encodings.

•

The

decoding

stages,

decodings.

•

When block

•

In the

the

receiver

is erased

event

transmission

and

fails

to decode

the

receiver

of an erasure, or accept

a received raises

we could

the

erroneous

274

block,

the

a flag.

either

request

blockwith

a realarm.

r

k2

_J

b-bit

1st •

byte

•

•

Section

m-th Section

Ist

k=-th

n2 -th

Segment

Segment

Segment

Figure

I

A Segment-Array

275

ERROR OF •

Let

THE

Po,

P.,

decoding,

•

P,,

be

an erasure received

Lower

bound

• Let

OVERALL

and

entire

have

PERFORMANCE

been t5

on

block

for

probabilities

of

an incorrect

a correct

decoding

for

an

respectively.

Pc and

derived

denote

the

and

code

SCHEME

upper

bounds

an AWGN

on

P,,

and

P°,

channel.

a lower

bound

on P,.

is an upper

bound

on the

V

• Then

l-P,

of a decoding • Let •

/_°,

The

failure

denote

a decoding

an upper

performance

modulation

and

bound

of the

scheme

total

probability

error.

on

proposed

P,,. concatenated

is measured

by

the

coded

pair,

/_,,

and

1-Po. We

can

scheme either terms

in

compute

the

over

uncoded

terms

of decoded

the of

coding

gains

QPSK

decoded

bit-error

the

proposed

modulation

block-error rates.

276

of

rates

system or

in

•

For

data

used

as

file the

transfer,

the

measure

block-error

of the

error

rates

should

performance

be

of

the

scheme.

• There

are

two

types

of bit-error

rates,

denoted

P.,

and

P,2.

•

P_,

is computed

1=',, using

the

based

on

the

block

P_, posed

• P,,

is a measure scheme

using

the

when

failure

performance

retransmission

based and

on the

of the

pro-

is allowed.

total

a decoding

probability error

1-Pc

of a code

of

block

approximation,

P,2

•

). P.,

of bit-error

is computed

a decoding

probability

approximation,

P,, = •

error

P,,

is used

as the

the

scheme

when

= (d,/2n,

measure

).

(1 -

P, ).

of bit-error

retransmission

lowed.

277

is not

performance available

of or

al-

TWO CONCATENATED

SPECIFIC

CODED

MODULATION

SCHEME-

• The

outer

code

code

over

GF(2')

used

to correct

• The

inner

16, D[C,

code

I

C2 is the NASA which

standard

has minimum errors.

C,

code

is an 8-PSK

(255,223)

distance

up to 16 symbol

]= 4, R[C,

SCHEMES

with

RS

33. It is

n, = 8, k, =

]= 1 and _/[C, ]= 3 dB (over

uncoded

QPSK).

• The

outer

• The

overall

code

is interleaved

effective

to a depth

rate of the

scheme

of m = 2.

is

R., = (k, /n, ). R[C,] = 0.STS.

• The

inner

be decoded

code with

has

a 4-state

a soft-decision

278

trellis

structure

Viterbi

decoder.

and

can

ERROR

PERFORMANCE

• With

SNR

= 9 dB/symbol

• With

SNR

= 10 dB/symbol

P,,

and

1-Pc

is very

small.

(6.57 dB/infor,

(5.57

dB/infor,