T-user Decoding Techniques

In the noiseless chan nel conditions, the deco d er is ca p a b le o f decoding every rec e iv e d com posite c o d e w o rd vector, without am biguity, in to T - c od e w ord that w ere transmitted by the T -e n c o d e r. H ow ever, i f the channel is noisy, th e received com posite cod ew ord m ay d iffe r fr o m the transmitted cod ew ord . In this case, the decoder chooses the cod ew ord w hich is c lo s e s t to the received as measured b y s o m e m etric distance. T h e

gen eral d eco d in g process in v o lve s searching am ongst all th e p ossib le composite codew ords and choosing the c o d e w o rd that satisfies certain d eco d in g strategy. T h e m etric distance values are the d e co d in g strategy measure o f the rec e iv e d cod ew ord with respect to a ll th e codewords. T h e d eco d in g o f T-user c olla b o ra tive c o d in g schemes is based here on t w o techniques, hard and soft decision decoding. T h e s e t w o decoding techniques are e m p lo yed to d eco d e collaborative c o d in g schemes [ A l i and Honary 1992].

5.3.1 H a r d D ecisio n (H D ) D e c o d in g

In H D d eco d in g o f C C M A schem es, the demodulator set CT) d ecisio n thresholds to detect the ( T + l ) possible signal le v e ls transmitted b y the T-user. H ere, each received sym bol is detected independently o v e r N received sym bols. T h is process is called sym b ol-b y-sym bo l H D (S B S _ H D ) d eco d in g technique [ A l i and H on ary 1990]. H ow ever, this d eco d in g technique cannot b e used on its o w n to perform fu ll d eco d in g process to d eliver the individual users in fo rm atio n to their intended destinations. T h is is due to the fact that, so m e tim es in n o isy con ditions, the S B S _ H D d eco d in g w ill result in a cod ew ord w h ich is not adm issible. In this case the deco d er w ill fa il to d eliver the individual users information. T h e refo re , L-distance H D d eco d in g is used in conjunction w ith S B S _ H D to com plete the d eco d in g process and r e s o lve this am biguity. This com plete process is referred t o as H D _ C C M A d eco d in g technique [ A l i and Honary 1991a, and A l i and Honary 1991b].

T h e H D _ C C M A decoder, calculates all the L-distances betw een the S B S _H D cod ew ord and all the possible adm issible codewords. Then, th e co d e w o rd w ith least L- distance is chosen. This kind o f deco d in g, guarantees correct d eco d in g in the noiseless

un iquely decodable co d in g scheme. H o w e v e r , in the noisy case, th e number o f errors w h ich can b e corrected under this d e co d in g is t=i-(dmi.- l)/

2

j , w h ere LxJ means integer number less than o r equal to x, [P eterson and W eld on 1972]. T h e generalised H D _ C C M A decoding algorithm can b e summarised in the fo llo w in g steps: Step 1: P erfo rm S B S _ H D decoding o n th e received N -sym bo l co d ew o rd . Step 2: Calculate the L-distance m etric valu es betw een the S B S _ H D co d ew o rd and all the adm issible codew ords.

Step 3: C h oo se the c o d ew o rd w ith the least L-distance m etric v a lu e to represent the d eco ded codew ord.

Step 4: A lo o k up table is used to d e c o d e the individual users’ co d e w o rd s and hence their origin a l sink inform ation.

5.3.2 M a x imum L ik lie h o o d S o ft D e c isio n (M L S D ) D ecodin g

It is seen in the previou s section that the H D _ C C M A d e c o d e r operates on the dem odu lator hard sym bol decisions. T h is , h o w ever, neglected th e fa c t that there is an additional inform ation in the r ec e iv e d signal w h ich can b e m ad e availab le by the dem odu lator and fe d forw a rd to the deco d er. T h e technique w h ich m ake use o f this extra inform ation in the received sign a l is called so ft decisio n (S D ) d eco d in g [Sklar 1988 pp329-331, and C atterm ole 1986 p p l8 0 ]. T h erefo re, w h en th e dem odu lator sends a hard sym b o l decisio n t o the d eco der, it sends a sin gle sym b ol. H o w e v e r , when the dem odu lator sends a soft sym bol d e cis io n , it e ffe c tiv e ly sends a w o rd in place o f a single sym b o l w h ich is equivalent to sen d in g the deco d er a m easure o f con fid en ce along w ith the sym b ol. In such a case, the dem odu lator can be co n fig u red to ha ve a number o f quantisation levels g reater than ( T + 1). O ptim um S D d eco d in g is obta ined b y havin g

infin ite number o f quantisation levels. T h e S D decoding is m ost r e a d ily understood as a discrete approxim ation to maxim um lik e lih o o d (M L ) detection.

T h e S D sch em e is also used here in conjunction w ith S B S _ H D decoding as in the previou s case o f H D _ C C M A decoding. T h e demodulator sets a n u m ber o f decision thresholds to d e cid e w hich o f the possible signal levels have b een transmitted. In addition, the dem odu lator assigns each s ym b o l a con fidence le v e l w h ich is extracted fro m the received sign al quantisation. T h e S D distance between the S B S _ H D codeword

w ith i t ’ s sym bols con fidence le v e l and all th e adm issible codew ords is calculated. The adm issible cod ew o rd s are stored w ith the highest con fidence le v el o f e a c h symbol. The cod ew ord w ith least S D distance is chosen to represent the S D d eco d in g. This SD deco d in g techn ique can be summarised in th e fo llo w in g steps:

Step 1: Perform S B S _ H D decoding on th e rec e iv e d N -sym bo l c o d e w o rd . Step 2: Calculate the S D m etric values b etw een the S B S _ H D c o d e w o rd and all the

adm issible codew ords.

Step 3: C h oo se the codew ord with the least S D metric value t o represent the SD decoding.

Step 4: A lo o k up table is used to d eco d e the individual users’ c o d e w o rd s and hence their origin al sink data messages.

C onsider a set o f com posite cod ew o rd s each com prising N -s y m b o l. T h e received signal is W = ( w „ w

2

...w N), w h ere

w-

is th e magnitude o f the ele m e n t representing the i-th sym bol. In principle, join t M L d ecisio n carried out on the c o m p le te w o rd is a very p ow erfu l detection technique [C atterm ole 1986 p p l8 0 ]. T h erefo re, i f th e actual signal m agnitude o f N -sym bo l codew ord is m ad e available to the d eco d er, then a M L deco d in g fo r C C M A schemes can be p erform ed . T h is is a ch ieved b y calculating the

Euclidean distances between the received co d ew o rd and all the adm issible codew ords. T h e codew ord w ith minimum Euclidean distance (M E D ) is chosen to represen t the M L S D decoding cod ew ord . P ro vided the codew ords are all equ ally lik ely, th is strategy is optimum in the sense that it m inim ises the p ro b a b ility o f error in the d eco d er. A generalised M L S D decoding technique algorithm steps can be sum marised here as fo llo w s:

Step 1: Calculate the Euclidean distances b etw een the received soft inform ation codew ord and all th e possible codewords.

Step 2: T h e co d ew o rd w ith the M E D is chosen to represent the M L S D d eco d in g . Step 3: A lo o k up table is used to decode the in dividu al users’ cod ew o rd s and their origin al sink inform ation.

H ow ever, this technique is d ifficu lt to im plem en t in practice, because th is would require the storage o f the precise amplitudes o f all sym bols as received. In addition , the decoding table b eco m es unmanageably large as the length o f the cod e and th e number o f active users increases. Th erefo re, what is n eed ed is a sim ple means o f calculating the possible transmitted codew ords fro m the r e c e iv e d cod ew ord w ith least number o f operations possible.

In document Collaborative coding multiple access communications (Page 129-133)