470:
42:
For an optimized detector for digital signals the priority is not to reconstruct the transmitter signal, but it should do a best estimation of the transmitted data with the least possible number of errors. The receiver emulates the distorted channel. All possible transmitted data streams are fed
426:
43:
into this distorted channel model. The receiver compares the time response with the actual received signal and determines the most likely signal. In cases that are most computationally straightforward,
282:
172:
534:
G. Bosco, P. Poggiolini, and M. Visintin, "Performance
Analysis of MLSE Receivers Based on the Square-Root Metric," J. Lightwave Technol. 26, 2098–2109 (2008)
619:
596:
Katz, G., Sadot, D., Mahlab, U., and Levy, A.(2008) "Channel estimators for maximum-likelihood sequence estimation in direct-detection optical communications",
658:
653:
491:
453:
325:
576:
557:
513:
212:(MAP) estimation approach. This is more complex than maximum likelihood sequence estimation and requires a known distribution (in
432:
448:
587:"Performance evaluation of maximum likelihood sequence estimation receivers in lightwave systems with optical amplifiers"
79:
via a transformation that may be nonlinear and may involve attenuation, and would usually involve the incorporation of
626:
484:
478:
663:
44:
495:
27:
84:
234:
208:
In contrast, the related method of maximum a posteriori estimation is formally the application of the
124:
209:
87:
of this transformation are assumed to be known. The problem to be solved is to use the observations {
620:"Maximum-Likelihood Sequence Estimation of Nonlinear Channels in High-Speed Optical Fiber Systems"
217:
213:
107:
572:
553:
316:
601:
586:
299:) denotes the conditional joint probability density function of the underlying series {
647:
436:
189:) denotes the conditional joint probability density function of the observed series {
435:, the problem of maximum likelihood sequence estimation can be reduced to that of a
80:
31:
47:
can be used as the decision criterion for the lowest error probability.
618:
W. Sauer-Greff; A. Dittrich; M. Lorang & M. Siegrist (2001-04-16).
228:)} is defined to be a sequence of values which maximize the functional
118:)} is defined to be a sequence of values which maximize the functional
605:
431:
In cases where the contribution of random noise is additive and has a
106:
Maximum likelihood sequence estimation is formally the application of
548:
Andrea
Goldsmith (2005). "Maximum Likelihood Sequence Estimation".
625:. The Telecommunications Research Center Vienna. Archived from
421:{\displaystyle P(x)=p(x\mid r)={\frac {p(r\mid x)p(x)}{p(r)}}.}
463:
567:
Philip Golden; Hervé Dedieu & Krista S. Jacobsen (2006).
220:) for the underlying signal. In this case the estimate of {
307:)} given that the observed series has taken the values {
585:
Crivelli, D. E.; Carrer, H. S., Hueda, M. R. (2005)
328:
237:
127:
197:)} given that the underlying series has the values {
420:
276:
166:
552:. Cambridge University Press. pp. 362–364.
8:
55:Suppose that there is an underlying signal {
110:to this problem. That is, the estimate of {
16:Algorithm for analyzing noisy data streams
514:Learn how and when to remove this message
365:
327:
236:
126:
477:This article includes a list of general
527:
20:Maximum likelihood sequence estimation
71:)} is available. The observed signal
7:
454:Partial-response maximum-likelihood
483:it lacks sufficient corresponding
14:
95:)} to create a good estimate of {
63:)}, of which an observed signal {
30:that extracts useful data from a
468:
433:multivariate normal distribution
277:{\displaystyle P(x)=p(x\mid r),}
167:{\displaystyle L(x)=p(r\mid x),}
591:Latin American Applied Research
571:. CRC Press. pp. 319–321.
659:Error detection and correction
569:Fundamentals of DSL Technology
409:
403:
395:
389:
383:
371:
359:
347:
338:
332:
268:
256:
247:
241:
158:
146:
137:
131:
1:
654:Telecommunications techniques
449:Maximum-likelihood estimation
680:
45:root mean square deviation
550:Wireless Communications
498:more precise citations.
593:, 35 (2), 95–98.
422:
278:
168:
85:statistical parameters
28:mathematical algorithm
423:
279:
169:
326:
235:
210:maximum a posteriori
125:
598:Optical Engineering
418:
274:
218:prior distribution
164:
108:maximum likelihood
664:Signal estimation
606:10.1117/1.2904827
524:
523:
516:
413:
671:
640:
638:
637:
631:
624:
600:47 (4), 045003.
582:
563:
535:
532:
519:
512:
508:
505:
499:
494:this article by
485:inline citations
472:
471:
464:
427:
425:
424:
419:
414:
412:
398:
366:
283:
281:
280:
275:
173:
171:
170:
165:
679:
678:
674:
673:
672:
670:
669:
668:
644:
643:
635:
633:
629:
622:
617:
614:
579:
566:
560:
547:
544:
542:Further reading
539:
538:
533:
529:
520:
509:
503:
500:
490:Please help to
489:
473:
469:
462:
445:
399:
367:
324:
323:
233:
232:
123:
122:
53:
40:
17:
12:
11:
5:
677:
675:
667:
666:
661:
656:
646:
645:
642:
641:
613:
612:External links
610:
609:
608:
594:
583:
577:
564:
558:
543:
540:
537:
536:
526:
525:
522:
521:
504:September 2010
476:
474:
467:
461:
458:
457:
456:
451:
444:
441:
439:minimization.
429:
428:
417:
411:
408:
405:
402:
397:
394:
391:
388:
385:
382:
379:
376:
373:
370:
364:
361:
358:
355:
352:
349:
346:
343:
340:
337:
334:
331:
317:Bayes' theorem
285:
284:
273:
270:
267:
264:
261:
258:
255:
252:
249:
246:
243:
240:
214:Bayesian terms
175:
174:
163:
160:
157:
154:
151:
148:
145:
142:
139:
136:
133:
130:
75:is related to
52:
49:
39:
36:
15:
13:
10:
9:
6:
4:
3:
2:
676:
665:
662:
660:
657:
655:
652:
651:
649:
632:on 2012-03-11
628:
621:
616:
615:
611:
607:
603:
599:
595:
592:
588:
584:
580:
578:9780849319136
574:
570:
565:
561:
559:9780521837163
555:
551:
546:
545:
541:
531:
528:
518:
515:
507:
497:
493:
487:
486:
480:
475:
466:
465:
459:
455:
452:
450:
447:
446:
442:
440:
438:
437:least squares
434:
415:
406:
400:
392:
386:
380:
377:
374:
368:
362:
356:
353:
350:
344:
341:
335:
329:
322:
321:
320:
319:implies that
318:
314:
310:
306:
302:
298:
295: |
294:
290:
271:
265:
262:
259:
253:
250:
244:
238:
231:
230:
229:
227:
223:
219:
215:
211:
206:
204:
200:
196:
192:
188:
185: |
184:
180:
161:
155:
152:
149:
143:
140:
134:
128:
121:
120:
119:
117:
113:
109:
104:
102:
98:
94:
90:
86:
82:
78:
74:
70:
66:
62:
58:
50:
48:
46:
37:
35:
33:
29:
25:
21:
634:. Retrieved
627:the original
597:
590:
568:
549:
530:
510:
501:
482:
430:
312:
308:
304:
300:
296:
292:
288:
286:
225:
221:
207:
202:
198:
194:
190:
186:
182:
178:
176:
115:
111:
105:
100:
96:
92:
88:
81:random noise
76:
72:
68:
64:
60:
56:
54:
41:
23:
19:
18:
496:introducing
648:Categories
636:2010-09-02
479:references
460:References
51:Background
32:noisy data
378:∣
354:∣
263:∣
153:∣
443:See also
34:stream.
492:improve
26:) is a
575:
556:
481:, but
287:where
177:where
83:. The
38:Theory
630:(PDF)
623:(PDF)
573:ISBN
554:ISBN
315:)}.
216:, a
205:)}.
103:)}.
24:MLSE
602:doi
650::
589:,
639:.
604::
581:.
562:.
517:)
511:(
506:)
502:(
488:.
416:.
410:)
407:r
404:(
401:p
396:)
393:x
390:(
387:p
384:)
381:x
375:r
372:(
369:p
363:=
360:)
357:r
351:x
348:(
345:p
342:=
339:)
336:x
333:(
330:P
313:t
311:(
309:r
305:t
303:(
301:x
297:r
293:x
291:(
289:p
272:,
269:)
266:r
260:x
257:(
254:p
251:=
248:)
245:x
242:(
239:P
226:t
224:(
222:x
203:t
201:(
199:x
195:t
193:(
191:r
187:x
183:r
181:(
179:p
162:,
159:)
156:x
150:r
147:(
144:p
141:=
138:)
135:x
132:(
129:L
116:t
114:(
112:x
101:t
99:(
97:x
93:t
91:(
89:r
77:x
73:r
69:t
67:(
65:r
61:t
59:(
57:x
22:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.