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Electrical Communications Systems ECE.09.331 Spring 2007PlanECOMMS: TopicsDigital CommunicationsDigital Communications: RationalePrincipleDigital Communication ParadigmsDigital Communications TransceiverSource EncodingSource Encoding RequirementsHuffman CodingSlide 12Error Control CodingError Control CodesParity Check CodesRemediation for Detected Errors: ARQ(7, 4) Hamming CodeSlide 18Slide 19Hamming EncoderSyndrome DecodingHamming DecoderSlide 23SummaryS. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityElectrical Electrical Communications SystemsCommunications SystemsECE.09.331ECE.09.331 Spring 2007Spring 2007Shreekanth MandayamECE DepartmentRowan Universityhttp://engineering.rowan.edu/~shreek/spring07/ecomms/ Lecture 9aLecture 9aMarch 20, 2007March 20, 2007S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityPlanPlan•Digital Communications•Introduction•Digital Communications Transceiver (CODEC/MODEM)•Digital Baseband Communications•Source Encoding•Huffman Coding•Error Control Coding•Hamming Distance•Error Detection Coding•Parity Check Code•Error Correction Coding•Hamming CodeS. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityECOMMS: TopicsECOMMS: TopicsP r o b a b i l i t yI n f o r m a t i o nE n t r o p yC h a n n e l C a p a c i t yD i s c r e t eP o w e r & E n e r g y S i g n a l sC o n t i n u o u s F o u r i e r T r a n s f o r mD i s c r e t e F o u r i e r T r a n s f o r mB a s e b a n d a n d B a n d p a s s S i g n a l sC o m p l e x E n v e l o p eG a u s s i a n N o i s e & S N RR a n d o m V a r i a b l e sN o i s e C a l c u l a t i o n sC o n t i n u o u sS i g n a l sA MS w i t c h i n g M o d u l a t o rE n v e l o p D e t e c t o rD S B - S CP r o d u c t M o d u l a t o rC o h e r e n t D e t e c t o rC o s t a s L o o pS S BW e a v e r ' s M e t h o dP h a s i n g M e t h o dF r e q u e n c y M e t h o dF r e q u e n c y & P h a s e M o d u l a t i o nN a r r o w b a n d / W i d e b a n dV C O & S l o p e D e t e c t o rP L LA n a l o gS o u r c e E n c o d i n gH u f f m a n c o d e sE r r o r - c o n t r o l E n c o d i n gH a m m i n g C o d e sS a m p l i n gP A MQ u a n t i z a t i o nP C ML i n e E n c o d i n gT i m e D i v i s i o n M u xT 1 ( D S 1 ) S t a n d a r d sP a c k e t S w i t c h i n gE t h e r n e tI S O 7 - L a y e r P r o t o c o lB a s e b a n dC O D E CA S KP S KF S KB P S KQ P S KM - a r y P S KQ A MB a n d p a s sM O D E MD i g i t a lD i g i t a l C o m m T r a n s c e i v e rS y s t e m sE l e c t r i c a l C o m m u n i c a t i o n S y s t e m sS. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityDigital CommunicationsDigital Communications•Some Milestones•Claude Shannon, 1948•X.25 (Telephony)•IEEE 802.3 (Ethernet)•ARPANET, 1969•IEEE 802.5 (FDDI)•ISO-OSI 7-layer Network Reference Model•CDMA•GSM•VOIP•SIPprotocols.comS. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityDigital Communications: Digital Communications: RationaleRationale•Information Theory:•What is the fundamental limit on the compression and refinement of information generated by the source?•What is the fundamental limit on the transmission rate of information over a noisy channel?•How do we approach these limits?S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityPrinciplePrinciple1 0 1 0………1 10 0Analog messageDigitalcodeDigital messageSinusoidal carriermodulateAMFMPMAM &PM1 0 1 0S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityDigital Communication ParadigmsDigital Communication ParadigmsMultiplexerMessage 2Message 3 Message 1123S1223SDemultiplexerMessage 2Message 3 Message 1PacketizingMessage 2Message 3 Message 11HH23HH21H3HH21H3HMessage 2Message 3 Message 1Depacket-izingDepacket-izingDepacket-izingCircuit SwitchingPacket SwitchingSync bitsHeader bitsS. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityDigital Communications TransceiverDigital Communications TransceiverAnti-aliasingFilterSampling QuantizationDataEncryptionEncoderSourceEncoderErrorControlEncoderChannel/LineEncoderModulatorMUXAudioAmpSourceDecoderDataEncryptionDecoderErrorControlDecoderEqualization /DecisionCircuitsDemod-ulatorDEMUXReconstruction/DACADCCODECMODEMAnalog o/pMultiple access channelAnalog i/pS. Mandayam/ ECOMMS/ECE Dept./Rowan UniversitySource EncodingSource Encoding•Why are we doing this?AnalogMessageA/DConverterDigitalSourceSourceEncoderSourceSymbols (0/1)Source EntropyEncodedSymbols (0/1)Source-CodedSymbol EntropyS. Mandayam/ ECOMMS/ECE Dept./Rowan UniversitySource Encoding Source Encoding RequirementsRequirements•Decrease Lav•Unique decoding•Instantaneous decodingS. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityHuffman CodingHuffman Coding2-Step Process•Reduction•List symbols in descending order of probability•Reduce the two least probable symbols into one symbol equal to their combined probability•Reorder in descending order of probability at each stage•Repeat until only two symbols remain•Splitting•Assign 0 and 1 to the final two symbols remaining and work backwards•Expand code at each split by appending a 0 or 1 to each code word•Examplem(j) A B C D E F G HP(j) 0.1 0.18 0.4 0.05 0.06 0.1 0.07 0.04S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityDigital Communications TransceiverDigital Communications TransceiverAnti-aliasingFilterSampling QuantizationDataEncryptionEncoderSourceEncoderErrorControlEncoderChannel/LineEncoderModulatorMUXAudioAmpSourceDecoderDataEncryptionDecoderErrorControlDecoderEqualization /DecisionCircuitsDemod-ulatorDEMUXReconstruction/DACADCCODECMODEMAnalog o/pMultiple access channelAnalog i/pS. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityError Control CodingError Control Coding•Hamming DistanceThe number of locations (bits) at which two code words differ•Theorem 1A code with a Hamming distance of d >= t+1 can detect t errors in the received code word•Theorem 2A code with a Hamming distance of 2t+1 <= d <= 2t+2 can detect and correct t errors in the received code wordError Detection(ARQ Technique)Error Correction(FEC Technique)S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityError Control CodesError Control CodesPrincipleBlock Codes(memoryless)Convolutional Codes(with memory)Will not discuss!Block CoderkinformationbitsnencodedbitsInformation bitsParity bitskn-kn-bit codeword(n, k) systematic block codeAddRedundancy!!S. Mandayam/ ECOMMS/ECE Dept./Rowan UniversityParity Check


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