ChannelCapacityDigitalSystems copy

ChannelCapacityDigitalSystems copy - CHANNEL CAPACITY AND...

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1 C HANNEL C APACITY AND S HANNON L IMIT IN D IGITAL C OMMUNICATION S YSTEMS SANG HYUCK HA ABSTRACT In this paper, we establish the channel capacity and the Shannon limit in digital communication systems. For this purpose, we introduce two kinds of channel models, that is, the binary-input, binary-output Gaussian channel and the binary-input, continuous-output Gaussian channel. For each channel, we obtain both the channel capacity and the Shannon limit. 1. D IGITAL C OMMUNICATION S YSTEM Every basic digital communication system consists of a transmitter, an additive noise channel, and a receiver. The transmitter is composed of the discrete-input, discrete-output channel encoder and the modulator. The channel encoder introduces some redundant binary bits in the binary information sequence and the modulator maps each bit or a block of bits in the encoded sequence into one of the possible waveforms. On the other hand, the receiver includes the demodulator/detector and the channel decoder. The function of the demodulator is to process the channel-corrupted waveform and to reduce each waveform to a scalar or a vector that represents an estimate of the transmitted data symbol. The detector may decide on whether the transmitted bit is a 0 or 1 – two-level quantization (hard decision detector). Or, the detector may generate a multi-level (more than two) quantized version of the estimate (soft decision detector). The output from the detector is fed to the channel decoder. The performance and complexity of a receiver depends on which kind of detector/decoder combination is used. 2. S ETTING C HANNEL M ODELS In order to determine the channel capacity for a digital communication system, we should first establish the appropriate channel model. If we are interested in the design and performance analysis of the discrete channel encoder and decoder, it is appropriate to consider channel models in which the modulator and demodulator/detector are a part of the composite channel. In this paper, two channel models are considered since these models help us observe the channel capacity and the Shannon limit from the extreme standpoints.
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2 BINARY-INPUT, BINARY-OUTPUT GAUSSIAN CHANNEL If the modulator employs binary waveforms and the detector makes hard decisions, then the composite channel has a binary input sequence and a binary output sequence. Such a composite channel is characterized by the set X = {0, 1} of possible inputs, the set of Y = {0, 1} of the possible outputs to the possible inputs. If the channel
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This note was uploaded on 12/27/2011 for the course CMPSC 225 taught by Professor Vandam during the Fall '09 term at UCSB.

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ChannelCapacityDigitalSystems copy - CHANNEL CAPACITY AND...

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