6.37 Information communication problems  (Page 7/8)

Selective error correction

We have found that digital transmission errors occur with a probability that remains constant no matter how "important"the bit may be. For example, in transmitting digitized signals, errors occur as frequently for the most significantbit as they do for the least significant bit. Yet, the former errors have a much larger impact on the overallsignal-to-noise ratio than the latter. Rather than applying error correction to each sample value, why not concentratethe error correction on the most important bits? Assume that we sample an 8 kHz signal with an 8-bit A/D converter.We use single-bit error correction on the most significant four bits and none on the least significant four. Bits aretransmitted using a modulated BPSK signal set over an additive white noise channel.

1. How many error correction bits must be added to provide single-bit error correction on the mostsignificant bits?
2. How large must the signal-to-noise ratio of the received signal be to insure reliablecommunication?
3. Assume that once error correction is applied, only the least significant 4 bits can be received in error.How much would the output signal-to-noise ratio improve using this error correction scheme?

Compact disk

Errors occur in reading audio compact disks. Very few errors are due to noise in the compact disk player; mostoccur because of dust and scratches on the disk surface. Because scratches span several bits, a single-bit error israre; several consecutive bits in error are much more common. Assume that scratch and dust-inducederrors are four or fewer consecutive bits long. The audio CD standard requires 16-bit, 44.1 kHz analog-to-digitalconversion of each channel of the stereo analog signal.

1. How many error-correction bits are required to correct scratch-induced errors for each 16-bitsample?
2. Rather than use a code that can correct several errors in a codeword, a clever 241 engineer proposes interleaving consecutive coded samples. As the cartoon shows, the bits representing coded samples are interpersed before they are written onthe CD. The CD player de-interleaves the coded data, then performs error-correction. Now, evaluate thisproposed scheme with respect to the non-interleaved one.

Communication system design

RU Communication Systems has been asked to design a communication system that meets the following requirements.

• The baseband message signal has a bandwidth of 10 kHz.
• The RUCS engineers find that the entropy $H$ of the sampled message signal depends on how many bits $b$ are used in the A/D converter (see table below).
• The signal is to be sent through a noisy channel having a bandwidth of 25 kHz channel centered at 2 MHzand a signal-to-noise ration within that band of 10 dB.
• Once received, the message signal must have a signal-to-noise ratio of at least 20 dB.

Can these specifications be met? Justify your answer.