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Wireless Workshop -   Coding Theory

Tropper Technologies' Wireless Workshop is designed to explore various aspects of emerging wireless technologies...

One of the primary drivers in the move from analog to digital communications were the benefits of spectral efficiency and the ability to detect and correct errors.  These capabilities are achieved via the use of coding.  Coding is usually applied in one of two domains, either source (speech) coding or channel coding.

 
 
  • Background

 

The purpose of the source coder is to remove as much redundancy as possible from the transmitted signal while maintaining fidelity.  Channel codes are usually bandwidth expanding and are used to improve the robustness of the link (BER vs.SNR).

  • Source Coding

Speech coders can be generally grouped into one of two categories: "Waveform" coders or "Vocoders". PCM speech coders (which belong to the class of waveform coders) achieve moderate compression ratios, via a process of endeavoring to recreate the transmitted waveform exactly. Enhanced Variable Rate (EVRC) speech coders (which belong to the class of vocoders) achieve a higher compression ratio (as compared to waveform coders) at the expense of complexity and associated delay. Vocoders tend to achieve higher compression ratios than waveform speech coders since vocoders either use a-priori knowledge of the transmitted waveform or make estimates beforehand.

Unlike waveform speech coders which introduce quantization distortion, vocoder based speech compression algorithms tend to introduce non-linear distortion.


The 8kb/s enhanced variable rate coder (EVRC) is standardized as IS-127. Bell Labs, played a large role in developing the vocoder as part of the Telecommunications Industry Association's (TIA) standards process.

EVRC technology is based on a relaxed code-excited linear predictive coding (RCELP) algorithm. RCELP is a generalization of the CELP speech-coding algorithm.   (See TIA/EIA/IS-127 Enhanced Variable Rate Codec, Speech Service Option 3 for Wideband Spread Spectrum Digital Systems, page 4-1).

  • Channel Coding

One typical measure of communication link performance is the familiar BER vs SNR curve (as a function of detection type, fading characteristics, etc.) .  These families of parametric curves are actually divined from the decision regions found above.  Once the decision regions are derived, the probability of error is computed.  The probability of error is simply the probability that a given decision variable U2 exceeds the decision variable U1.  This probability is related to the distance between the decision regions via the Q function.

As the density of the transmitted symbol alphabet grows, the spacing between the decision regions shrinks.  This degrades the BER vs. SNR performance.  An increase in measurement bandwidth increases the number of degrees of freedom available with which to make signal vs noise decisions and hence can be used to accommodate the symbol alphabet expansion.  Sometimes however, in bandwidth limited applications, bandwidth expansion is not an option.  In this case, Forward Error Correction (FEC) codes are used to combat errors to improve symbol estimates made at the detector.

These FEC codes can be of the block (Reed Solomon, Hamming, BCH, Cyclic, Linear) family, or convolutional family (with Viterbi decoders).

  • The Big Picture

The coding scheme and the modulation scheme are very tightly coupled together to create a robust communication link.  Moreover, the bandwidth expansion incurred via the use of FEC is balanced against the messaging overhead in the protocol layer that would be required to resend messages should FEC not be in place.