Fixed-length Codewords Research Articles

Quantizing Noise of ΔM/PCM Encoders

We consider the pulse-code-modulation encoder that contains a delta modulator for analog-to-digital conversion, and a finite impulse response digital filter that suppresses high-frequency components of the delta modulation signal. A PCM word generator produces fixed-length binary code words by rounding and amplitude limiting the filter output samples. The quantizing noise of the resulting PCM signal has four components: delta modulation slope overload noise, filtered delta modulation granular noise, amplitude overload noise, and word generator roundoff noise. We analyze the total quantizing noise for the case where the encoder input is a Gaussian random process and the digital filter impulse response is uniform (all coefficients equal). Such filters possess important implementation advantages and appear to be near optimal with respect to signal-to-noise performance. Our analysis results in curves which show the relationship of signal-to-noise ratio to filter order, delta modulation sampling rate, and PCM word length.

A class of simple and optimal strategies for block coding on the binary symmetric channel with noiseless feedback

A class of simple feedback strategies is developed. The fixed-length codewords can be described by an interesting sequence of trees. The decoder scans the received block in the reverse direction, starting at the most recent bit. As this scan progresses, a certain pair of characteristic bit patterns are replaced by the digits 0 or 1, respectively. For certain values of the information rate <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</tex> , this class of strategies corrects the largest error fraction possible.