Title :
Source and channel rate allocation for channel codes satisfying the Gilbert-Varshamov or Tsfasman-Vladut-Zink bounds
Author :
Méhes, András ; Zeger, Kenneth
Author_Institution :
R. Inst. of Technol., Stockholm, Sweden
fDate :
9/1/2000 12:00:00 AM
Abstract :
We derive bounds for optimal rate allocation between source and channel coding for linear channel codes that meet the Gilbert-Varshamov or Tsfasman-Vladut-Zink (1984) bounds. Formulas giving the high resolution vector quantizer distortion of these systems are also derived. In addition, we give bounds on how far below the channel capacity the transmission rate should be for a given delay constraint. The bounds obtained depend on the relationship between channel code rate and relative minimum distance guaranteed by the Gilbert-Varshamov bound, and do not require sophisticated decoding beyond the error correction limit. We demonstrate that the end-to-end mean-squared error decays exponentially fast as a function of the overall transmission rate, which need not be the case for certain well-known structured codes such as Hamming codes
Keywords :
channel capacity; channel coding; decoding; delays; error correction codes; linear codes; mean square error methods; optimisation; source coding; vector quantisation; Gilbert-Varshamov bound; Hamming codes; Tsfasman-Vladut-Zink bound; channel capacity; channel code rate; channel coding; channel rate allocation; decoding; delay constraint; end-to-end mean-squared error; error correction limit; high resolution vector quantizer distortion; linear channel codes; optimal rate allocation; relative minimum distance; source coding; source rate allocation; structured codes; transmission rate; Algorithm design and analysis; Channel capacity; Channel coding; Decoding; Delay; Error correction codes; Error probability; Gaussian channels; Source coding; Vector quantization;
Journal_Title :
Information Theory, IEEE Transactions on
