Source and Channel Rate Allocation for Channel Codes Satisfying the Gilbert-Varshamov or Tsfasman-Vladut-Zink Bounds

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 bounds. Formulas giving the high resolution vector quantizer distortion of these systems are also derived. In addition, we give bounds on how far below 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

Source and Channel Rate Allocation for Channel Codes Satisfying the Gilbert-Varshamov or Tsfasman-Vladut-Zink Bounds

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 bounds. Formulas giving the high resolution vector quantizer distortion of these systems are also derived. In addition, we give bounds on how far below channel capacity the transmission rate should be for a given delay constraint. Index Terms: vector quantization, source and channel coding, linear error correcting codes, error exponent, Gilbert-Varshamov bound. Department of Electrical and Computer Engineering, University of California, San Diego, CA 92093-0407. fandras,[email protected] The research was supported in part by the National Science Foundation. This work was presented in part at CISS-97 in Baltimore, MD. 1 Introduction One commonly used approach to transmit source information across a noisy channel is to cascade a vector quantizer designed for a noiseless channel, and a block channel coder designed independe..