Source and Channel Rate Allocation for Channel Codes Satisfying the Gilbert-Varshamov or

We derive bounds for optimal rate allocation between source and channel coding for linear channel codes that meet the Gilbert-Varshamov or Tsfasman-Vl˘ ¸-Zink bounds. Formulas giving the high resolution vector quantizer distortion of these sys- tems 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 be- tween channel code rate and relative minimum distance guaran- teed by the Gilbert-Varshamov bound, and do not require sophisti- cated 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.