Binary lattice vector quantization with linear block codes andaffine index assignments

We determine analytic expressions for the performance of some low-complexity combined source-channel coding systems. The main tool used is the Hadamard transform. In particular, we obtain formulas for the average distortion of binary lattice vector quantization with affine index assignments, linear block channel coding, and a binary-symmetric channel. The distortion formulas are specialized to nonredundant channel codes for a binary-symmetric channel, and then extended to affine index assignments on a binary-asymmetric channel. Various structured index assignments are compared. Our analytic formulas provide a computationally efficient method for determining the performance of various coding schemes. One interesting result shown is that for a uniform source and uniform quantizer, the natural binary code is never optimal for a nonsymmetric channel, even though it is known to be optimal for a symmetric channel     

Performance of quantizers on noisy channels using structuredfamilies of codes

Achievable distortion bounds are derived for the cascade of structured families of binary linear channel codes and binary lattice vector quantizers. It is known that for the cascade of asymptotically good channel codes and asymptotically good vector quantizers the end-to-end distortion decays to zero exponentially fast as a function of the overall transmission rate, and is achieved by choosing a channel code rate that is independent of the overall transmission rate. We show that for certain families of practical channel codes and binary lattice vector quantizers, the overall distortion can be made to decay to zero exponentially fast as a function of the square root of transmission rate. This is achieved by carefully choosing a channel code rate that decays to zero as the transmission rate grows. Explicit channel code rate schedules are obtained for several well-known families of channel codes     

Source and channel rate allocation for channel codes satisfying theGilbert-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 (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     

Properties of optical transition radiation for charged particle inclined flight through a finite thick plate IX

In this paper the OTR angular distributions are considered in the general case of inclined particle incidence on a finite width plate with strong absorption. A sufficient increase of the OTR intensity in the case of grazing flight through a thin (as compared to λ) plate is shown to be caused by the Vavilov-Cherenkov radiation emitted from metal to vacuum. Attention is paid to peculiar interferential effects occurring in the OTR angular distributions in the plate case.