Minimization of mean-square error for data transmitted via group codes

Interframe Adaptive Data Compression Techniques for Images.

“…6 Gn,k(h) = I ®h-gj (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) j=l where j ®denotes the exclusive-or summation, the dot represents the binary product (or 'and' operation), and gj's are the basis vectors of Table 6-2. We use (6-2) for decoding and (6-3) for the calculation of the channel distortion.…”

“…We note from (6-2) that the decoder is dependent upon the channel bit-reversal probability p. While from (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18) and (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) we note that the encoder is independent of p for a givenG. In practice p might vary from time to time and thus cannot be known exactly.…”

“…1-1), e.g., in the design of quantizer [41], design of predictor coefficients for DPCM transmission [14], periodic reinitialization of DPCM loops, etc. In [18,19] the decoding rule is restricted to map back into the set S. Wolf and Redinbo [78,79] Except when y is uniformly distributed the set S of its quantized values cannot be equispaced and equiprobable at the same time for k > 1. If y is non-uniformly distributed and is quantized using the minimum mean square error Max quantizer, the set S is neither equispaced nor equiprobable for k > 1.…”

Channel-optimized scalar quantizers with erasure correcting codes

“…The usual goal to design an index *Correspondence: ye.li@siat.ac.cn 1 Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China Full list of author information is available at the end of the article assignment for noisy channels is to minimize the endto-end MSD over all possible index assignments. Some famous index assignments, such as natural binary code (NBC), Gray code and randomly chosen index assignments, are studied on a binary symmetric channel (BSC) in [16][17][18][19][20][21]. In [16], it is proved that NBC is optimal for uniform scalar quantizers and uniform source.…”

Quantizers with uniform encoders and channel optimized decoders

“…They also asserted (without a published proof) the optimality of the Natural Binary Code for the binary symmetric channel. Crimmins et al [1] studied the uniform scalar quantizer for the uniform source and proved the Yamaguchi-Huang assertion, that the Natural Binary Code is the best possible index assignment in the mean squared sense for the binary symmetric channel. McLaughlin, Neuhoff, and Ashley [2] generalized this result for certain uniform vector quantizers and uniform vector sources.…”