科研之友
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摘要
The code termed a 'zoom' code incorporates several levels of check digits. The zeroth level is just the data sequence itself, and the ith level is such that it would correct all transmission errors at earlier levels if it were itself transmitted without error. The density of check digits in time decreases exponentially with increasing i, at a rate dependent on the transmission error rate. The construction then gives an optimizing rationale for a generalized convolutional code, a 'multipulse' code, invariant under a time shift whose size varies with the level. The zoom code gives just the 'liberated' version of a Bose-Chauduri-Hocquenhem code if a Galois construction is used at every level; 'liberated' in that the optimality-negating constraint of cyclicity is relaxed to the multipulse property. The notion of cascading checks is not wholly new, but the approach taken exploits the intrinsically recursive character thus generated. Decoding recursions (between levels) are developed. If the criterion of minimizing the probability of any error is replaced by the more realistic one of minimizing the BER, it is found that checks should have the sparse character of a low-density parity check code. However, recursive decodings replace the iterative decodings of the latter.
- 出版日期2012-7
