Correcting Wavelet Codes UsingInterleaving and Trapping
G. Robert Redinbo · IEEE Transactions on Signal Processing · 2015
A rate k/n wavelet code, a form of real convolutional code, that encodes k numbers into n numerical code symbols using the present and past input numbers, may be used to transport numerical data with redundancy factor (n-k). Such codes offer detection and correction within roundoff tolerances. Wavelet codes can be processed using two different algebraic representations, vector-matrix or polyphase polynomial. When an interleaver intersperses the code symbols, any burst of errors within the interelaver's frame length, appears in only one component of the polyphase format. A special extended polyphase parity-check matrix exposes the error bursts directly for redundancies greater than 1 or a deconvolver operation achieves the same when the redundancy factor is 1. The trapped errors correct the symbols by subtraction. Simulations verify the effectiveness of this trapping technique.