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Nonlinear Codes: The Product Construction

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1 Author(s)
Amrani, O. ; Tel-Aviv Univ., Tel-Aviv

The standard product construction is discussed with respect to nonlinear codes. Thus, so-called nonlinear product codes are obtained that are better than linear product codes of similar length and code rate, and at the same time, amenable for encoding/decoding. On the other hand, it is shown that certain notorious nonlinear codes have an augmented product construction, namely, they can be constructed by taking the union of a product code and certain of its cosets. The binary Hamming codes are shown to have similar construction. A simple two-stage decoder is proposed for nonlinear product (NLP) codes. The decoder is shown to be a bounded-distance (BD) information decoder that is the nonlinear equivalent of the BD decoder employed for linear codes. A list-based maximum-likelihood decoder is also discussed.

Published in:

Communications, IEEE Transactions on  (Volume:55 ,  Issue: 10 )

Date of Publication:

Oct. 2007

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