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This chapter presents a new class of codes, called unequal error control (UEC) codes and unequal error protection (UEP) codes, that has different error control levels in a codeword such that ome part of the word is more strongly controlled from errors than other parts [FUJI98, FUJI95, MASN67]. The discussion is organized as follows: Error models for the UEC codes and the UEP codes are clari ed rst. Then this chapter demonstrates some types of UEC codes and UEP codes and their applications to holographic memories and to lossless compressed text data, respectively. for visual basic.net. Draw 39 barcode for .net use .net vs 2010 crystal code39 printer tocreate code39 .Related: Generate Code 39 C# , VB.NET Data Matrix Generation , .NET ITF-14 Generation

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Control qr bidimensional barcode image with visual c# using barcode printing for net In our example with iris, the ECC is designed to encode 140 bits into 2048-bit codeword he redundancy rate of such ECC is quite high; 2048/140 = 1463 On enrollment, the codeword is simply XOR-ed with the iris template, and the resulting biometrically encrypted key is stored Neither the codeword nor the biometric template can be retrieved from the helper data, which is similar to a one-time-pad cryptosystem known in cryptography It is interesting to note that there are no speci c locations where the 140-bit key is hidden; it is dispersed over all 2048 bits On veri cation, a fresh 2048-bit iris template is obtained Some bits may have errors The fresh template is XOR-ed with the stored biometrically encrypted key If there were no errors, the original codeword would be obtained.

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However, since errors are unavoidable in biometrics, the result of the XOR will differ from the correct codeword Here the ECC decoder comes into play: If the number of errors is not too large, the ECC can correct all the errors and obtain the original codeword Since the codewords are deterministically mapped to 140-bit keys, the correct 140-bit key will be retrieved If, on the other hand, the number of errors exceeds the ECC s capability, the decoder will declare a failure Therefore, the output of BE algorithm is either a key or a failure message Ideally, the failure should be output for an impostor only; however, it could happen for a legitimate user as well that is, the system could have a false rejection, as in conventional biometrics As we can see, in the case of BE the ECC replaces a simple threshold-based Yes/No scheme of conventional biometrics.

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Designing a good (2048, 140) ECC for BE is itself a serious technological challenge, since the error rate for a biometric template is usually high Hao et al [31] used a combination of Hadamard (aka 1st order Reed Muller) and Reed Solomon ECCs Normally, a block ECC corrects up to 25% of errors in a hard decoding mode, which would be 511 errors in our example However, the authors ran the Reed Muller ECC in a soft decoding mode (ie, the decoder always outputs the nearest codeword, even in the case of possible failure), which allowed it to achieve better error-correcting capabilities To make sure that the algorithm always outputs the correct key (eg, in the soft decoding mode the ECC may output any key), a hashed value of the key is stored into the helper data, as shown in Figure 263.

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