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Bose and Lin introduced a class of systematic codes for detection of binary asymmetric errors. Later, in [4] this class was generalized and the Generalized Bose-Lin (GBL) codes were introduced. In this note, we describe a Generalized Bose-Lin codes of limited magnitude l. For these codes, the possible undetectable errors are characterized, the undetectable errors of minimum weight are determine...

A frequent and well-founded criticism of the maximum a posteriori (MAP) and minimum mean squared error (MMSE) estimates of a continuous parameter γ taking values in a differentiable manifold Γ is that they are not invariant to arbitrary ‘reparametrizations’ of Γ. This paper clarifies the issues surrounding this problem, by pointing out the difference between coordinate invariance, which is a si...

Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and their relation to a variety of other reported bounds. Within the class of lower bounds, we address de Caen’s based bounds and their improvements, sphere-packing ...