Maximum likelihood (ML) decision criteria have been developed for channels suffering from signal independent offset mismatch. Here, such criteria are considered for signal dependent offset, which means that the value of the offset may differ for distinct signal levels rather than being the same for all levels. An ML decision criterion is derived, assuming uniform distributions for both the noise and the offset. In particular, for the proposed ML decoder, bounds are determined on the standard deviations of the noise and the offset which lead to a word error rate equal to zero. Simulation results are presented confirming the findings.

We consider the transmission and storage of encoded strings of symbols over a noisy channel, where dynamic threshold detection is proposed for achieving resilience against unknown scaling and offset of the received signal. We derive simple rules for dynamically estimating the unknown scale (gain) and offset. The estimates of the actual gain and offset so obtained are used to adjust the threshold levels or to re-scale the received signal within its regular range. Then, the re-scaled signal, brought into its standard range, can be forwarded to the final detection/decoding system, where optimum use can be made of the distance properties of the code by applying, for example, the Chase algorithm. A worked example of a spin-torque transfer magnetic random access memory (STT-MRAM) with an application to an extended (72, 64) Hamming code is described, where the retrieved signal is perturbed by additive Gaussian noise and unknown gain or offset.

Besides the omnipresent noise, other important inconveniences in communication and storage systems are formed by gain and/or offset mismatches. In the prior art, a maximum likelihood (ML) decision criterion has already been developed for Gaussian noise channels suffering from unknown gain and offset mismatches. Here, such criteria are considered for Gaussian noise channels suffering from either an unknown offset or an unknown gain. Furthermore, ML decision criteria are derived when assuming a Gaussian or uniform distribution for the offset in the absence of gain mismatch.

We investigate a Knuth-like scheme for balancing q-ary code words, which has the virtue that lookup tables for coding and decoding the prefix are avoided by using precoding and error correction techniques. We show how the scheme can be extended to allow for error correction of single channel errors using a fast decoding algorithm that depends on syndromes only, making it considerably faster compared with the prior art exhaustive decoding strategy. A comparison between the new and prior art schemes, both in terms of redundancy and error performance, completes the study.