Decoders minimizing the Euclidean distance between the received word and the candidate codewords are known to be optimal for channels suffering from Gaussian noise. However, when the stored or transmitted signals are also corrupted by an unknown offset, other decoders may perform better. In particular, applying the Euclidean distance on normalized words makes the decoding result independent of the offset. The use of this distance measure calls for alternative code design criteria in order to get good performance in the presence of both noise and offset. In this context, various adapted versions of classical binary block codes are proposed, such as (i) cosets of linear codes, (ii) (unions of) constant weight codes, and (iii) unordered codes. It is shown that considerable performance improvements can be achieved, particularly when the offset is large compared to the noise.@en

Data transmission is ubiquitous in all walks of life, ranging from basic home and office appliances like compact disc players and hard disk drives to deep space communication. More often than not, the communication and storage channels are noisy, and data might be distorted during transmission. However, noise is not the only disturbance during the data transmission, and information can sometimes be seriously distorted by the phenomena of unknown channel gain or offset (drift) mismatch. The conventional minimum Euclidean distance based detection, where the receiver picks a codeword from the codebook to minimize the Euclidean distance with the received word, has a poor performance under the gain and/or offset mismatch. Recently, a Pearson distance based detection was introduced, which is immune to unknown offset and/or gain mismatch, but the drawback is that it is pretty sensitive to errors caused by the noise. This thesis investigates possible coding techniques to improve decoders’ performance in noisy channel conditions while maintaining the resistance against the gain and/or offset mismatch. The results discussed in the thesis are divided into four parts, based on different assumptions on the gain and/or offset mismatch. @en

We consider noisy data transmission channels with unknown scaling and varying offset mismatch. Minimum Pearson distance detection is used in cooperation with a difference operator, which offers immunity to such mismatch. Pair-constrained codes are proposed for unambiguous decoding, where in each codeword certain adjacent symbol pairs must appear at least once. We investigate the cardinality and redundancy of these codes.@en

In many channels, the transmitted signals do not only face noise, but offset mismatch as well. In the prior art, maximum likelihood (ML) decision criteria have already been developed for noisy channels suffering from signal independent offset . In this paper, such ML criterion is considered for the case of binary signals suffering from Gaussian noise and signal dependent offset . The signal dependency of the offset signifies that it may differ for distinct signal levels, i.e., the offset experienced by the zeroes in a transmitted codeword is not necessarily the same as the offset for the ones. Besides the ML criterion itself, also an option to reduce the complexity is considered. Further, a brief performance analysis is provided, confirming the superiority of the newly developed ML decoder over classical decoders based on the Euclidean or Pearson distances.@en

In many channels, the transmitted signals do not only face noise, but offset mismatch as well. In the prior art, maximum likelihood (ML) decision criteria have already been developed for noisy channels suffering from signal independent offset . In this paper, such ML criterion is considered for the case of binary signals suffering from Gaussian noise and signal dependent offset . The signal dependency of the offset signifies that it may differ for distinct signal levels, i.e., the offset experienced by the zeroes in a transmitted codeword is not necessarily the same as the offset for the ones. Besides the ML criterion itself, also an option to reduce the complexity is considered. Further, a brief performance analysis is provided, confirming the superiority of the newly developed ML decoder over classical decoders based on the Euclidean or Pearson distances.@en

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.@en

In communication and storage systems, noise and interference are not the only disturbances during the data transmission, sometimes the error performance is also seriously degraded by offset mismatch. We consider a simple channel such that the received signal is distorted by noise and offset mismatch, that is, r = x+v+b1, where x=(x1, x2, . . . , xn) is the transmitted codeword from a codebook, v = (v1, v2, . . . , vn) 2 Rn is the noise vector, where the vi are independently normally distributed with mean 0 and standard deviation _, b is a real number representing the channel offset, 1 is the real all-one vector (1, . . . , 1) of length n, and r 2 Rn is the received vector. Minimum modified Pearson distance (MMPD) detection has been proposed [1] as an alternative to minimum Euclidean distance (MED) detection to counter the effects of offset mismatch. A major concern, however, is the fact that the evaluation of MMPD is an exhaustive search over all candidate codewords which is infeasible for large codes. Various block codes have been proposed [2] to get good performance for channels with both noise and offset if the MMPD detection is used. @en

Reliability is a critical issue for modern multi-level cell memories. We consider a multi-level cell channel model such that the retrieved data is not only corrupted by Gaussian noise, but hampered by scaling and offset mismatch as well. We assume that the intervals from which the scaling and offset values are taken are known, but no further assumptions on the distributions on these intervals are made. We derive maximum likelihood (ML) decoding methods for such channels, based on finding a codeword that has closest Euclidean distance to a specified set defined by the received vector and the scaling and offset parameters. We provide geometric interpretations of scaling and offset and also show that certain known criteria appear as special cases of our general setting.@en

Data storage systems may not only be disturbed by noise. In some cases, the error performance can also be seriously degraded by offset mismatch. Here, channels are considered for which both the noise and offset are bounded. For such channels, Euclidean distance-based decoding, Pearson distance-based decoding, and Maximum Likelihood decoding are considered. In particular, for each of these decoders, bounds are determined on the magnitudes of the noise and offset intervals which lead to a word error rate equal to zero. Case studies with simulation results are presented confirming the findings.@en