Better data protection for short communications
The recent trend to communicate in brief bursts has undermined assumptions in theoretical analysis. Mathematical tools valid for very long transmission durations, such as the asymptotic analysis implicit in large-deviation theory, need to be replaced by methods valid for finite transmission lengths. The MDITWACM (Mismatched decoding in information theory with applications to channel modelling) project has focused on developing new methods and tools that address challenges in mismatched decoding at arbitrary transmission lengths. Gallager’s cost-constrained ensemble was generalised to include multiple auxiliary costs. This ensemble serves as an alternative to constant-composition codes to improve the performance of independent and identically distributed (i.i.d.) random variable coding. A new simple method, fixed-energy renormalisation reduces the error of both coded modulation and bit-interleaved coded modulation (BICM) over additive white Gaussian noise channels. The generalised Gallager’s cost-constrained ensemble is also relevant for joint source-channel coding and in the analysis of expurgated exponents. The team proposed and studied an almost-lossless multi-class source-channel coding scheme. Here, source messages are assigned to different classes and encoded with a channel code that depends on the class index. Two alternative exact characterisations of the minimal error probability of Bayesian M-ary hypothesis testing have been derived. When applied to the mismatched discrete memoryless multiple-access channel, an extension of the bounds in Gallager’s cost-constrained ensemble yield error exponents that are tight with respect to the ensemble average, and positive within the interior of Lapidoth's achievable rate region. In the setting of single-user mismatched decoding, similar analysis techniques were applied to two types of superposition coding. This superposition method was used for the mismatched decoding problem for binary-input discrete memoryless channels. A promising enhancement to large-deviation theory is the Laplace or saddlepoint approximation, which has shown its effectiveness in numerous applications in physics. The project demonstrated significant improvements in common estimates of error probabilities at no additional computational cost with significant implications for information and communication technology.
Keywords
Data protection, data integrity, mismatched decoding, i.i.d., Gaussian noise, Lapidoth's achievable rate region, superposition coding, Laplace, saddlepoint approximation
