2008/09/30 by Emmanuel Abbe, Emmanuel Abbé, Abbe, Emmanuel +2
Computer Science · Engineering · Mathematics · #Cooperative Communication and Network Coding #Error Correcting Code Techniques #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probability (math.PR) #Wireless Communication Security Techniques #cs.IT #math.IT #math.PR
paper · pdf · doi:10.48550/arxiv.0809.5217
arxiv created 2008/09/30 · openalex publication_date 2008/09/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Over discrete memoryless channels (DMC), linear decoders (maximizing additive metrics) afford several nice properties. In particular, if suitable encoders are employed, the use of decoding algorithm with manageable complexities is permitted. Maximum likelihood is an example of linear decoder. For a compound DMC, decoders that perform well without the channel's knowledge are required in order to achieve capacity. Several such decoders have been studied in the literature. However, there is no such known decoder which is linear. Hence, the problem of finding linear decoders achieving capacity for compound DMC is addressed, and it is shown that under minor concessions, such decoders exist and can be constructed. This paper also develops a "local geometric analysis", which allows in particular, to solve the above problem. By considering very noisy channels, the original problem is reduced, in the limit, to an inner product space problem, for which insightful solutions can be found. The local setting can then provide counterexamples to disproof claims, but also, it is shown how in this problem, results proven locally can be "lifted" to results proven globally.