Compute-Forward for DMCs: Simultaneous Decoding of Multiple Combinations
Algebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations of codewords can sometimes be decoded more...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Centre Tecnològic de Telecomunicacions de Catalunya (CTTC) |
| Repositorio: | r-CTTC. Repositorio Institucional Producción Científica del Centre Tecnològic de Telecomunicacions de Catalunya (CTTC) |
| OAI Identifier: | oai:cttc.fundanetsuite.com:p3073 |
| Acceso en línea: | https://cttc.fundanetsuite.com/Publicaciones/ProdCientif/PublicacionFrw.aspx?id=3073 |
| Access Level: | acceso abierto |
| Palabra clave: | Decoding Lattices Linear codes Receivers Relay networks (telecommunications) Random variables Compute-forward joint decoding linear codes multiple-access channel |
| Sumario: | Algebraic network information theory is an emerging facet of network information theory, studying the achievable rates of random code ensembles that have algebraic structure, such as random linear codes. A distinguishing feature is that linear combinations of codewords can sometimes be decoded more efficiently than codewords themselves. The present work further develops this framework by studying the simultaneous decoding of multiple messages. Specifically, consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible. This technique has historically been used in conjunction with random i.i.d. codebooks to establish achievable rate regions for networks. Recently, it has been shown that, in certain scenarios, nested linear codebooks in conjunction with "single-user" or sequential decoding can yield better achievable rates. For instance, the compute-forward problem examines the scenario of recovering L <= K linear combinations of transmitted codewords over a K-user multiple-access channel (MAC), and it is well established that linear codebooks can yield higher rates. This paper develops bounds for simultaneous joint typicality decoding used in conjunction with nested linear codebooks, and applies them to obtain a larger achievable region for compute-forward over a K-user discrete memoryless MAC. The key technical challenge is that competing codeword tuples that are linearly dependent on the true codeword tuple introduce statistical dependencies, which requires careful partitioning of the associated error events. |
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