Towards an Algebraic Network Information Theory: Distributed Lossy Computation of Linear Functions

Abstract

Consider the important special case of the K-user distributed source coding problem where the decoder only wishes to recover one or more linear combinations of the sources. The work of Körner and Marton demonstrated that, in some cases, the optimal rate region is attained by random linear codes, and strictly improves upon the best-known achievable rate region established via random i.i.d. codes. Recent efforts have sought to develop a framework for characterizing the achievable rate region for nested linear codes via joint typicality encoding and decoding. Here, we make further progress along this direction by proposing an achievable rate region for simultaneous joint typicality decoding of nested linear codes. Our approach generalizes the results of Körner and Marton to computing an arbitrary number of linear combinations and to the lossy computation setting.

Improved Communication Efficiency for Distributed Mean Estimation with Side Information

“…The motivation is based on the fact that the server could store publicly accessible data, and also at each iteration, the server has already received data sent by clients at previous iterations, which can be viewed as side information. Rather than using random coding with joint typicality tools such as in [17], [20], which is impractical to implement, we follow the work in [16] which proposed a Wyner-Ziv estimator based on coset coding. Unfortunately, they only utilized the side information at the server, but failed to exploit correlation between clients' vectors.…”