동종 부호를 활용한 연산을 위한 최적 전송률 분석

Abstract

Recent studies by Padakandla and Pradhan, and by Lim, Feng, Pastore, Nazer, and Gastpar built the framework of nested coset codes for the computation problem, namely, computing a desired linear combination of sources over a multiple accesschannel. This paper presents an outer bound on the optimal rate region for the computation problem when the encoding strategy is restricted to random ensembles of homologous codes, namely, structured nested coset codes from the same generator matrix and individual shaping functions based on joint typicality encoding. The optimal rate region is characterized when the desired linear combination and the channel structure are matched. Under this condition, a suboptimal joint typicality decoding rule is shown to achieve the optimal rate region. This result implies that the performance of random homologous code ensembles cannot be improved by using the optimal maximum likelihood decoder for the aforementioned classof computation problems.