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We consider a coded compressed sensing approach for the unsourced randomaccess and replace the outer tree code proposed by Amalladinne et al. with thelist recoverable code capable of correcting t errors. A finite-length randomcoding bound for such codes is derived. The numerical experiments in the singleantenna quasi-static Rayleigh fading MAC show that transition to listrecoverable codes correcting t errors improves the performance of codedcompressed sensing scheme by 7-10 dB compared to the tree code-based scheme. Wepropose two practical constructions of outer codes. The first is a modificationof the tree code. It utilizes the same code structure, and a key difference isa decoder capable of correcting up to t errors. The second is based on theReed-Solomon codes and Guruswami-Sudan list decoding algorithm. The firstscheme provides an energy efficiency very close to the random coding bound whenthe decoding complexity is unbounded. But for the practical parameters, thesecond scheme is better and improves the performance of a tree code-basedscheme when the number of active users is less than 200.

Coded Compressed Sensing with List Recoverable Codes for the Unsourced Random Access