Nested LDPC Codes for Random Access Communication

This paper proposes a nested low-density parity-check (LDPC) code design. Combining this nested LDPC code with the random access coding strategy introduced by Yavas, Kostina, and Effros yields a random access LDPC (RA-LDPC) code for reliable communication in random access communication environments where neither the transmitters nor the receiver knows which or even how many transmitters wish to communicate at each moment. Coordination is achieved using sparse scheduled feedback. Bounds on the finite-blocklength performance of the RA-LDPC code under maximum likelihood (ML) decoding are derived using both error exponent and dispersion style analyses. Results include bounds on the penalty of the RA-LDPC code as a function of the LDPC code densities.