On Row-column-diagonal Codes As a Class of Ldpc Codes

The RCD codes are a class of regular low-density parity-check (LDPC) codes constructed on square arrays with the rows, columns, and diagonals of the array defining the parity-check equations. These codes are attractive because of their high code rates coupled with the possibility of decoding via a large number of techniques of varying complexity. The relatively simple construction of RCD codes makes them amenable to combinatorial analysis, which is helpful in computing bounds on their performance for several channels and decoding schemes. Availability of these bounds, in turn, makes RCD codes excellent candidates for the testing and validation of importance sampling (IS) simulation techniques that estimate code performance to very low word-error rates (WER). Two IS simulation techniques: (a) dual adaptive importance sampling (DAIS) for soft-decision decoding, and (b) SNR-invariant importance sampling (IIS) for hard-decision decoding, are developed and validated via comparison with the computed analytical bounds for RCD codes. Finally, RCD codes and codes based on diagonals in square arrays are shown to serve as useful building blocks for constructing quantum-error-correcting codes.