Testing of Error-Correcting Sparse Permutation Channel Codes

A computer program performs Monte Carlo direct numerical simulations for testing sparse permutation channel codes, which offer strong error-correction capabilities at high code rates and are considered especially suitable for storage of digital data in holographic and volume memories. A word in a code of this type is characterized by, among other things, a sparseness parameter (M) and a fixed number (K) of 1 or “on” bits in a channel block length of N (see figure).

In a test, random user data words are generated and mapped into code words. Transmission of the words through a noisy channel is simulated by adding simulated white Gaussian noise whose amplitude is determined by the signal-to-noise ratio. Detection of each word is performed via strict Maximum Likelihood detection algorithm starting with the initially detected codeword, which is produced by sorting the resulting bit values and assigning a value of 1 to the highest K of them and 0 to the rest. A newly developed permutation sorting algorithm is further applied to determine the maximum weight valid code word. The maximum likelihood valid sparse codeword is decoded, by means of an inverse of an enumerative scheme used in generating code words, to obtain the original use data. From the results of this simulation, block error rates (BERs) and other statistics that characterize the performance of the code are calculated. Sparse permutation channel codes satisfy the balanced channel coding constraint and, as determined from the direct numerical simulation, also simultaneously provide high error correction with use of BER as low as 10–10 and less even for fairly large raw bit error rates. Channel codes of sufficiently large block size (N > 100) asymptotically approach the information theoretic limits for communications channel capacity.

This program was written by Kirill V. Shcheglov and Sergei S. Orlov of Stanford and was tested numerically by Hongtao Liu and Snezhana I. Abarzhi of Illinois Institute of Technology for NASA’s Jet Propulsion Laboratory.

This software is available for commercial licensing. Please contact Karina Edmonds of the California Institute of Technology at (626) 395-2322. Refer to NPO-45196.

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