Iterated Codes with Improved Performance.
ARMY MATERIEL SYSTEMS ANALYSIS ACTIVITY ABERDEEN PROVING GROUND MD
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Shannons celebrated theorem for noisy channels published in 1948 demonstrated that error correcting codes exist which enable information to be received at a finite rate and free of errors after transmission over noisy communication channels. The first general class of coding schemes to produce arbitrarily low error probability without simultaneously reducing the information rate to zero was presented by Elias in 1954. A more sophisticated class of codes was given by Forney in 1966 and generalized by Justesin in 1972. None of these schemes, however, achieves even the lower bound of Varsharmov and Gilbert. Using the ratio of channel capacity to information rate, this paper presents the performance of a generalization of Eliass iterated Hamming single error correcting codes. Linear block codes which correct multiple errors have been iterated using a search algorithm to select candidate codes for iteration from a general sub-class of codes. Results obtained for relatively quiet channels are used as foundation for coding and decoding on noisier channels. Comparisons with Eliass original work and with computed improvements to Eliass original results are presented. A new method of constructing and decoding iterated codes is presented. Based upon the properties of shortened codes, this method provides additional improvements to the rates provided by iterated multiple error correcting, linear block codes. Author
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