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Correction Coding Apparatus for Decimal Like Codes

IP.com Disclosure Number: IPCOM000094499D
Original Publication Date: 1965-Feb-01
Included in the Prior Art Database: 2005-Mar-06
Document File: 3 page(s) / 71K

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The devices encode and decode decimal-like codes for the detection and correction of multiple errors.

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Correction Coding Apparatus for Decimal Like Codes

The devices encode and decode decimal-like codes for the detection and correction of multiple errors.

A decimal number is based on ten and 10=2x5. Since both 2 and 5 are prime numbers, 10 is of the form p(1) p(2). A decimal-like number is a number of the form n=p(1) p(2) p(3) ... p(k) where all p's are different and are prime. The following table shows all the decimal-like numbers under one hundred:

Decimal-like codes for multiple error correction can be constructed from codes of prime base and suitably converting them. To construct a code of length n and base m where m=p(1), p(2)... p(k), first there is constructed codes of length n modulo p. (i = 1, 2... k) which have the same error-correcting properties and find the parity check matrix of each code. A suitable combination of the parity check matrices yields the desirable parity check matrix in base m. This involves conversion of a number with a residue number system and vice versa. The conversion can be carried out in two different sequences or orders of operation. By the first sequence shown in drawing A, the parity check matrices can be converted to obtain a parity check matrix modulo m. Then code words are selected as those which satisfy these parity checks.

The second method utilizes the fact that initial encoding can be into piary code of same length and then converting the encoded message to miary signals. This sequence is shown in drawing B.

Decoding operations are quite similar to encoding. It is a matter of simply performing the parity check according to either sequence scheme A or B and obtaining the syndrome in modulo pi (i = 1, 2... k). Computations of error pattern are performed with modulo p(i) logic as in ordinary prime based codes. The two decoding methods are shown diagrammatically at C and D.

An example of a double error-correcting decimal code assumes that n=31, m= 10=2x5, p(1) =2 and p(2) =5. A decimal conversion chart appears as follows:

Balanced Modulators (BM' s) I and II cooperate to perform single sideband modulation. BM I receives a signal from both oscillators f(1) and f(2). BM III receives these same two signals after they are phase-shifted 900. The outputs from BM's I...