Some Results on Generalized Codeword length of variable length error-correcting codes

                   It is well known that a lower bound on the average length is obtained in terms of Shannon entropy [12] for instantaneous codes in noiseless channel (Abramson [1] ). Bernard and Sharma [6] studied variable length codes for noisy channels and presented some combinatorial bounds for these variable length, error correcting codes. Bernard and Sharma [5] obtained a lower bound on average length for variable length error correcting codes satisfying the criterion of “promptness”.   In this paper a lower bound of generalized code length of order and type for variable length error correcting codes is obtained in terms of a measure similar to that of ‘useful’ inaccuracy of order and type given by Tuteja and Bhaker [14]. This generalizes the result due to Bernard and Sharma [5], Baig and Zaheeruddin [4] and well known Shannon’s inequality.

(1)         Abramson, N, “Information theory and coding” McGraw Hill, New York (1963). (2)         Autar, R and Soni, R.S, “Inaccuracy and coding theorem,” Journal of Applied probability, 12, 845-851(1975). (3)         Baig, M.A.K and Zaheeruddin, “ Coding theorem and a measure of inaccuracy”, Soochow Journal of Mathematics, 19(4), 1-7 (1993). (4)         Bernard, M and Sharma, B.D,“A Lower bound on average code word length of variable length error correcting codes”, IEEE Transaction on Information theory,36(6), 1474-1745 (1990). (5)         Bernard, M and Sharma, B.D, “Some combinatorial results on variable length error correcting codes”, ARS Combinatoria, 25(B), 181-194 (1988). (6)         Hamming, R.W, “Error detecting and error correcting codes”, Bell System Tech. Journal 29, 147-160 (1950). (7)         Hartnett, W.E(ed), “Foundation of coding theory” D.Reidling Publishing Co., Dordietcht, Holland, 1974. (8)   Kerridge, D.F, “Inaccuracy and Inference”, Journal of Royal Statistical Society B, 23, 184-194 (1961). (10)Kraft, L.J,“A device for quantizing grouping and coding amptitude modulated pulses”, M.S Thesis Electrical Engineering Department  Massach Institute of Technology, 1949.