Design of Balanced and Constant Weight Codes for VLSI Systems
IEEE Transactions on Computers
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A balanced code with k information bits and r check bits is a binary code of length n = k + r and cardinality 2^k such that the number of 1''s in each code word is equal to the floor of (n/2). This paper describes the design of efficient balanced codes with parallel encoding and parallel decoding; i.e., balanced codes whose encoding and decoding algorithms can be implemented efficiently as combinational circuits. In this case, since area and delay of such circuits are critical factors, another parameter is introduced in the definition of balanced code: the "number of balancing functions used in the code design", p. Parallel encoding and decoding algorithms independent from the chosen balancing method are given, and these can be implemented by aVLSI circuit of size O(pk) and depth O(log -base 2- p). This paper presents a new balancing method: the permutation method, which for infinitely many values of k (such as, k = 8, 10, 20, 22, 32, 34, ...) is more efficient that Knuth''s complementation method. This new method results in efficient balanced codes with k is an element of twice the natural numbers information bits, r = 2 floor(k/12) + 2 check bits and pp = 6 balancing functions. Further Knuth''s complementation method is generalized to obtain efficient code designs for any value of the parameters k, r and p, provided that k = 2 sum i=0 to m of [(r choose i) + p(r-2m-1)-[(kr+k+r)mod 2]] where m is such that (r choose m-1) p = (r chose m).