Bounds on the Asymptotic Coding Gain of Long Binary Block Codes
Srdjan Budisin, Vladan M. Jovanovic · IRE Transactions on Communications Systems · 1987
For some time it has been known that, for fixed code lengthn, binary BCH codes appear to be most efficient when the number of information bitskis between1/4 nand3/4 n[1, p. 443], [2, p. 219]. In this correspondence the efficiency of block codes on an binary-quantized additive white Gaussian noise channel is analyzed as a function of the code rater = k/nfor hard decision decoding. A closed form analytical expression for the upper and lower bounds on block code performance is derived for large code lengthsn. They show that, for best codes, a relatively broad maximum occurs for rates of approximately 0.4. The performance of the BCH codes is also compared with the bounds.