On structured trellises of some best [n,k,d] codes

Abstract

The paper presents new linear binary block codes, with codeword length, n, number of information symbols in codewords, k, and code distance, d, which reach the upper or lower bounds on maximal code-distance, using the construction of M. Kasahara et al. (see IEEE Trans. on Inform. Theory, vol.IT-22, p.462-8, 1976) for some combination of the mentioned parameters. The paper presents, as well, the structured trellises for these codes, using the construction method presented by P. Farka et al. (see Proc. 5th Int. Symp. on Wireless Personal Multimedia Communications, p.1262-4, 2002). The practical importance for wireless communications is that knowledge of the structured trellis can allow decoding of the corresponding code using different soft (turbo) algorithms. In this way, the set of useful codes for practical applications is broadened to 'best' codes, that would otherwise be difficult to decode using soft algorithms.