Title :
On the Optimum Cyclic Subcode Chains of
for Increasing Message Length
Author :
Xiaogang Liu ; Yuan Luo ; Shum, Kenneth W.
Author_Institution :
Dept. of Comput. Sci. & Eng., Shanghai Jiao Tong Univ., Shanghai, China
Abstract :
The distance profiles of linear block codes can be employed to design variational coding scheme for encoding message with variational length and getting lower decoding error probability by large minimum Hamming distance, where one example is in the design of transport format combination indicators (TFCIs) in CDMA. Considering convenience for encoding, we focus on the distance profiles with respect to cyclic subcode chains (DPCs) of cyclic codes over GF(q) with length n such that gcd(n, q) = 1. In this paper, the optimum DPCs and the corresponding optimum cyclic subcode chains are investigated on the punctured second-order Reed-Muller code RM(2, m)* for increasing message length, where two standards on the optimums are studied according to the rhythm of increase. Ignoring the dimension profile, the device will coincide with that of TFCI.
Keywords :
Hamming codes; Reed-Muller codes; block codes; code division multiple access; linear codes; Boolean function; CDMA; large minimum Hamming distance; linear block codes; message length; optimum cyclic subcode chains; punctured second-order Reed-Muller code; symplectic matrix; transport format combination indicator; variational coding scheme; Block codes; Decoding; Dictionaries; Multiaccess communication; Polynomials; Standards; Boolean function; Reed??Muller code; distance profile with respect to cyclic subcode chain (DPC); exponential sum; symplectic matrix;
Journal_Title :
Communications, IEEE Transactions on
DOI :
10.1109/TCOMM.2014.2320739