A new computational decoding complexity measure of convolutional codes

EURASIP Journal on Advances in Signal Processing

Table 3 Good convolutional codes of rate 4/7 for various TC( M _min ) and MC( M _min ) values

TC	MC	TCC^a	d _f	Number	*G(D)*
20 ^b	5	185	4	6,12,21,58,143	[1 1 1 1 0 1 0; 0 1 1 1 1 0 1;2 2 1 1 0 0 0; 2 0 0 1 1 1 0]
22 ^b	6	210	4	3,7,18,54,125	[0 2 2 2 0 1 1; 2 0 2 0 1 1 0;0 0 0 1 1 1 1; 3 3 1 0 1 0 0]
22 ^c	7	223	4	1,9,21,45,118	[1 1 0 1 1 0 1; 0 1 1 0 1 1 0;2 2 0 1 1 1 0; 0 0 2 2 1 1 1]
26 ^d	8	260	5	7,17,39,96,249	[1 1 0 1 1 1 1; 2 1 1 1 0 0 1;0 2 2 1 1 1 0; 2 2 0 2 0 1]
28 ^e	8	272	5	3,14,29,72,205	[0 1 1 1 1 1 1; 3 1 0 0 1 1 0;2 3 1 0 0 2 3; 2 3 3 1 1 0 0]
40 ^b	12	396	5	3,11,31,70,176	[1 0 1 0 1 1 1; 2 3 1 1 1 1 0;2 0 2 1 0 1 1; 2 2 2 2 1 3 0]
40 ^b	14	422	6	24,0,144,0,1021	[3 1 1 0 1 0 1; 0 0 3 3 0 1 1;2 2 2 0 1 1 1; 0 2 2 2 2 3 0]
44 ^b	14	446	6	23,0,140,0,993	[3 1 0 1 0 1 1; 2 3 1 2 1 1 1; 2 2 2 1 1 1 0; 0 2 2 2 2 1 1]
48 ^b	14	470	6	17,0,133,0,855	[1 1 1 0 1 1 1; 2 1 2 1 3 0 0; 2 2 1 1 1 1 0; 2 0 0 2 2 3 1]
48 ^c	16	496	6	15,0,120,0,795	[3 0 1 0 1 1 1; 0 1 3 2 1 0 1; 2 2 2 1 1 1 0; 2 2 2 2 2 3 1]
56 ^c	16	544	6	7,21,47,132,359	[3 1 1 1 1 1 0; 2 3 0 2 3 1 0;2 2 2 1 1 1 1; 2 0 0 0 2 3 3]
80 ^b	24	792	6	3,18,36,96,291	[1 3 2 1 1 0 1; 2 3 1 2 1 1 1;2 2 0 1 3 1 0; 0 0 2 2 2 3 3]
88 ^b	28	892	6	1,18,35,73,258	[3 3 2 1 0 1 0; 2 1 1 3 1 1 1;0 2 0 3 3 3 0; 2 2 2 2 2 1 3]
88 ^b	32	944	7	18,44,77,234,703	[3 3 1 1 1 0 0; 0 1 3 2 1 1 1; 0 2 0 3 3 3 0; 4 0 2 2 2 3 3]
104 ^d	32	1040	7	15,34,72,231,649	[1 3 2 1 1 1 1; 0 1 1 3 2 3 1; 2 2 0 3 3 1 0; 6 2 2 0 0 3 3]

^aSpecific measure for the TMS320C55xx DSP. ^bNew code found in this study. ^cCode with the same TC (M_min) and MC (M_min) as a code listed in [5], but with a better distance spectrum. ^dCode with the same TC (M_min), MC (M_min), and distance spectrum as a code listed in [5]. ^eCode with the same TC (M_min), MC (M_min), and distance spectrum as a code listed in [8].