Encoder device, decoder device, and methods thereof

1. A device, comprising:

an encoder comprising a tail biting convolutional code having a constraint length, wherein L represents a length of the constraint length of the tail biting convolutional code, the encoder being configured to:

receive K information bits c i of an information word c=[c 0 , c 1 , . . . , c K-1 ], wherein K represents a number of information bits c i received, K is less than L minus one; and

encode the K information bits to provide an encoded code word using the tail biting convolutional code.

2. The device according to claim 1 , wherein the encoder comprises an initial state of bit values and a final state of bit values for encoding of the K information bits, and wherein the initial state of bit values is the same the final state of bit values.

3. The device according to claim 2 , wherein the encoder further is configured to:

append at least one bit to the information word c to obtain an appended information word c′ having K′ information bits, wherein c′=[c′ 0 , c′ 1 , . . . , c′ K′-1 ] and K′≥L−1; and

use the appended information word c′ as the initial state of bit values.

4. The device according to claim 3 , wherein the at least one appended bit has a predetermined value.

5. The device according to claim 3 , wherein the encoder further is configured to append L−1−K fixed bits, f 0 , . . . , f L-2-K , to the information word c to obtain the appended information word c′ according to:

c

π

k

′

=

{

c

k

,

k

=

0

,

…

⁢

,

K

-

1

f

k

-

K

,

k

=

K

,

…

⁢

,

L

-

2

where π=[π 0 , . . . , π L-2 ] is a permutation of integers [0, . . . , L−2].

6. The device according to claim 3 , wherein the device is configured to:

input the appended information word c′ to the encoder to encode the K information bits.

7. The device according to claim 3 , wherein the at least one appended bit is obtained from a cyclic extension of the information word c.

8. The device according to claim 7 , wherein the initial state of bit values are:

s i =c (K-1-i)mod K , i= 0, . . . , L− 1

where (K−1−i)mod K is the smallest non-negative integer that can be expressed as (K−1−i)+pK for an integer p.

9. The device according to claim 7 , wherein the device further is configured to:

input the information word c to the encoder to encode the K information bits.

10. The device according to claim 2 , wherein the encoder comprises a shift register of length L−1 for encoding the K information bits, and wherein the initial state of the bit values in the shift register s=[s 0 , s 1 , . . . , s L-2 ], is the same as the final state of the bit values in the shift register.

11. A device, comprising:

a decoder comprising a tail biting convolutional code having a constraint length, wherein L represents a length of the constraint length of the tail biting convolutional code, the decoder being configured to:

receive an input sequence;

compute at least one reliability parameter based on the received input sequence; and

determine an information word c using the tail biting convolutional code and based on the at least one reliability parameter, wherein the information word c=[c 0 , c 1 , . . . , c K-1 ] has K information bits c i , wherein K represents a number of information bits c i , K is less than L minus 1.

12. The device according to claim 11 , wherein the decoder further is configured to compute the at least one reliability parameter based on:

the received input sequence; and

information comprising an initial state of bit values and a final state of bit values used in encoding the K information bits.

13. A method comprising:

receiving, by an encoder, K information bits c i of an information word c=[c 0 , c 1 , . . . , c K-1 ], wherein K represents a number of information bits c i received; and

encoding, by the encoder, the K information bits using a tail biting convolutional code to provide an encoded code word, wherein the tail biting convolutional code has a constraint length, L represents a length of the constraint length of the tail biting convolutional code, and K is less than L minus one.

14. The method according to claim 13 , further comprising:

appending at least one bit to the information word c to obtain an appended information word c′=[c′ 0 , c′ 1 , . . . , c′ K′-1 ] having K′≥L−1 bits; and

using the appended information word c′ as an initial state of bit values to encode the K information bits.

15. The method according to claim 14 , wherein the at least one appended bit has a predetermined value.

16. The method according to claim 14 , wherein the at least one appended bit is obtained from a cyclic extension of the information word c.

17. The method according to claim 16 , wherein the initial state of bit values are:

s i =c (K-1-i)mod K , i= 0, . . . , L− 1

where (K−1−i)mod K is the smallest non-negative integer that can be expressed as (K−1−i)+pK for an integer p.

18. A method, comprising:

receiving, by a decoder, an input sequence;

computing, by the decoder, at least one reliability parameter based on the received input sequence; and

determining, by the decoder, an information word c=[c 0 , c 1 , . . . , c K-1 ] using a tail biting convolutional code and based on the at least one reliability parameter, wherein the information word c has K information bits c i , K is a number of information bits c i , the tail biting convolutional code has a constraint length, L represents a length of the constraint length of the tail biting convolutional code, and K is less than L minus one.

19. The method according to claim 18 further comprising:

computing the at least one reliability parameter based on the received input sequence and information comprising an initial state of bit values and a final state of bit values used in encoding the K information bits.