Methods and apparatus for encoding and decoding of data using concatenated polarization adjusted convolutional codes

1. A concatenated encoder apparatus for use in a communication system, the concatenated encoder comprising:

an outer encoder configured to receive a concatenated encoder input block d, split the concatenated encoder input block d into an outer code input array a, and encode the outer code input array a in accordance with a plurality of outer codes to generate an outer code output array b; and

an inner encoder configured to generate, from the outer code output array b, a concatenated code output array x in accordance with a layered polarization adjusted convolutional (LPAC) code, and send the concatenated code output array x to a channel,

wherein the plurality of outer codes comprises at least two outer codes, wherein the LPAC code comprises at least two layers.

2. The concatenated encoder apparatus of claim 1 , wherein the inner encoder is further configured to compute a precoding array c from the outer code output array b and insert the precoding array c into the data container array v.

3. The concatenated encoder apparatus of claim 1 , wherein the LPAC code comprises a data index set and a partition of the data index set into a plurality of layer index sets ( 1 , 2 , . . . , L ), wherein the plurality of layer index sets ( 1 , 2 , . . . , L ) are chosen in accordance with a score function, wherein the score function is one of a Hamming score function, a reliability score function, a decoding order score function, or a combination thereof.

4. A concatenated decoder apparatus for use in a communication system, the concatenated decoder apparatus comprising:

a layer counter configured to count a number of layers;

an inner decoder configured to carry out an ith layer inner decoding operation in accordance with a layered polarization adjusted convolutional (LPAC) code to generate an ith inner decoder decision {tilde over (b)} i from a concatenated decoder input array y and an (i−1)th cumulative decision feedback ({circumflex over (b)} 1 , {circumflex over (b)} 2 , . . . , {circumflex over (b)} i−1 );

an outer decoder configured to carry out an ith layer outer decoding operation to generate from the ith inner decoder decision {tilde over (b)} i an ith outer decoder decision â i ; and

a reencoder configured to carry out an ith layer reencoding operation to generate an ith decision feedback {circumflex over (b)} i from the ith outer decoder decision â i ,

wherein the number of layers is equal to an integer m, wherein the integer m is greater than one, and wherein the outer decoder is further configured to generate a concatenated decoder output block {circumflex over (d)} from outer decoder decisions (â 1 , â 2 , . . . , â m ) and send the concatenated decoder output block {circumflex over (d)} to a destination.

5. The concatenated decoder apparatus of claim 4 , wherein at least one of the ith layer inner decoding operations comprises employing a sequential decoder for decoding the LPAC code.

6. The concatenated decoder apparatus of claim 5 , wherein the sequential decoder is equipped with a computational time-out limit.

7. A concatenated encoder method for use in a communication system, the concatenated encoder method:

at an outer encoder, receiving a concatenated encoder input block d, splitting the concatenated encoder input block d into an outer code input array a, and encoding the outer code input array a in accordance with a plurality of outer codes to generate an outer code output array b; and

at an inner encoder, generating, from the outer code output array b, a concatenated code output array x in accordance with a layered polarization adjusted convolutional (LPAC) code, and sending the concatenated code output array x to a channel,

wherein the plurality of outer codes comprises at least two outer codes, wherein the LPAC code comprises at least two layers.

8. The concatenated encoder method of claim 7 , further comprising:

at the inner encoder, computing a precoding array c from the outer code output array b and inserting the precoding array c into the data container array v.

9. The concatenated encoder method of claim 7 , wherein the LPAC code comprises a data index set and a partition of the data index set into a plurality of layer index sets ( 1 , 2 , . . . , L ), wherein the plurality of layer index sets ( 1 , 2 , . . . , L ) are chosen in accordance with a score function, wherein the score function is one of a Hamming score function, a reliability score function, a decoding order score function, or a combination thereof.

10. A concatenated decoder method for use in a communication system, the concatenated decoder method comprising:

counting a number of layers;

at an inner decoder, carrying out an ith layer inner decoding operation in accordance with a layered polarization adjusted convolutional (LPAC) code to generate an ith inner decoder decision {tilde over (b)} i from a concatenated decoder input array y and an (i−1)th cumulative decision feedback ({circumflex over (b)} 1 , {circumflex over (b)} 2 , . . . , {circumflex over (b)} i−1 );

at an outer decoder, carrying out an ith layer outer decoding operation to generate from the ith inner decoder decision {tilde over (b)} i an ith outer decoder decision â i ; and

at a reencoder, carrying out an ith layer reencoding operation to generate an ith decision feedback {circumflex over (b)} i from the ith outer decoder decision â i ,

wherein the number of layers is equal to an integer m, wherein the integer m is greater than one, the concatenated decoder method further comprising, at the outer decoder, generating a concatenated decoder output block {circumflex over (d)} from outer decoder decisions (â 1 , â 2 , . . . , â m ) and sending the concatenated decoder output block {circumflex over (d)} to a destination.

11. The concatenated decoder method of claim 10 , wherein at least one of the ith layer inner decoding operations comprises employing a sequential decoder for decoding the LPAC code.

12. The concatenated decoder method of claim 11 , wherein the sequential decoder is equipped with a computational time-out limit.