Method and apparatus for additive trellis encoding

1. A method of additive encoding of data words, the method comprising:

receiving a plurality of data words; and

searching a trellis representation of additive code words to identify a path in the trellis representing a sequence of patterns to be used to encode the data words.

2. The method of claim 1 , wherein searching the trellis representation of additive code words to identify the path in the trellis further comprises searching the trellis representation to identify a sequence of flags representing the sequence of patterns to be used to encode the data words.

3. The method of claim 2 , wherein searching the trellis representation of additive code words further comprises searching the trellis representation of all possible combinations of matching patterns in a sequence of additive code words to identify the sequence of flags representing the sequence of patterns to be used to encode the data words.

4. The method of claim 2 , and further comprising modulation encoding the plurality of data words using the additive code words corresponding to the identified path in the trellis.

5. The method of claim 4 , wherein modulation encoding the plurality of data words comprises additive coding the plurality of data words by adding patterns in the identified sequence of patterns to the plurality of data words.

6. The method of claim 5 , wherein additive coding the plurality of code words further comprises beginning additive coding before terminating the step of searching the trellis representation of additive code words at a final state, wherein the flags already produced at the earlier stages of the trellis search are used to choose the matching patterns.

7. The method of claim 4 , wherein receiving the plurality of data words further comprises receiving N data words to be encoded in a sector, and wherein searching the trellis representation of additive code words to identify the path in the trellis further comprises searching the trellis representation of additive code words to identify the path which optimizes a metric.

8. The method of claim 7 , wherein the metric includes and accumulated variance, and wherein searching the trellis representation of additive code words to identify the path in the trellis further comprises searching the trellis representation of additive code words to identify the path which will minimize an absolute value of the accumulated variance.

9. The method of claim 8 , and further comprising calculating the accumulated variance metric by distinguishing positive and negative values of running digital sum for a given sequence of N additive code words, calculating an accumulated variance of positive values of running digital sum for the given sequence of N additive code words, calculating an accumulated variance of negative values of running digital sum for the given sequence of N additive code words, and adding the calculated accumulated variance of positive values and the accumulated variance of negative values to obtain the accumulated variance metric.

10. The method of claim 7 , wherein receiving the plurality of data words further comprises receiving the N data words to be encoded into N additive code words of a sector, wherein each flag comprises r bits, wherein a state of the trellis is a block of v flag bits, and wherein searching the trellis representation of additive code words further comprises searching 2 v states of the trellis corresponding to rN/v sections of the trellis to identify the path.

11. The method of claim 10 , wherein searching the trellis representation of additive code words to identify the path which optimizes the metric further comprises:

at a first time t=1, for each state s∈S in the trellis, calculating and storing a running digital sum value RDS(1,s) of a first block of nv bits and a metric μ(1,s) of a code sequence;

at times t>1 after the first time, and for each section of the trellis, for each state s∈S in the corresponding section of the trellis, analyzing all preceding states s′ to define and store a final value of the running digital sum value RDS(t,s) of a new code sequence comprising a survivor of the preceding states s′ and an extension of a code word defined by the state s, and to define a new metric μ(t,s) of the new code sequence defined by the states s′ and s;

after comparing all preceding states s′, for each section of the trellis, discarding all preceding states s′, except a survivor state, and saving a direction to the survivor state s′;

after analyzing all states in all sections of the trellis, determining a best final state, wherein a best survived path is identified as the best final state and the surviving sequence of states; and

using a sequence of flags corresponding to the best survived path in the trellis to generate an output coded sector.

12. An apparatus for additively encoding data words, the apparatus comprising:

an input which receives a plurality of data words; and

modulation encoding circuitry configured to search a trellis representation of additive code words to identify a path in the trellis representing a sequence of patterns to be used to encode the received plurality of data words.

13. The apparatus of claim 12 , wherein the modulation encoding circuitry comprises:

a trellis generator which receives the plurality of data words and the sequence of patterns as an input, and in response generates the trellis representation of the additive code words; and

a trellis search component coupled to the trellis generator which searches the trellis representation of additive code words to identify the path.

14. The apparatus of claim 13 , and further comprising a trellis storage component, coupled to the trellis generator and to the trellis search component, which stores the generated trellis representation of the additive code words.

15. The apparatus of claim 13 , wherein the trellis search component provides as an output flags representative of the identified path.

16. The apparatus of claim 15 , and further comprising an encoder which receives the flags as an input and provides code words as an output.

17. The apparatus of claim 16 , wherein the encoder provides as the output an encoded sector comprising the code words and the flags.

18. The apparatus of claim 12 , wherein the modulation encoding circuitry is configured to search the trellis representation of additive code words to identify the path in the trellis by searching the trellis representation to identify a sequence of flags representing the sequence of patterns to be used to encode the data words.

19. The apparatus of claim 18 , wherein the modulation encoding circuitry is configured to search the trellis representation of all possible combinations of matching patterns in a sequence of additive code words to identify the sequence of flags representing the sequence of patterns to be used to encode the data words.

20. The apparatus of claim 18 , wherein the modulation encoding circuitry is further configured to modulation encode the plurality of data words using the additive code words corresponding to the identified path.

21. The apparatus of claim 20 , wherein the plurality of data words received at the input comprises N data words to be encoded in a sector, and wherein the modulation encoding circuitry is configured to search the trellis representation of additive code words to identify the path which optimizes a metric.

22. The apparatus of claim 21 , wherein the metric includes and accumulated variance, and wherein the modulation encoding circuitry is configured to search the trellis representation of additive code words to identify the path which will minimize an absolute value of the accumulated variance.

23. The apparatus of claim 22 , and wherein the modulation encoding circuitry is further configured to calculate the accumulated variance metric by distinguishing positive and negative values of running digital sum for a given sequence of N additive code words, by calculating an accumulated variance of positive values of running digital sum for the given sequence of N additive code words, by calculating an accumulated variance of negative values of running digital sum for the given sequence of N additive code words, and by adding the calculated accumulated variance of positive values and the accumulated variance of negative values to obtain the accumulated variance metric.

24. The apparatus of claim 21 , wherein the N data words received at the input are to be encoded into N additive code words of a sector, wherein each flag comprises r bits, wherein a state of the trellis is a block of v flag bits, and wherein the modulation encoding circuitry is configured to search the trellis representation of additive code words by searching 2 v states of the trellis corresponding to rN/v sections of the trellis to identify the path in the trellis.

25. The apparatus of claim 12 , wherein the modulation encoding circuitry comprises a direct current free encoder.