Error correctible channel coding method

1. A method for encoding a series of M-bit message words into a series of N-bit codewords having a bounded unbalance, a part of the message words being used to index bits and others source words, wherein the M and N are positive integer and the N is larger than the M, comprising steps of:

grouping the message words to a plurality of subsets using the index bits;

classifying the unbalanced codewords to a plurality of sets based on a state transition in a trellis having states and levels, each of the classified unbalanced codewords being stored at a codebook for each codeword set, respectively, the codebook having the source words, a codeword ID for each of the source words and the classified unbalanced codewords;

encoding the message words into the respective codeword in the codebook, respectively, by using the index bits of the message words and the state transition in the trellis, the codewords being selected by transition for each state at each level of the trellis based on correlations.

2. The method of claim 1, wherein the M and the N are 9 and 12, respectively.

3. The method of claim 2, wherein the unbalanced codewords have a Hamming weight of 5 or 7, wherein the Hamming weight 7 is obtained by complementing the codewords of Hamming weight 5.

4. The method of claim 3, wherein the codewords belonging to a set of codewords have a minimum Hamming distance 4.

5. The method of claim 4, wherein the number of states in the trellis are 8.

6. A recoding medium containing data encoded by the method of claim 1.

7. A method for decoding a codeword, which is encoded by the method of claim 1, from a series of data word representing intensities of an analog signal, comprising steps of:

receiving the data word;

calculating branch metrics between the data word and each codeword in the codeword set classified by the state transition in the trellis to obtain minimum branch for each bottom states;

figuring out path metric for each bottom state based on the calculated branch metrics to select a minimum path metric thereamong for each bottom state in the trellis;

selecting a best path having the smallest path metric of the calculated path metrics;

tracing back the selected best path and decoding a codeword corresponding to a state transition into a message word by using the codeword ID in the codebook.

8. The method of claim 7, wherein the data word is output from a volume holographic storage device.

9. The method of claim 8, wherein the unbalanced codewords have a Hamming weight of 5 or 7, wherein the Hamming weight 7 is obtained by complementing the codewords of Hamming weight 5.

10. The method of claim 9, wherein the codewords belonging to a set of codewords have a minimum Hamming distance 4.

11. The method of claim 10, wherein the number of states in the trellis are 8.