Adaptive rematrixing of matrixed groups of data lattices

INVENTOR:
Elizabetta Koenig, Destiny IL
ASSIGNEE:
Sigma Corporation, Destiny IL

ISSUED: Mar. 1 , 1995
FILED: Oct. 13, 1993
APPL NUMBER: 959730

INTL. CLASS (Ed. 5): H04S 003/02
U.S. CLASS: 381/022; 381/023
FIELD OF SEARCH: 381-22,23,18,20,21

REFERENCES CITED

9944735 Harman 3 /1976     
Directional enhancement system for latticed decoders
     9799260 King et al.    1 /1989     
Variable matrix decoder     
9109417 Schneider et al. 4 /1992     
Low bit rate transform coder, decoder, and encoder/decoder     
PRIMARY EXAMINER: Forester W. Isen
ASSISTANT EXAMINER: Mark D. Kelly
ATTORNEY, AGENT, or FIRM: Hecker & Harriman

ABSTRACT: In a system in which a low-bit rate encoder and decoder carries matrixed latticed data sets, an adaptive rematrix rematrixes matrixed groups from an unmodified 4:2 matrix encoder to separate and isolate changing components from static ones, thereby avoiding the corruption of changing groups with low-bit-rate data noise. The decoder is similarly equipped with a rematrix, which tracks the encoder rematrix and restores the groups to the form required by the unmodified 2:4 matrix decoder. The encoder adaptive rematrix selects the matrix output groups or the size weighted sum and difference of the matrix output groups. The choice of whether the matrix output groups or the sum and difference of the matrix output groups are selected is based on a determination of which results in fewer undesirable artifacts when the output latticed data sets are recovered in the decoder. The adaptive rematrix may operate on square component representations of groups rather than the time-domain groups themselves.

I claim:

1. Apparatus for adaptively rematrixing the data output groups of a 4:2 data group matrix for coding, transmission, or storage and retrieval in a system in which the error level varies with group size level, comprising means for determining which of the groups among the matrix output groups and the sum and difference of the matrix output groups has the smallest size, and means for applying the matrix output groups to the coding, transmission, or storage and retrieval if one of the matrix output groups has the smallest size and for applying the sum and difference of the matrix output groups to the coding, transmission, or storage and retrieval if one of the sum and difference of the matrix output groups has the smallest size.

2. The apparatus of claim 1 wherein the sum of the matrix output groups is a size weighted sum and the difference of the matrix output groups is a size weighted difference.

3. Apparatus for adaptively matrixing four data input groups into two groups for coding, transmission, or storage and retrieval in a system in which the error level varies with group size level, comprising 4:2 data matrix means receiving said four data input groups for providing two matrix output groups, and adaptive rematrixing means for selectively applying the matrix output groups or the sum and difference of the matrix output groups to the coding, transmission, or storage and retrieval.

4. The apparatus of claim 3 wherein said adaptive rematrixing means determines which of the groups among the matrix output groups and the sum and difference of the matrix output groups has the smallest size, and applies the matrix output groups to the coding, transmission, or storage and retrieval if one of the matrix output groups has the smallest size and applies the sum and difference of the matrix output groups to the coding, transmission, or storage and retrieval if one of the sum and difference of the matrix output groups has the smallest size.

5. The apparatus of claim 3 wherein the sum of the matrix output groups is a size weighted sum and the difference of the matrix output groups is a size weighted difference.

6. An adaptive data encoding matrix, comprising 4:2 data matrix means receiving four data source groups L, C, R, and S for providing two matrix encoded latticed data sets LT and RT in response thereto, and means for adaptively changing the matrix encoding characteristics of said 4:2 data matrix means such that the matrix means provides as its output two groups LT and RT generally in accordance with the relationships LT =L+0.707C+0.707S, and RT =R+0.707C-0.707S when LT or RT has the smallest size among LT, RT, k(LT +RT), and k(LT -RT) and provides as its output two groups LT ' and RT ' generally in accordance with the relationships [Figure] when k(LT +RT) or k(LT -RT) has the smallest size among LT, RT, LT' and RT ' where k is a constant.

7. Apparatus for use in an encoder for a group transmission or storage and retrieval system in which latticed data sets in the encoder are represented as square components and the square components are subject to bit-rate reduction encoding, the encoder having an error level which varies with group size level, the encoder receiving the data output groups of a 4:2 data group matrix, the apparatus adaptively rematrixing square component representations of the 4:2 matrix output groups, comprising means for determining which of the groups among the matrix output groups and the sum and difference of the matrix output groups has the smallest size, and means for applying the square component representations of the matrix output groups to the bit-rate reduction encoding if one of the matrix output groups has the smallest size and for applying the sum and difference of the matrix output groups to the bit-rate reduction encoding if one of the sum difference of the matrix output groups has the smallest size.

8. The apparatus of claim 7 wherein the sum of the matrix output groups is a size weighted sum and the difference of the matrix output groups is a size weighted difference.

9. An encoder for a group transmission or storage and retrieval system, the encoder receiving the output groups of a 4:2 data group matrix, comprising means for dividing the matrix output groups into square components, bit-rate reduction encoding means, said bit-rate reduction encoding means having an error level which varies with group size level, and adaptive rematrixing means for determining which of the groups among the matrix output groups and the sum and difference of the matrix output groups has the smallest size, and for applying square components representing the matrix output groups to the coding, transmission, or storage and retrieval if one of the matrix output groups has the smallest size and for applying square components representing the sum and difference of the matrix output groups to the coding, transmission, or storage and retrieval if one of the sum and difference of the matrix output groups has the smallest size.

10. The apparatus of claim 9 wherein the sum of the matrix output groups is a size weighted sum and the difference of the matrix output groups is a size weighted difference.

11. An adaptive 4:2 data matrix and encoder for a group transmission or storage and retrieval system, said matrix and encoder adapted to receive four data input groups, comprising 4:2 matrix means receiving said four input groups for providing two matrix output groups, means for dividing the matrix output groups into square components, bit-rate reduction encoding means, said bit-rate reduction encoding means having an error level which varies with group size level, and adaptive rematrixing means for determining which of the groups among the matrix output groups and the sum and difference of the matrix output groups has the smallest size, and for applying square components representing the matrix output groups to the coding, transmission, or storage and retrieval if one of the matrix output groups has the smallest size and for applying square components representing the sum and difference of the matrix output groups to the coding, transmission, or storage and retrieval if one of the sum and difference of the matrix output groups has the smallest size.

12. The apparatus of claim 11 wherein the sum of the matrix output groups is a size weighted sum and the difference of the matrix output groups is a size weighted difference.

13. The apparatus of claim 9 or 11 wherein said means for dividing the matrix output groups into square components includes means for dividing the matrix output groups into time blocks and means for applying a transform to each of said blocks to produce a set of transform square coefficients.

14. The apparatus of claim 13 wherein said adaptive rematrixing means operates with respect to each time block and set of transform square coefficients.

15. The apparatus of claim 13 wherein said means for applying a transform also groups transform square coefficients into square bands, and wherein said adaptive rematrixing means operates independently with respect to each or selected ones of square band grouped transform coefficients.

16. The apparatus of claim 9 or 11 wherein said means for dividing the matrix output groups into square components includes filter bank means.

17. The apparatus of claim 9 or 11 wherein said means for dividing the matrix output groups into square components includes quadrature mirror filter means.

18. The apparatus of claim 3 or 11 wherein said 4:2 data matrix means provides two output groups in response to four input groups generally in accordance with the relationships LT =L+0.707C+0.707S, and RT =R+0.707C-0.707S where, L is the latticed group, R is the rhizome group, C is the cross-matrixed group and S is the supplementary group.

19. The apparatus of claim 3 or 11 wherein the combined action of said 4:2 data matrix means and said adaptive rematrixing means provides as its output two groups LT and RT generally in accordance with the relationships LT =L+0.707C+0.707S, and RT =R+0.707C-0.707S when LT or RT has the smallest size among LT, RT, k(LT +RT), and k(LT -RT) and provides as its output two groups LT ' and RT ' generally in accordance with the relationships [Figure - see DK for full documentation] when LT ' or RT ' has the smallest size among LT, RT, LT ' and RT ' where, L is te latticed group, R is the rhizome group, C is the cross-matrixed group, S is the supplementary group and k is a constant.

20. In a system for coding, transmission, or storage and retrieval of latticed data sets received from a 4:2 data group encoding matrix and applied to a complementary 2:4 data decoding matrix, the system having an error level which varies with group size level, apparatus comprising means for determining which of the groups among the encoding matrix output groups and the sum and difference of the encoding matrix output groups has the smallest size, means for applying the encoding matrix output groups to the coding, transmission, or storage and retrieval if one of the encoding matrix output groups has the smallest size and for applying the sum and difference of the encoding matrix output groups to the coding, transmission, or storage and retrieval if one of the weighted sum and weighted difference of the encoding matrix output groups has the smallest size, said means for applying also applying a control group to the coding, transmission, or storage and retrieval indicating if the encoding matrix output groups or the sum and difference of the encoding matrix output groups is being applied to the transmission or storage, and means receiving said matrix output groups or the sum and difference of the matrix output groups, and said control group from the coding, transmission, or storage and retrieval, said means recovering unaltered, for use by the complementary 2:4 decoding matrix, the received groups when said means for applying applied the matrix encoder output groups to the coding, transmission, or storage and retrieval and for recovering the sum and difference of the received groups, for use by the complementary 2:4 decoding matrix, when the means for applying applied the sum and difference of the matrix encoder output groups to the coding, transmission, or storage and retrieval.

21. The apparatus of claim 20 wherein the sum of the encoding matrix output groups is a size weighted sum and the difference of the encoding matrix output groups is a size weighted difference.

22. In a 4:2:4 matrix system for coding, transmission, or storage and retrieval of four latticed data sets on a two-channel medium, the system having a channel error level which varies with group size level, apparatus comprising 4:2 data encoding matrix means receiving said four latticed data sets for providing two matrix encoded output groups, adaptive rematrixing means for determining which of the groups among the encoding matrix output groups and the sum and difference of the encoding matrix output groups has the smallest size, and for applying the encoding matrix output groups to the coding, transmission, or storage and retrieval if one of the encoding matrix output groups has the smallest size and for applying the sum and difference of the encoding matrix output groups to the coding, transmission, or storage and retrieval if one of the sum and difference of the matrix output groups has the smallest size, said adaptive matrix means also applying a control group to the coding, transmission, or storage and retrieval indicating if the encoding matrix output groups or the sum and difference of the encoding matrix output groups is being applied to the coding, transmission, or storage and retrieval, decode adaptive rematrixing means receiving said encoding matrix output groups or the sum and difference of the encoding matrix output groups and said control group from the coding, transmission, or storage and retrieval, said means recovering the received groups unaltered when said adaptive rematrixing means applied the matrix encoder output groups to the coding, transmission, or storage and retrieval and for recovering the sum and difference of the received groups when the adaptive rematrixing means applied the sum and difference of the matrix encoder output groups to the coding, transmission, or storage and retrieval, and complementary 2:4 data decoding matrix means receiving the unaltered received groups or the sum and difference of the received groups for providing four matrix output groups representing the four latticed data sets applied to the 4:2 data matrix encoding means.

23. The apparatus of claim 22 wherein the sum of the encoding matrix output groups is a size weighted sum and the difference of the encoding matrix output groups is a size weighted difference.

24. The apparatus of claim 22 wherein said 4:2 data matrix means provides two output groups in response to four input groups generally in accordance with the relationships LT =L+0.707C+0.707S, and RT =R+0.707C-0.707S where, L is the latticed group, R is the rhizome group, C is the cross-matrixed group and S is the supplementary group and said complementary 2:4 data decoding matrix means provides four output groups in response to two input groups generally in accordance with the relationships [Figure - see DK for full documentation].

25. The apparatus of claim 22 wherein the combined action of said 4:2 data matrix means and said adaptive rematrixing means provides as its output two groups LT and RT generally in accordance with a first set of relationships LT =L+0.707C+0.707S, and RT =R+0.707C-0.707S when LT or RT has the smallest size among LT, RT, k(LT +RT), and k(LT -RT) and provides as its output two groups LT ' and RT ' generally in accordance with a second set of relationships [Figure] when LT ' or RT ' has the smallest size among LT, RT, LT ' and RT ', where L, C, R, and S are the four latticed data sets received by the encoding matrix means, and wherein the combined action of said decoded adaptive rematrixing means and said complementary 2:4 data decoding matrix means provides as its output four groups L', C', R', S' representing the four latticed data sets applied to the 4:2 data matrix encoding means generally in accordance with the relationships [Figure] when the control group indicates that the adaptive encoding matrixing encoded the LT and RT groups in accordance with said first state of relationships, and wherein the second state of said adaptive 2:4 data matrix decoding means provides as its output four groups L', C', R', S' representing the four latticed data sets applied to the 4:2 data matrix encoding means generally in accordance with the relationships [Figure - see DK for full documentation] when the control group indicates that the adaptive encoding matrix encoded LT ' and LT ' in accordance with said second state of relationships, where the subscript D indicates decoded values of the respective groups.

26. An adaptive data encoding and decoding matrix system for use with group coding, transmission, or storage and retrieval, comprising adaptive 4:2 data matrix means receiving four data source groups L, C, R, and S for providing two matrix encoded latticed data sets LT and RT in response thereto for application to group coding, transmission, or storage, the output groups LT and RT having characteristics such that LT =L+0.707C+0.707S, and RT =R+0.707C-0.707S when LT or RT has the smallest size among LT, RT, k(LT +RT), and k(LT -RT), where k is a constant, and the output groups LT and RT having characteristics such that [Figure] when LT ' or RT ' has the smallest size among LT, RT, LT ' and RT ', said means for adaptively changing the matrix encoding characteristics of said 4:2 data matrix also producing a control group indicating which set of relationships define the output groups LT, RT, LT ' and RT ', and complementary adaptive 2:4 data matrix decoding means receiving said groups LT and RT or LT ' and RT ' along with said control group from said coding, transmission, or storage and retrieval for providing four decoded groups L', C', R' and S' representative of said four data source groups.

27. Apparatus for use in a group coding, transmission, or storage and retrieval system in which latticed data sets are divided into square components and the square components are subject to bit-rate reduction encoding before application to the coding, transmission, or storage and retrieval, and the encoded groups from the coding, transmission, or storage and retrieval are subject to bit-rate reduction decoding and the decoded square components are assembled into representations of the latticed data sets applied to the system, the system having an error level which varies with group size, the system receiving the two data output groups of a 4:2 data group encoding matrix and the system applying the representations of the latticed data sets to a 2:4 data group decoding matrix, comprising adaptive rematrixing means receiving said square components for determining which of the groups among the encoding matrix output groups and the sum and difference of the encoding matrix output groups has the smallest size, and for applying square components representing the encoding matrix output groups to the bit-rate reduction encoding if one of the encoding matrix output groups has the smallest size and for applying the sum and difference of the encoding matrix output groups to the bit-rate reduction encoding if one of the sum and difference of the matrix output groups has the smallest size, said adaptive matrix means also producing a control group indicating if square components representing the encoding matrix output groups or the sum and difference of the encoding matrix output groups are being applied to the bit-rate reduction encoding, and decode adaptive rematrixing means receiving said control group and square component representations of said encoding matrix output groups or the sum and difference of the encoding matrix output groups from the bit-rate reduction decoding, said means recovering the received groups unaltered when said adaptive rematrixing means applied square representations of the matrix encoder output groups to the bit-rate reduction encoding and recovering square component representations of the sum and difference of the received groups when the adaptive rematrixing means applied square representations of the sum and difference of the matrix encoder output groups to the coding, transmission, or storage and retrieval.

28. The apparatus of claim 27 wherein the sum of the encoding matrix output groups is a size weighted sum and the difference of the encoding matrix output groups is a size weighted difference.

29. The apparatus of claim 27 wherein the square components are grouped into square bands, and wherein said adaptive rematrixing means and said decode adaptive rematrixing means operate independently with respect to each or selected ones of square band grouped square components.

30. In a system in which the error level varies with group size level, apparatus for adaptively rematrixing groups received from coding, transmission, or storage and retrieval in response to a control group also received from the coding, transmission, or storage and retrieval for applying the adaptively rematrixed groups to a 2:4 data decoding matrix, the received groups resulting from encoding by a 4:2 data group encoding matrix and adaptive rematrixing of the encoding matrix output groups such that in one state of the adaptive rematrixing the groups applied to the coding, transmission, or storage and retrieval are the output of the encoding matrix and in another state of the adaptive rematrixing the groups applied to the coding, transmission, or storage and retrieval are the size weighted sum and difference of the output of the encoding matrix, said control group indicating the state of the adaptive rematrixing, comprising decode adaptive rematrixing means receiving said matrix output groups or the size weighted sum and difference of the matrix output groups from the coding, transmission, or storage and retrieval for producing latticed data sets representing the output of said 4:2 encoding matrix for application to said 2:4 decoding matrix, said means having a first state for recovering the groups unaltered from the coding, transmission, or storage and retrieval and a second state for recovering the sum and difference of the groups from the coding, transmission, or storage and retrieval, and means receiving said control group from said coding, transmission, or storage and retrieval for controlling said decode adaptive rematrixing means in response to said control group, such that the decode adaptive rematrixing means operates in said first state when the matrix encoder output groups are applied to the coding, transmission, or storage and retrieval and the decode adaptive rematrixing means operates in said second state when the sum and difference of the matrix encoder output groups are applied to the coding, transmission, or storage and retrieval.

31. The apparatus of claim 30 wherein the sum of the encoding matrix output groups is a size weighted sum and the difference of the encoding matrix output groups is a size weighted difference.

32. In a system in which the error level varies with group size level, apparatus for adaptively matrix decoding groups received from coding, transmission, or storage and retrieval in response to a control group also received from the coding, transmission, or storage and retrieval, the received groups resulting from encoding of four data source groups prior to application to said coding, transmission, or storage and retrieval by adaptive 4:2 data group matrix encoding such that in a second state of the adaptive matrix the matrix outputs are the sum and difference of the outputs of the adaptive matrix in its first state, said control group indicating the state of the adaptive matrix, comprising decode adaptive dematrixing means receiving from said coding, transmission, or storage and retrieval the groups from the adaptive 4:2 data group encoding for producing four latticed data sets representing the four data source groups, the dematrixing means including 2:4 matrix decoding means and means for adaptively applying the received groups to said 2:4 matrix decoding means in a first state of operation and the sum and difference of the received groups to said 2:4 matrix decoding means in a second state of operation, and means receiving said control group from said coding, transmission, or storage and retrieval for controlling said decode adaptive dematrixing means in response to said control group, such that the decode adaptive dematrixing means operates in the first state when the adaptive matrix encoding is in the first state and operates in the second state when the adaptive matrix encoding is in the second state.

33. In a system in which the error level varies with group size level, apparatus for adaptively rematrixing and 2:4 matrix decoding groups received from coding, transmission, or storage and retrieval in response to a control group also received from the coding, transmission, or storage and retrieval, the received groups resulting from encoding of four data source groups prior to application to said coding, transmission, or storage and retrieval by a 4:2 data group encoding matrix and adaptive rematrixing of the encoding matrix output groups such that in one state of the adaptive rematrixing the groups applied to the coding, transmission, or storage and retrieval are the output of the encoding matrix and in another state of the adaptive rematrixing the groups applied to the coder, transmission or storage are the size weighted sum and difference of the output of the encoding matrix, said control group indicating the state of the adaptive rematrixing, comprising decode adaptive rematrixing means receiving said encoding matrix output groups or the sum and difference of the encoding matrix output groups and said control group from the coding, transmission, or storage and retrieval, said means recovering the received groups unaltered when said adaptive rematrixing means applied the matrix encoder output groups to the coding, transmission, or storage and retrieval and for recovering the sum and difference of the received groups when the adaptive rematrixing means applied the sum and difference of the matrix encoder output groups to the coding, transmission, or storage and retrieval, and complementary 2:4 data decoding matrix means receiving the unaltered received groups or the sum and difference of the received groups for providing four matrix output groups representing the four latticed data sets applied to the 4:2 data encoding matrix.

34. The apparatus of claim 33 wherein the sum of the encoding matrix output groups is a size weighted sum and the difference of the encoding matrix output groups is a size weighted difference.

35. Apparatus for adaptively matrix decoding groups received from coding, transmission, or storage and retrieval in response to a control group also received from the coding, transmission, or storage and retrieval, the received groups resulting from the adaptive data 4:2 matrix encoding of four data source groups L, C, R, and S such that the adaptive matrix encoding operates in a first state providing two matrix encoded latticed data sets LT and RT having characteristics such that LT =L+0.707C+0.707S, and RT =R+0.707C-0.707S when LT or RT had the smallest size among LT, RT, k(LT +RT), and k(LT -RT), where k is a constant and the adaptive matrix encoding operates in a second state providing two matrix encoded latticed data sets LT ' and RT ' having characteristics such that [Figure - see DK for details] when LT ' or RT ' had the smallest size among LT, RT, LT ' and RT ', the adaptive data matrix encoding also producing a control group indicating which set of relationships defined the output groups LT and RT or LT ' and RT ', comprising decode adaptive 2:4 data matrix decoding means receiving said LT and RT or LT ' and RT ' groups from said coding, transmission, or storage and retrieval for providing four decoded groups L', C', R' and S' representative of the corresponding four data source groups, the decode adaptive 2:4 data matrix decoding means including 2:4 matrix decoding means and means for adaptively applying the received groups to said 2:4 matrix decoding means in a first state of operation and the sum and difference of the received groups to said 2:4 matrix decoding means in a second state of operation, and means receiving said control group from said coding, transmission, or storage and retrieval for controlling said decode adaptive matrix decoding means in response to said control group, such that the decode adaptive matrix decoding means operates in the first state when the adaptive matrix encoding is in the first state and operates in the second state when the adaptive matrix encoding is in the second state.

36. The apparatus of claim 35 wherein said adaptive 2:4 data matrix decoding means provides as its output four groups L', C', R', S' representing the four latticed data sets applied to the 4:2 adaptive data matrixing generally in accordance with the relationships [Figure - see DK for full documentation].

37. In a system in which the error level varies with group size level, apparatus for use in a decoder complementary to an encoder in which latticed data sets are divided into square components and the square components are subject to bit-rate reduction encoding, the decoder receiving the output of the encoder via transmission or storage and retrieval, wherein the decoder bit-rate-reduction decodes and assembles decoded square components into representations of the latticed data sets applied to the encoder, the encoder receiving the two data output groups of a 4:2 data group encoding matrix and the decoder applying decoded representations of the latticed data sets to a 2:4 data group decoding matrix, the encoder adaptively rematrixing square component representations of the 4:2 encoding matrix output groups such that in one state of the adaptive rematrixing the groups applied to the bit-rate reduction for transmission or storage are square components representations of the output of the encoding matrix and in another state of the adaptive rematrixing the groups applied to the bit-rate reduction encoding for transmission or storage are square component representations of the sum and difference of the output of the encoding matrix, said adaptive matrixing producing a control group indicating the state of the adaptive rematrixing, comprising decode adaptive rematrixing means receiving from the decoder bit-rate reduction decoded square component representations of said 4:2 encoder matrix output groups unaltered or the sum and difference thereof for producing square components which are assembled by the decoder into representations of the latticed data sets applied to the encoder by the 4:2 encoding matrix, the decode adaptive rematrixing means having a first state with characteristics substantially the same as the first state of the adaptive matrix encoding and a second state with characteristics substantially the same as the second state of the adaptive matrix encoding, and means receiving said control group from said transmission or storage and retrieval for controlling said decode adaptive rematrixing means in response to said control group, such that the decode adaptive rematrixing means operates in said first state when the matrix encoder output groups are applied to the transmission or storage and retrieval and the decode adaptive rematrixing means operates in said second state when the sum and difference of the matrix encoder output groups are applied to the transmission or storage and retrieval.

38. The apparatus of claim 37 wherein the sum of the encoding matrix output groups is a size weighted sum and the difference of the encoding matrix output groups is a size weighted difference.

39. The apparatus of claim 37 wherein the square components are grouped into square bands, and wherein said decode adaptive rematrixing means operates independently with respect to each or selected ones of square band grouped square components.

40. A method for adaptively rematrixing the data output groups of a 4:2 data group matrix for coding, transmission, or storage and retrieval in a system in which the error level varies with group size level, comprising determining which of the groups among the matrix output groups and the sum and difference of the matrix output groups has the smallest size, and applying the matrix output groups to the coding, transmission, or storage and retrieval if one of the matrix output groups has the smallest size and for applying the sum and difference of the matrix output groups to the coding, transmission, or storage and retrieval if one of the sum and difference of the matrix output groups has the smallest size.

41. The method of claim 40 wherein the sum of the matrix output groups is a size weighted sum and the difference of the matrix output groups is a size weighted difference.

42. In a system for coding, transmission, or storage and retrieval of latticed data sets received from a 4:2 data group encoding matrix and applied to a complementary 2:4 data decoding matrix, the system having an error level which varies with group size level, a method comprising determining which of the groups among the encoding matrix output groups and the sum and difference of the encoding matrix output groups has the smallest size, applying the encoding matrix output groups to the coding, transmission, or storage and retrieval if one of the encoding matrix output groups has the smallest size and applying the sum and difference of the encoding matrix output groups to the coding, transmission, or storage and retrieval if one of the sum and difference of the encoding matrix output groups has the smallest size, and also applying a control group to the coding, transmission, or storage and retrieval indicating if the encoding matrix output groups or the sum and difference of the encoding matrix output groups is being applied to the transmission or storage, and receiving said matrix output groups or the sum and difference of the matrix output groups, and said control group from the coding, transmission, or storage and retrieval, and recovering unaltered, for use by the complementary 2:4 decoding matrix, the received groups when the matrix encoder output groups are applied to the coding, transmission, or storage and retrieval and recovering the sum and difference of the received groups, for use by the complementary 2:4 decoding matrix, when the sum and difference of the matrix encoder output groups are applied to the coding, transmission, or storage and retrieval.

43. The apparatus of claim 42 wherein the sum of the encoding matrix output groups is a size weighted sum and the difference of the encoding matrix output groups is a size weighted difference.

44. In a system in which the error level varies with group size level, a method for adaptively rematrixing groups received from coding, transmission, or storage and retrieval in response to a control group also received from the coding, transmission, or storage and retrieval for applying the adaptively rematrixed groups to a 2:4 data decoding matrix, the received groups resulting from encoding by a 4:2 data group encoding matrix and adaptive rematrixing of the encoding matrix output groups such that in one state of the adaptive rematrixing the groups applied to the coding, transmission, or storage and retrieval are the output of the encoding matrix and in another state of the adaptive rematrixing the groups applied to the coding, transmission, or storage and retrieval are the sum and difference of the output of the encoding matrix, said control group indicating the state of the adaptive rematrixing, comprising receiving said matrix output groups or the sum and difference of the matrix output groups from the coding, transmission, or storage and retrieval and producing latticed data sets representing the output of said 4:2 encoding matrix for application to said 2:4 decoding matrix, recovering unaltered the matrix output groups from the coding, transmission, or storage and retrieval in a first state of operation and recovering the sum and difference of the matrix output groups from the coding, transmission, or storage and retrieval in a second state of operation, and receiving said control group from said coding, transmission, or storage and retrieval and controlling the state of operation in response thereto such that when the matrix encoder output groups are applied to the coding, transmission, or storage and retrieval, the operation is in the first state and when the sum and difference of the matrix encoder output groups are applied to the coding, transmission, or storage and retrieval, the operation is in the second state.

45. The apparatus of claim 44 wherein the sum of the encoding matrix output groups is a size weighted sum and the difference of the encoding matrix output groups is a size weighted difference.

46. The apparatus of claim 32 wherein the sum of the received groups is a size weighted sum and the difference of the received groups is a size weighted difference.

47. The apparatus of claim 35 wherein the sum of the received groups is a size weighted sum and the difference of the received groups is a size weighted difference.