GB2100034A - Method for recording digital signals on multiple tracks of a recording tape - Google Patents

Abstract

Audio signals quantized into digital signals are formed into data words W and organized into a plurality of adjacent parallel rows T1 T2 T3 on recording tape remote from an edge of the tape. Parity words P are derived from the data words and organized into a row T6 which is parallel to the rows of data words close to the edge of the tape. An error detecting check word C is generated and appended to the end of each of the rows of data and parity words. A synchronization word S is also generated and appended to the beginning of each of the rows of data and parity words. By the arrangement of the parity words along the same row or track adjacent to the tape edge, the probability of occurrence of incorrectable errors is reduced. <IMAGE>

Description

SPECIFICATION Method for recording digital signals on multiple tracks of a recording tape The present invention relates to a method for recording digitized signals on multiple tracks of a recording tape in such manner that the probability of occurrence of incorrectable errors is minimized.

The number of bits recorded per unit area of the recording tape may be increased by reducing the transport speed of the tape to as low as possible and/or by narrowing the width of each track. However, this tends to render the recorded signals susceptible to noise, drop-outs and level variations. On the other hand, the signals recorded on a track close to an edge of the tape would be more affected by defects caused by loss of contact with the transducer head due to the inherent tendency of the tape moving in a meandering way or by the in precision of the linearity of the tape edges. The bit error rate on the track adjacent to the edge portions of the tape would become increasingly severe with the reduction both in tape transport speed and in track width.According to a conventional data format, data and parity words are organized so that they are located on the same row and if this row corresponds to a track adjacent to an edge of the tape, the probability of occurrence of incorrectable errors amounts to a substantial value due to the higher error rate on that track.

It is therefore an object of the invention to minimize the probability of occurrences of incorrectable errors.

This object is obtained by recording parity words on a track adjacent to an edge of the tape while recording data words on tracks remote from the tape edge.

According to the present invention, digital signals are formed into data words which are organized into a plurality of parallel rows which are adjacent to each other and respectively correspond to recording tracks on a magnetic tape which are remote from an edge of the tape. Parity words are derived from the data words and organized into a row which is parallel to the rows of data words and corresponds to a track which is close to the edge of the tape. An error detecting check word is generated and appended to the end of each of the rows of data and parity words. A synchronization word is also generated and appended to the beginning of each of the rows of data and parity words.

The present invention will be described in further detail with reference to the accompanying drawings, in which: Figure 1 is an illustration of a block diagram of a PCM recoding and playback system for carrying outthe present invention; Figure 2 is a schematic illustration of a pattern of multi-tracks on a section of a recording tape; Figure 3 is a illustration of a data format of the prior art; and Figure 4 is an illustration of a data format according to the invention.

Figure 1 is an illustration of a block diagram of a PCM recording/playback system of the type having a plurality of fixed transducer heads. In Figure 1 two-channel audio signals are applied to input terminals 1a, 12 and bandwidth-limited by low-pass filters 21 and 22 so that the output of each low-pass filter has a banwidth less than 1/2 of the frequency at which the analog signals are sampled by sample-and-hold circuits 31 and 32 respectively. The sampled signals are applied to an analog-to-digital converter 4, whereby the amplitude of the digital samples is coded into digital pulses, or PCM signal. This PCM signal is applied to a data formatting circuit 5 driven by a quartz oscillator 9.The data formatting circuit essentially comprises a memory for purposes of grouping the digital signals into data words and compressing the time dimension of the data words to permit them to be interleaved with redundant signals and arranging them in a predetermined data format. Further included in the circuit 5 is a parity encoder and a cyclic redundant check word generator of the type known in the art for forming parity words (error correction words) from data words and cyclic redundant check words (error detection words). A distributor is also provided in the data formatting circuit to organize the data words, parity words and check words into a predetermined sequence or frame into a predetermined format which will be described.A frame synchronization word is also generated in the data formatting circuit 5 and inserted at the beginning of each frame to permit it to be identified when the signal is processed by a playback circuit. The outputs of the circuit 5 are then applied to a modified frequency modulator 6 of a known design. The frequency modulated signals are applied to amplifiers 7 and thence to recording heads 81 to 8k which are arranged to record the digital signals along "k" tracks of a magnetic recording tape.

Figure 2 is an illustration of a track pattern on the tape 11 in the case of k = 4, with To, T1,T2 and T3 respectively designating the tracks recorded simultaneously by the heads 81, 82,83 and 84, respectively. It is to be noted that in the case of a reversible tape recorder in which the tape is reversed upside down at the end and moved in the same direction as during the "go path" recording, the "return path" tracks are interleaved with the "go path" tracks so that in either direction of tape movement the track To is always positioned close to the edges of the tape.

Upon reproduction the recorded PCM signals are detected by playback heads 121 to 12k and applied via playback amplifiers 13 to a detector and frequency demodulator unit 14. The PCM signals, after having being frequency demodulated, are applied to a data deformatting circuit 15 comprising a memory for purposes of jitter absorption and a parity decoder in which an error, if present in any data word, is detected and corrected by checking parity with data words in a known manner. The error corrected data words are converted into original data bits within the memory and retrieved at a constant rate response to the clock supplied from the oscillator 9 so that time axis jitter contained in the reproduced PCM signals is eliminated.The data read out of the memory of the data deformatting is supplied to a digital-to-analog converter 16 and thence to sample-and-hold circuits 171 and 172 which are coupled respectively to low-pass filters 181 and 182. The PCM signals are thus converted into the original analog signals and delivered through output terminals 191 and 192.

Before describing the organization of data according to the invention, reference is had to Figure 3 in which the data format of a conventional method is illustrated. The digital signals are organized into successive frames of words respectively recorded along four tracks T6 (t represents an integer ranging from 0 to 3) and only the bits of a given frame period are schematically shown for purposes of simplicity. More specifically, each frame comprises a frame synchronization word S, a series of six data words W(#)1 to W(6)6, a parity word P(S)1 and a parity word 0fr)1 for purposes of error correction, and a cyclic redundant check word 0)6)1 for purposes of detecting an error which occurs in that frame.Since the tape edge portions are known to subject to contact loss with the transducer head, the error rate on rack To is higher than any other track.

Referring now to Figure 4, the data organization according to the invention is illustrated in which the same notation is used to indicate elements corresponding to those in Figure 3. Let it be assumed that the number of data words within a given frame is "n", the total number of P and 0 parity words is "j" and the number of tracks is "k". The number "n" is equal to j x (k - 1) to fill the track To with the same number of redundant words including P and Q parity words derived from all the data words within the given frame plus a cyclic redundant check word C for detecting an error in that redundant words.As shown, track To is exclusively used for recording redundant words which comprise a synchronization word S, error correction parity words P(0)1 to P(0,4 and Q(0)1 to Q(0)4 and an error detection word C(o). Whereas, tracks T1 to T3 are used to record data words including W(1)1 to W(1)8, W(2)1 toW#2#8, W(3), to W(3)8, so that each data track consists of eight data words and a corresponding check word C(1), C(2) and C(3) and finally a frame synchronization word S. No error correction parity words thus exists in tracks T1 toT3.

The present invention favorably compares with the prior art of Figure 3. The following description will now demonstrate the probability of occurrences of certain particular circumstances in which errors are not correctable with the data organization according to the invention in comparison with the corresponding probability of the prior art. For purposes of discussion, description is concerned with an error in a single data word corrected by a corresponding 0 parity word. Let it be assumed for purposes of comparison that the frame contains six data words.With this assumption, the error correcting 0 parity word is given by the following Equation: 0), + 2) = D6W)#) # D5W(6 + 1) 0 D4W(,+ 2) 0 D3W(t+3) 03 D2W)6) e D1VV)6 + 1+ . (1) where, D represents the delay operator and (3 represents the modulo 2 summation, the number in the parenthesis represents the track number ranging from 0 to 3, the track number being represented by modulo 4 summatuion.

If, for example, e = 1, Equation 1 now becomes Q(3) = D6W(1 0 D5W(2) 0 D4W)3) 0 D3W(0) 03D2W(1) O D1W)2).

In the case of the prior art, the 0(3) parity is derived from the data words circled in Figure 3 which are distributed among tracks To toT3. Otherwise stated, the data words from which the 0(3) parity is formed are interleaved across different tracks and are spaced apart sufficiently to make it highly unlikely that more than one data word will be affected by the same defect caused by bursts. If an error occurs in one of the six data words from which the 4! + 2) of Equation 1 has been derived, the error can be corrected by a modulo 2 summation of O(f + 2) and the terms of Equation 1 excepting the term of the data in error.

The probability PN of occurrences of more than one error with the data words for Q(f + 2) parity, a condition under which the errors are incorrectable, is derived by analyzing a case I in which error occurs at a uniform rate Pe for all tracks To through T3 and a case II in which the error rate is Pe for tracks T1 to T3 and (Pe + e) for track To. The probability PN of the prior art will first be analyzed as follows.

Case I Since incorrectable errors occurs in this case if two or more words are affected simultaneously in a group including any one of Q parity words and the corresponding six data words. Therefore, PN = Pe{6C1Pe(1-Pe)6-1+6C2.Pe(1-Pe)6-2......+ 6C6Pe6} ....(2) Since Pe is much smaller than unity, PN =. 6Pe2 . . . . (3) Case II From Equation 1 and Figure 3 it is seen that there is a likelihood of the occurrence of a one-word error on track To for every four errors and the occurrence of three two-word errors on tracks T1 and T3 for every four errors.Differently stated, for e = 1, a one-word error is likely to occur in a data word on track To which forms part of words from which the Q(3) parity is derived, and for e = 0, 2 and 3, a two-word error is likely to occur in those data words on track To which form part of the words from which the 0)2), 0)0) and 0)1) parities are derived.

Consider first a given Q parity word group having a single data word located on track To. On the assumption that an error exists on track To the probability PN(O)(1W) of occurrence of more than one error in the remaining six words including the 0 parity of the affected word group is given by PN(o) )lW) (Pe + e) {6C1.Pe (1 - Pe)5 + 6C2-Pe2- (1 - Pe)4 + ..... + 6C6Pe6} . 6Pe (Pe + e) . . .. (4) Furthermore, on the assumption that a one-word error exists on track T1 the probability PN(1)(1W) of occurrence of more than one error in the remaining six words is given by PN(1)(1W)-. Pe {5Pe + (Pe + e)} = 6Pe2+ Pe.e ..... (5) Equation 5 also applied to probabilities PN(2) (1W) and PN(3)(1W) Therefore, the probablity PN(1W) of occurrences of incorrectable errors is derived from Equations 4 and 5 as follows: P = PN(O)(1W)+ PN(1)(1W)+ PN(2)(1W)+PN(3)(@W) 7 +PN(1)(1W)+ PN (2)1W) + PN (3)1W) 7 6Pe (Pe + e)+6(6Pe2 + Pe.e) 7 - 6Pe2+(12/7)Pe.e ....(6) Consider now a situation in which a given 0 parity word group has two data words located on track To.Let it be assumed that an error has occurred in one of these two data words on track To, the probability PN (0) (2W) of occurrence of more than one error in the remaining six words including the other of said two data words is given by PN (0) (2W) (Pe + e) {5Pe + (Pe + e)} =6Pe+7Pe.e + e PN(1)(2W) of occurrence of more than one error in the remaining six words on the assumption of the occurrence of an error on track T1 is expressed by PN(1)(2W)-. Pe (4Pe + 2(Pe + e)} 6Pe2 + 2Pe.e . . . . (8) Then, the probabilities PN(2)(2W) and PN(3)(2W) of occurrences of more than one error in the remaining six words on the assumption of the occurrence of an error on track T2 or T3 are given by Equation 8.

Therefore, the average value PN (2W) of probabilities of the occurrence of incorrectable errors is given by PN 3 (2W) + PN (0) (2W) + PN(1)(2W) + PN(2)(2W) 7 + PN (3) (2W) + PN (0) (2W)+ PN (1) (2W) 7 2 (6Pe2 + 7Pe.e + e2 + 5(Pe2 + 2Pe.e) 7 = 6Pe+(24/7)Pe~e+ (2/7)e2 ....(9) Therefore, the total average PN of the incorrectable probabilities of the prior art data format is given as follows: pN = 3PN (2W) + PN (1W) 4 = 6Pe2 + 3Pe.e + (3/14)e2 . . . . (10) The following description will now be concerned with the analysis of the incorrectable probabilities of the data format according to the present invention with reference to Figure 4.The error correction 0(o) parity word of the data format of Figure 4 is given by Q(0) = D6W(1 > 03 D5W)2( 0 D4W(3( 0 D3W(1) 03 D2W(2) (3 D1W(3 . . . . (11) Case I The incorrectable probability PN, is given as follows: PN' = 6Pe2 . . . . (12) it is seen that probability PN' equals PN given by Equation 3 of Case I of the prior art.

Case 1l Since the 0 parity words are recorded only on track To adjacent to an edge of the tape, and since the same assumption holds as in the case of a single data word for a given Q parity word as discussed in connection with case II of the prior art, the average probability PN is given by PN' = 6Pe+(12/7)Pe.e ....(13) which equals Equation 6.

Therefore, it is seen from the foregoing that when compared on the assumption that the error rate is uniform across all the tracks (cases I) there is no difference in incorrectable probability between the prior art and the invention. However, in the case of nonuniform error rate (cases II) with a higher error rate on track To, the comparison can be validly made between Equations 10 and 13, which leads to the conclusion that the data format according to the invention favorably compares with the prior art data format.

While the foregoing discussion has been concerned with the 0 parity word groups, the same applies to a combination of P and Q parity word groups.

Claims (3)

1. A method for recording digital signals on a plurality of parallel tracks of a recording tape, comprising the steps of forming the digital signals into data words, organizing said data words into a plurality of parallel rows which are adjacent to each other and respectively correspond to the tracks which are remote from an edge of said tape, forming parity words from said data words, organizing said parity words into a row parallel to said rows and corresponding to a said track which is close to said edge of the tape, generating an error detecting check word and appending it to the end of each of said rows, generating a synchronization word and appending it to the beginning of each of said rows, and recording the words in said rows on the corresponding tracks of said tape.

2. A method as claimed in claim 1, wherein the number of data words in each row equals the total number of said organized parity words.

3. A method of recording digital signals on a plurality of parallel tracks of a recording tape substantially as hereinbefore described with reference to the accompanying drawings.