PRML coding

Abstract: There is disclosed a rate 8/9, constrained partial response class IV code having run length limitation parameters (0,3/5) is provided for any partial response (PR) signalling system employing maximum likelihood (ML) detection.

Description: The present invention relates to PRML coding and provides what is considered to be an advance on PRML coding techniques disclosed and claimed in copending application EP-A-0 243 708 (forming part of the state of the art under a.54(3)EPC). Partial Response Maximum Likelihood techniques have long been associated with digital communication channels. ML detection is typically used in PR class-IV channels (hereinafter, the acronym PRML is used to denote the combination of PR class-IV channels with ML detection). Further, encoding data for use with recording channels is also known. The (d,k) constraints, which specify the minimum and maximum run lengths of zeroes, respectively, in RLL codes used in peak-detection systems, reduce intersymbol interferences (hereinafter, ISI) while maintaining self-clocking characteristics of the data signal. See, for example, IBM TECHNICAL DISCLOSURE BULLETIN, Vol. 28, No. 5, October 1985, pp. 1938-1940, entitled 'Improved Encoder and Decoder for a Byte-Oriented (0,3) 8/9 Code', IBM TECHNICAL DISCLOSURE BULLETIN, Vol. 18, No. 1, June 1975, pp. 248-251, entitled 'Encoder and Decoder for a Byte-Oriented (0,3) 8/9 Code', and the above-identified related application EP-A-0 243 708 which discloses both a (0,3/6) and a (0,4/4) PRML method and apparatus. In a PRML channel, a channel code can also be used to provide clocking and automatic gain control (AGC) information. Since the maximum run length of nominally zero samples must be limited, the k constraint is still appropriate when specifying the channel code requirements for PRML channels. However, RLL codes with d greater than zero are not necessary in PRML channels because compensation for ISI is inherent in the ML detector. Thus, there is no need to reduce interference by coding with a d constraint. On the other hand, the k constraint is not the only constraint required for the PRML channel. The k₁ constraint is an additional constraint that is used to limit both detector delay and hardware complexity. If a data sequence of the input signal is demultiplexed into an even indexed sample subsequence and an odd indexed sample subsequence, and ML detection is applied to each subsequence independently, a constraint on the number of successive nominally zero samples in each subsequence adequately limits the detector delay and hardware. Thus, in terms of NRZI data representation, the required limitation is on the maximum number of sequential zeroes in both the even-indexed and the odd-indexed subsequences. The maximum number of sequential NRZI zeroes in either subsequence is referred to as the k₁ constraint, and is analogous to the k constraint for the interleaved sequence of data. Codes having run length constraints restrict the allowed code sequences to less than 2 to the power of n sequences possible, where n specifies the number of data symbols in a sequence. The rate of such a code is less than 1 data bit to 1 code bit, which can be expressed as a ratio of small integers. Thus, if an 8-bit data byte is mapped into a 9-bit codeword, the code rate is 8/9. An article entitled 'Run length restriction on the output of PR4 channels' IBM TECHNICAL DISCLOSURE BULLETIN, Vol. 28, No. 3, August 1985, pp. 1048-1051 discloses a data transmission system in which 8 data bits are encoded into 9 bit codewords, the odd and even subsequences including maximum of six consecutive zero samples with the overall sequence including a maximum of 4 consecutive zero samples. The (0,3/6) and (0,4/4) codes disclosed in EP-A-0 243 708 (inventor - Eggenberger) differ in the following manner. The k parameter is desirable for accurate timing and gain control. Therefore, the (0,3/6) code disclosed by Eggenberger, which used a smaller value of k (3) will provide more accurate timing and gain control than the (0,4/4) code. However, it has a disadvantage relative to the (0,4/4) code in that it requires more hardware in the Viterbi detector path memory. Alternatively, a small k₁ parameter will reduce the size of the path memory required in the ML detector. Therefore, the (0,4/4) code will require a smaller path memory than the (0,3/6) code. Likewise, the (0,4/4) code has a disadvantage relative to the (0,3/6) code in that it does not have timing and gain control equal to the (0,3/6) code. Since these codes cannot be simultaneously used, a design choice must be made depending on the relative importance of the advantages inherent in each code. It can be said that this invention avoids the above design choice having to be made by providing a single class-IV PRML modulation code which has the timing and gain control advantages of the (0,3/6) PRML code, and the reduced Viterbi detector path memory hardware requirement advantages of the (0,4/4) PRML code. The details of a (0,3/5) modulation code suitable for class-IV PR channels employing ML detection are set out hereinafter. The disclosed (0,3/5) code receives input data comprised of a preselectable number of bits of binary data which are encoded into sequences of codewords having a preselectable number of bits. The sequences of codewords are arranged into odd and even interleaved subsequences, each subsequence having no more than three consecutive zero bits of binary data and each odd and even subsequence having no more than five consecutive zero bits of binary data. In like fashion, the codewords produced by the encoder can be used as input to a decoder. The decoder receives the codewords and produces sequences of binary data in response to the codewords. The present invention will be described further by way of example with reference to embodiments thereof as illustrated in the accompanying drawings in which: - Fig. 1 is a schematic diagram of a PRML system modulation code encoder for a code having rate 8/9 and run length constraints (0,3/5); and Fig. 2 is a schematic diagram of a PRML system modulation code decoder for a code having rate 8/9 and run length constraints (0,3/5). The disclosed (0,3/5) PRML modulation code is used to encode 8 bit binary data into codewords comprised of 9 bit code sequences. The maximum number of consecutive zeroes allowed within a code sequence is 3, and the maximum number of consecutive zeroes in the all-even or all-odd subsequences is 5 and, equally, to reverse the process by decoding. The (0,3/5) code is designed for a specific partial response (PR) channel, namely the so-called "class-IV" PR. Class-IV partial response refers to a channel response whose output waveform is described by taking the input waveform, and subtracting from it the same waveform delayed by 2 bit intervals. This is described digitally in terms of a channel polynomial, P(D). For class-IV partial response: P(D) = (1-D²) (1) The polynomial describes the effect of the channel on digital inputs. The D operator means "delay one bit time", and D² means "delay 2 bit times." Therefore, the class-IV channel produces output sample U at time t which is equal to the input W at time t, minus the input W at time t-2. In other words: U t = W t - W t-2 (2) The modulation code is characterised by three parameters d, k, and k₁ written (d,k/k₁). The parameters d and k represent the minimum and maximum run lengths of zeroes in the channel output code bit sequence, where a run length of zeroes may be regarded as a period of silence in the detection process. The parameter k₁ represents the maximum run length of zeroes in the particular all-even or all-odd subsequences. In the present invention, d equals 0 since a minimum run length of zeroes is inapposite in the context of PRML channel. The value of k is set to three and the value of k₁ is set to 5. A small value of k is desirable for accurate timing and gain control, and a small value of k₁ reduces the size of the path memory required in the ML detector. A rate 8/9 RLL block code having (0,3/5) constraints provides at most 251 9-bit codewords from 8-bit data bytes. Two hundred fifty six codewords can be derived by excluding the all-ones codeword and adding 6 state dependent codeword pairs for two state encoding. The states 1 and 2 are identified by the value of the last bit of the previous codeword concatenation. Thus, 256 codewords of 9 bits each can be defined where all catenations of such codewords comply with the d,k/k₁ constraint and two state encoding is used. The code provides for specific assignment of 8-bit data bytes to 9-bit codewords which creates partitions of bytes and codewords with similar structure. The partitions of bytes are uniquely identifiable and overall mapping of the codewords is produced by gating partition bits according to simple boolean functions. If Y denotes a 9-bit codeword in the (0,3/5) code, then Y = [Y₁, Y₂, Y₃, Y₄, Y₅, Y₆, Y₇, Y₈, Y₉] (3) The constraint k = 3 in the overall coded sequence can be produced by eliminating 9-bit sequences with run lengths of 3 zeroes at the left end thereof, run lengths of 2 zeroes at the right end thereof, or run lengths of 4 zeroes within each 9-bit sequence. Such a constraint is given by the following boolean relation: (Y₁+Y₂+Y₃) (Y₂+Y₃+Y₄+Y₅) (Y₃+Y₄+Y₅+Y₆) (Y₄+Y₅+Y₆+Y₇) (Y₅+Y₆+Y₇+Y₈) (Y₈+Y₉) = 1 (4) Similarly, the constraint k₁ = 5 is described by the following two equations for the sequence of all odd-bit positions and the sequence of all even-bit positions, respectively, in Equations (5) and (6) given below. (Y₁+Y₃+Y₅) (Y₅+Y₇+Y₉) = 1 (5) (Y₂+Y₄+Y₆+Y₈) = 1 (6) Two hundred fifty one valid 9-bit binary sequences satisfy Equations (4), (5), and (6), the decimal equivalents for which are given in Table III. Referring now to Fig. 1, an 8-bit binary data byte, denoted X, and its assigned 9-bit codeword, Y, are given by: X = [X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈] (7) Y = [Y₁, Y₂, Y₃, Y₄, Y₅, Y₆, Y₇, Y₈, Y₉] (8) The first partition of codeword assignments, denoted M, comprises the set of data bytes in which the first and last four bits of the 8-bit binary data bytes can be mapped without change into the first and last four bits, respectively, of the 9-bit codeword, Y. The middle bit, i.e. the fifth bit position, of the 9-bit codeword in this partition is always 1. Thus, partition M comprises 163 codewords which can be identified by the relation: M₁ = (X₁+X₂+X₃) (9) M₂ = (X₇+X₈) (10) M₃ = (X₂+X₄+X₅+X₇) (11) M = M₁M₂M₃ (12) The remaining codeword assignments are divided into partitions N₁, R₁, S₁, N₂, R₂ and S₂, which identify 24, 25, 9, 10, 20 and 6 codeword assignments, respectively. These assignments are given by the following structures of the bits in X: The six state-dependent codewords, together with decimal equivalents of the possible values, are given in Table IV. To avoid an all ones coded sequence, the middle bit, Y₅, is changed to zero which, in turn, creates another valid codeword. The partition E defines the all-ones codeword as follows: E = X₁X₂X₃X₄X₅X₆X₇X₈ (19) The logic equations for encoder 100 of Fig. 1 are given in Table I. The decoder function of Fig. 2 identifies the same partitions as those in the encoder, using the exclusive structures of bit patterns in the 9-bit sequence Y to obtain logic equations for the components of X. Decoder equations for the decoder 300 of Fig. 2 are provided in Table II. Referring now to Fig. 1, encoded variables, X₁-X₈ enter encoder 100 at receiver lines X₁ to X₈ of encoder 100. The receiver lines X₁ to X₈ are coupled to encoder gates 102-274. In response to such variables, codewords are produced by encoder gates 102-274 in the following manner. Encoder gates 102-146 produce codeword partitions M, N₁, R₁, S₁, N₂, R₂, S₂, and E respectively. Finally, encoded variables Y₁-Y₉ are produced by encoder gates 148-164, 166-182, 184-194, 196-204, 206-210, 212-220, 222-234, 236-254 and 256-274, respectively. Coded variables, Y₁-Y₉, enter decoder 300 at receiver lines Y₁ to Y₉ as shown in Fig. 2. The receiver lines Y₁ to Y₉ are coupled to decoder gates 302-426. Backward reading, codeword partitions, E, M, N₁, R₁, and S₁, for recreating uncoded variables, i.e. the data, are produced by decoder gates 302-322, respectively, in response to coded variables Y₁-Y₉. Similarly, partitions N₂, R₂ and S₂ are produced by decoder gates 324-328, respectively. Finally, the data, X₁-X₈, is provided by decoder gates 330-340, 342-348, 350-364, 366-374, 376-390, 392-410, 412-418 and 420-426, respectively. The code described in this specification is an optimum code in that k cannot be decreased without decreasing the rate. Similarly, k₁ cannot be decreased without increasing k, decreasing the rate, increasing the codeword length, or increasing the number of encoder states. This modulation code provides a reduced k parameter (k=3) relative to the (0,4/4) code (k=4) for improved timing and gain control information, and it achieves this without increasing the k₁ parameter as much as the (0,3/6) code (k₁=5 versus k₁=6). The k₁ parameter directly influences the hardware requirements in the Viterbi detector path memory, as well as the size of the most probable error bursts. The maximum error propagation of the (0,3/5) code is the same as that of the (0,3/6) code. While the invention has been particularly shown and described with reference to a preferred embodiment thereof, it will be understood by those skilled in the art that various changes in detail may be made therein without departing from the spirit, scope and teaching of the invention. For example, a software implementation of the encoder and decoder circuit functions is possible.

Claims: Apparatus for encoding a preselectable number of bits of binary data, for a PRML channel, into codewords having a preselectable number of bits, said apparatus comprising: receiver means for receiving the binary data; and encoder means, coupled to the receiver means, for producing sequences of encoded data from the binary data, each sequence comprising a plurality of codewords, each sequence having at least two interleaved odd and even subsequences; said sequences of interleaved subsequences having no more than three consecutive zeroes therein; said odd and even subsequences each having no more than five consecutive zeroes therein; the ratio of the number of bits in the encoded binary data to the number of bits in the codewords being 8/9; and each codeword having a state dependency on selected bits in the previous codeword produced by the encoder means. Apparatus as claimed in claim 1 wherein the encoder means includes a plurality of gating means for producing the codewords as partitions and output gating means for combining the partitions of codewords into the sequences of codewords. Apparatus as claimed in any preceding claim further including decoding means for decoding a preselectable number of codewords into a preselectable number of bits of binary data, said decoding means comprising: receiver means for receiving the codewords; and decoder means, coupled to the receiver means, for producing sequences of binary data in response to said codewords. Apparatus as claimed in claim 3 wherein the decoder means includes a plurality of gating means for producing the partitions of binary data and output gating means for combining the partitions of binary data into the sequences of binary data. A method for encoding a preselectable number of bits of binary data, for a PRML channel, into codewords having a preselectable number of bits, said method comprising the steps of: receiving the binary data; and producing sequences of encoded data from the binary data, each sequence comprising a plurality of codewords, each sequence comprising two interleaved subsequences, one of which consists only of odd bit positions and the other consists only of even bit positions; the sequences having no more than three consecutive zeroes therein; each subsequence having no more than five consecutive zeroes therein; the ratio of the number of bits in the encoded binary data to the number of bits in the codewords being 8/9; and each codeword having a state dependency on selected bits in the previous codeword.

Inventors: MARCUS BRIAN HARRY, PATEL ARVIND MOTIBHAI, SIEGEL PAUL HOWARD, MARCUS, BRIAN HARRY, PATEL, ARVIND MOTIBHAI, SIEGEL, PAUL HOWARD
Applicants: IBM, INTERNATIONAL BUSINESS MACHINES CORPORATION
Application year: 1988
Main classification: H03M5
IPC codes: H03M7, H03M5, H03M13, H04L25