## Duobinary modulation for optical systems

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This invention relates to error correction of a received data stream and more particularly to an error correction method and system which employs ambiguity zone detection, permutation and inverse permutation and iterative processing to perform the error correction action. A primary objective of any digital communication system is to transmit duobinary signaling and decoding strategies at the maximum possible rate and receive it with minimum errors or distortion.

Similarly, a main design objective of data storage system is to allow the system to store information with the maximum possible density and to retrieve it with the least possible errors.

A variety of error control coding schemes, channels with constraint, and digital modulation with constraint have been devised to improve data transmission and recording systems. Error control codes such as block codes and convolutional codes are usually applied to digital sequences for the purpose of coping with errors which may happen in bursts as well as randomly.

The encoded sequence then contains some constraint or redundancy. Such constraint is then duobinary signaling and decoding strategies by the receiver to identify possible errors that may exist in the received sequence. For example, if the received sequence does not satisfy parity-check equations, then the receiver detects the existence of some errors and, in some cases, can correct them.

In order to achieve a higher performance, a concatenation of two error correcting codes is sometimes adopted. Here the term "inner encoder" is used in the sense that the inner encoder is closer to the communication channel. Hence a subsystem including an inner encoder, the communication channel and an inner decoder, is often called an "outer channel". The outer encoder therefore sees the outer channel as the effective channel. An example is to use a block code e.

An "interleaver" is often placed between the two encoders, because when the inner decoder makes erroneous decisions, it tends to create bursts of errors due to the nature of the convolutional code. An interleaver is an example of a device which permutes a data stream in a manner which is reversible. An example of an interleaver is shown in FIG. An output is obtained by sequentially accessing adjacent columns of bits. The interleaving action disperses adjacent bit values and prevents a burst error from affecting a sequential run of bits in the original data stream.

By having the interleaver in front of the outer channel, the outer encoder and decoder do not have to deal with long bursts of errors. Fundamentals and Applications, Prentice-Hall, The type of system represented in FIG. The notion of concatenated system can be generalized to a system in which the inner encoder is not a conventional error correcting encoder such as a block code or convolutional codebut is a special type of signaling scheme or a channel with some constraint or memory.

A number of coding techniques have been developed to reduce adverse effects due to these factors. Partial-response channel coding is well recognized as a bandwidth-efficient transmission technique and can be viewed as a technique to shape the signal spectrum by introducing a controlled amount of ISI. An optimal decoding structure for a partial-response channel is known as maximum-likelihood ML decoding See e. A system with partial-response channel coding and maximum likelihood decoding has become popular in recent years and is often referred to as a PRML system see e.

Another class of codes, often used in digital recording, is run-length limited codes, denoted d,k -limited codes. The integer parameters d and k represent the minimum and maximum numbers of runs of either 0's or 1's that are allowed in the encoded sequence. The lower bound d is chosen from the ISI consideration, and the upper bound k is set to insure clock synchronization capability at the receiver side.

Both partial-response channels and run-length limited codes can be viewed as techniques that introduce some constraints into the digital sequence to be transmitted. Such constraints or memory should be exploited by the receiver to identify possible errors or biases duobinary signaling and decoding strategies may exist in the received sequence.

Techniques similar to partial-response signaling have been developed in digital modulation schemes. One important class of such modulation techniques is known as continuous phase modulation CPM or continuous envelope coded modulation see e. Here, some constraint is introduced in the modulated signal, because the phase values that the modulated signal is allowed to take are limited to a subset of the set of phase values duobinary signaling and decoding strategies for the modulation system.

An example of CPM is MSK minimum shift keying in which the phases that the modulated signal is permitted to take at a given symbol time duobinary signaling and decoding strategies only the phases adjacent to the previous symbol phase. Another class of digital phase modulation techniques with similar properties is those that use differential precoding of the data.

In this case, the correlation is caused by the preceding and consequent modulation. Since the amplitude of transmitted signals contains no information, one can reproduce the original information even if the amplitude has been significantly distorted. These classes of digital modulation techniques have come to be predominantly used in wireless communication systems.

Instead of concatenating two error control codes, an error control code may be concatenated with digital modulation.

A trellis-coded modulation TCM is a well-known example in which a convolutional code and digital-phase modulation are combined.

The receiver can correct most errors effectively, since the receiver can exploit the constraint that the received phase sequence must satisfy.

An optimal decoding structure for continuous phase modulation, precoded digital phase modulation and TCM is maximum-likelihood ML decoding, similar to that originally derived duobinary signaling and decoding strategies convolutional codes i. A receiver may be designed to decide that a symbol should be erased when it is received ambiguously. Suppose that a channel duobinary signaling and decoding strategies is binary, i.

When a received symbol is corrupted by strong noise or interference and its value is near the threshold between 0 and 1, then the receiver may opt duobinary signaling and decoding strategies to duobinary signaling and decoding strategies a hard decision regarding the value of the symbol, and labels it as "e", which stands for an erasure.

To implement an erasure, a quantizer is required with additional threshold ssee FIG. When the input is binary, the output with erasure option can be duobinary signaling and decoding strategies by two bits, e. A In coding theory a binary erasure channel BEC has been well studied see e. In other words 0 is never mistaken as 1 and vice versa. They showed that decoding with the generalized erasure, which they termed ambiguity zone duobinary signaling and decoding strategies can achieve a near-optimum performance, while retaining decoding complexity at a minimal level.

As discussed above, a large class of digital communication or recording systems can be viewed as concatenated systems in which each building block may be an error control encoder, a modulator with constraints, or a channel with constraints. **Duobinary signaling and decoding strategies** conventional method of receiving such signals is to perform the inverse operations of the transmitter's building blocks, in the reverse order.

In other words, building blocks at the receiver are an inner decoder, a de-interleaver and an outer decoder. The inner decoder attempts to do its best in correcting errors and delivers the resultant output to the outer decoder. Such a decoding procedure may be called a "one-path" decoding method.

Such a one-path method is still susceptible to being unable to correct duobinary signaling and decoding strategies error states, notwithstanding a general ability to correct for many error conditions. Accordingly, it is an object of the invention to improve error correction performance of a receiver system which receives digital data over a noisy communication channel e.

It is another object of the invention to improve error correction performance of a system which retrieves data from a memory e. The method includes the steps of: In a preferred embodiment, the data making up the received data stream duobinary signaling and decoding strategies been subjected to a permutation action to time-wise duobinary signaling and decoding strategies original contiguous data values.

The method duobinary signaling and decoding strategies the quantized data stream to an inverse permutation action in producing the error-corrected data stream and further re-permutes the error-corrected data stream in step c to return it to a format identical to that of the quantized data stream before the substitution is performed.

A system incorporating the invention is schematically shown in FIG. The transmitter side is almost the same as any of the concatenated systems discussed above, except that a "permutation" module has been inserted, for generalization purposes, instead of the interleaver between the outer and inner encoders.

A carefully designed permutation module can improve the system more than a conventional interleaver, however it is to duobinary signaling and decoding strategies understood that an interleaver is within the ambit of a permutation module and is a special and simple type of permutation module.

Similarly, a concatenated system without an interleaver FIG. Thus, the invention can be applied to a **duobinary signaling and decoding strategies** class of systems with little or no modification at the transmitter side.

The invention places an AZD ambiguity zone detector 10 at the receiver front end An AZD is a threshold detector or quantizer which assigns "erasure symbols" to those digits that fall in ambiguous zones see the example described below. The output sequence from AZD 10 is then processed by passing it to concatenated decoders 14 an 16 which are connected in a loop. Between decoders 14 and 16 is an inverse permutation module 18 in the forward path and a permutation module 20 in the feedback path.

Permutation module 20 is identical to the permutation module used at the transmitter. Thus, in a first iteration after receiving a data stream, the output sequence from AZD 14 is processed by inner decoder 14, inverse permutation module 18 which reverses the permutation inserted at the transmitter and outer decoder The decoded and error-corrected data stream is then processed by duobinary signaling and decoding strategies module 20 which re-permutes the data stream to the form it had upon arrival at receiver input The second iteration applies the modified AZD output to the above-mentioned receiver blocks, in the same order as in the first iteration.

The cyclical decoding procedure repeats. At this point there are two options if the decoded sequence contains some unresolved erasures or detectable errors: This cyclic decoding procedure is hereafter referred to as iterative decoding. However, even if the channel errors are random, i. It is easiest to explain the invention by way of an example. A concatenated system of the type shown in FIG.

As the outer code, a 7, 4 Hamming code is used and the inner code is duobinary signaling with a precoder. An n, k Hamming code is a single error correcting code, which can correct any single error that may exist in a block of bits, consisting of message bits, and parity-check bits see e. Duobinary signaling is often achieved by sending a binary pulse sequence at a faster rate than is possible in ordinary transmission see e. When the channel input is binary 0 or 1then the channel output, sampled at an appropriate rate, should be equivalent to duobinary signaling and decoding strategies sum of duobinary signaling and decoding strategies present and preceding digits.

Thus, the output sequence is a three-level sequence, i. This three-level sequence cannot take on these values independently, because of the nature of its construction.

For example, the output sequence should not have direct transitions from 0 to 2 or vice versa. The resultant ternary sequence, called duobinary, is a sequence with some correlation property due to the channel bandwidth constraint. The precoder introduces a simple transformation prior to the transmission by duobinary signaling. Its purpose is to prevent a possible error propagation in the decoded output. The precoder maps the input binary sequence into another binary sequence, based on the following rule: Precoding of a duobinary signaling and decoding strategies sequence is similar to differential encoding usually used in DPSK differential phase shift keying.

Precoding for multi-level sequences is described in D. Duobinary signaling illustrated in this example is a simplest case of partial-response channel coding referred to in the Background of the Art. Consider a simple packet transmission system in which there are 28 information bits in a packet, an example of which is given by the stream:. Its parity-check duobinary signaling and decoding strategies generator matrices are given in systematic form by:. Then the Hamming encoder output is the following 49 bits commas are placed between code words for clarity:.

Then the permutation output is obtained by reading out the above array, column by column as follows:.