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This book presents digital encoders for data communications. After an introduction on data communications and different sequences, the authors present the frey.

**Table of contents**

- Optical Encoders and Decoders for OCDMA | SpringerLink
- Product details
- Capacity estimates for optical transmission based on the nonlinear Fourier transform
- Rotary encoder
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Generalized Viterbi decoding techniques suffer from the same disadvantages. Among alternative channel codecs that could be considered for this are short block codes. Such channel codecs also utilize maximum likelihood techniques using soft decision like the convolutional channel decoder. In addition, such channel codecs offer the following additional advantages:.

The codeword generator matrix can be optimized to reduce the average number of bits in error for a given codeword error rate. Generalized decoding can be used to further reduce error rate and bit error rate with little extra cost. The error correcting power of such block codes is a function of their minimum Hamming distance.

Typically, longer block codes possess a larger minimum Hamming distance, but the cost of decoding such block codes also increases with its length, as does the complexity of decoding such block codes. Nordstrom and J. Robinson, Information and Control, November-December , pp. The NBC code has been known over two decades.

This code is optimal in terms of having the largest number of codewords possible for the given Hamming distance. Despite its optimality, this code has not received much attention in engineering circles because it is nonlinear. As a result, all linear techniques can now be applied to the NBC. It is an object of the present invention to provide improvements in error control coding schemes for low bit rate speech coders in order to improve their performance in the presence of transmission errors typical of the digital cellular channel.

According to the invention, an error control coding scheme exploits the newly discovered linear characteristics of nonlinear block codes NBCs for purposes of tailoring the NBC to the fading channel in order to provide superior error protection to the compressed half rate speech data. In the description of the preferred embodiment of the invention, the half rate speech codec is assumed to have a frame size of 40 ms.

The speech encoder puts out a fixed number of bits per 40 ms. These bits are divided into three distinct classes, referred to as Class 1, Class 2 and Class 3 bits. A subset of the Class 1 bits are further protected by a CRC for error detection purposes. The Class 2 bits are encoded by a punctured version of the Nordstrom Robinson code.

The Class 3 bits are left unprotected. At the receiver the coded Class 1 plus CRC bits, coded Class 2 bits, and Class 3 bits are extracted after de-interleaving. Maximum likelihood techniques using soft decision are employed to decode the Class 1 plus CRC bits as well as the Class 2 bits. The CRC is also used to further reduce the bit error rate BER of the subset of Class 1 bits over which it was applied by using generalized decoding techniques.

In addition to the CRC based bad frame indication flag, raw channel bit error rate estimates for each codeword are also sent to the speech decoder as well. The foregoing and other objects, aspects and advantages will be better understood from the following detailed description of a preferred embodiment of the invention with reference to the drawings, in which:. By way of introduction, the full rate TDMA digital cellular system will be first described, followed by a description of the invention as applied to a specific half rate codec. Referring now to the drawings, and more particularly to FIG.

## Optical Encoders and Decoders for OCDMA | SpringerLink

The encoded speech is further encoded by convolutional channel encoder 13, and the resulting encoded bit stream is supplied to a DQPSK modulator In FIG. At this point the reverse of the encoding process in the transmitter takes place. Specifically, decoding is performed by channel convolutional decoder 26 and the VSELP speech decoder The convolutional channel encoder 13 shown in FIG.

The Class 1 bits are extracted at Among the Class 1 bits, there are a few bits that are perceptually the most significant PMSB , and these are extracted at 32 and provided with error detection capability using a 7-bit cyclic redundancy check CRC over the twelve most perceptually significant bits by CRC calculation The remaining Class 1 bits and additional flush bits generated at 34 are reordered at 35 and supplied to convolutional encoder The Class 2 bits are extracted at 37 and are supplied unprotected to a two slot interleaver 38 where they are interleaved with the output of convolutional encoder The channel decoder 26 of FIG.

The coded bits are extracted at 41 and supplied to a Viterbi convolutional decoder From the decoded bits, the CRC bits are extracted at 43 and the Class 1 bits are extracted at If the two do not compare, a bad frame flag is set. The Class 1 bits extracted at 44 and the Class 2 bits extracted at 48 are combined in multiplexer 49 to generate the VSELP compressed speech bits. We now turn our attention to the half-rate channel encoder which is under consideration by the TIA standard body.

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Such a half rate channel requires the use of low rate speech and channel codecs that together only utilize 6. The compressed speech bits of any low rate codec need to be split into many classes that require different degrees of protection. This is done off line and is specific to the low rate codec in question.

This process of categorization of these compressed speech bits into various classes is based on a combination of A-factor analysis and informal listening tests. The effects of transmission errors on each bit of the speech encoder output can be studied by studying the drop in well defined "performance measure" when that bit is repeatedly forced to be in error. This drop in "performance" is expressed relative to the clean channel "performance" in dB and is referred to as the associated A-factor for that particular bit.

The more sensitive bits have very large drop in "performance" and hence have large A-factors.

## Capacity estimates for optical transmission based on the nonlinear Fourier transform

Unfortunately, for low bit rate voice coders, well defined "performance measures" are subjective measures that are too expensive to measure. A compromise is to use an objective performance measure and combine it with selective informal listening tests. One such measure is the segmental signal to noise ratio SNR. With this measure, one can prioritize bits of the same parameter accurately.

But comparison across parameters using this objective performance measure would be difficult. Thus, one can use these segmental SNR based A-factors for prioritizing all bits belonging to a certain parameter type, such as short term predictors, for the entire frame but comparisons between bits of different parameter types, such as between short term predictor bits and gain bits, would be misleading. We therefore use informal listening of a large speech utterance to judge an A-factor threshold for each parameter type. Those above this threshold can be grouped into one class, while those below are grouped into a second class.

Further categorization can be accomplished in a similar fashion to yield a multiplicity of classes. A flowchart describing this process of splitting compressed speech bits into multiple classes is illustrated in FIG.

The compressed speech bits are split into different parameter categories in the first step Each parameter category is prioritized using A-factors in processes 51 1 , 51 2 ,. A-factor thresholds are established in step 52 for each type that produces equivalent distortion using informal listening tests.

## Rotary encoder

These A-factors are normalized in step 53 using equivalent thresholds, and then in step 54, compressed speech bits are prioritized using normalized A-factors. The prioritized compressed speech bits are split into multiple classes in step 55 to generate as the output prioritized compressed speech bits grouped in multiple classes.

The half rate speech coder used in the preferred embodiment of the invention has a frame size of 40 ms and a bit rate of 4. Every frame, the compressed speech data consists of bits.

These bits are not all of equal importance from a perceptual stand point and, therefore, require different levels of protection. The subject invention outputs bits which are divided into three classes using the process defined above:. The 40 Class 1 bits are the most important compressed speech bits in the sense that they are most vulnerable to transmission impairment. Among these 40 bits are 24 bits denoted as the perceptually most significant bits PSMBs that require error detection as well.

These PSMBs are isolated using the procedure to prioritize bits within each class outlined above. The 8 CRC bits and the 40 Class 1 bits are provided the maximum error protection. The 48 Class 2 bits are less important than the Class 1 bits but still require error protection. Finally, the 80 Class 3 bits are left unprotected. Table 1 lists the allocation of bits prior to and after coding. Here, 16 refers to the codeword length, 8 refers to the message word length, and 6 denotes the minimum Hamming distance of the code.

The 40 Class 1 and 8 CRC bits are packed as 6 message words of length 8 each, and each message word is then coded independently to produce six codewords, each of length The distribution of PMSBs among these four message words is done in a way that the average importance per codeword using the normalized measure to prioritize all bits in each class is approximately the same.

The remaining 16 Class 1 bits are grouped into two message words in the same manner. The encoding process first transforms each 8-bit long message vector into four quaternary symbols by applying the mapping of Table 2 to every pair of adjacent bits in the input message vector. Multiplication and addition with these symbols are carried out using modulo 4 arithmetic. The NBC code is a linear code when interpreted as a Quaternary code. One can then define the encoding process in terms of a generator matrix defined as.

As noted before, all operations are carried out using modulo 4 arithmetic. The codeword quaternary symbols are transformed back to bit pairs using Table 2. The selection of the generator matrix is done so that the average number of bits in error for an erroneous codeword is kept to a minimum for the worst channel condition of interest, i. The generator matrix describe here does that and produces on the average three bits in error for every erroneous codeword for the worst channel condition of interest. The punctured code converts a message word of length 8 to a codeword of length The 48 Class 2 bits are grouped into six message words in the same manner as Class 1 bits.

The 8-bit long message words are transformed into four quaternary symbol vectors using the mapping in Table 2.

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The encoding process uses the same generator matrix defined as before but with the last column removed; i. The above generator matrix also produces the minimum average number of bits in error for an erroneous codeword for the worst channel condition of interest.

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This minimum average number is 1. The seven symbol long message vector is obtained by multiplying the message vector by the modified generator matrix G'. The seven symbol long codeword is then converted to a bit codeword using the mapping in Table 2. The Class 1 codewords occupy columns 1, 3, 5, 7, 9, and 11, respectively. The Class 2 codewords occupy columns 2, 4, 6, 8, 10, and 12, respectively. The Class 3 bits occupy the remaining two unfilled positions in each of the Class 2 codeword columns as well as columns 13, 14, 15, 16 and the first four rows of column Interleaving over two slots is accomplished by transmitting the even rows 2, 4, 6, 8, 10, 12, 14, 16 of the present interleaving array and the odd rows 1, 3, 5, 7, 9, 11, 13, 15 of the previous interleaving array.

Based on our investigations, this is accomplished by transmission of quaternary symbols of each Class 1 codeword c 0 , c 1 , c 2 , c 3 in one time slot and the remaining c 4 , c 5 , c 6 , c 7 in the other time slot.

Thus the c 0 bits occupy rows 1 and 3, the c 1 bits occupy rows 5 and 7, the c 2 bits occupy rows 9 and 11, the c 3 bits occupy rows 13 and 15, the c 4 bits occupy rows 2 and 4, the c 5 bits occupy rows 6 and 8, the c 6 bits occupy rows 10 and 12, and the c 7 bits occupy rows 14 and Similarly, for the Class 2 codewords, the codeword error rate is minimized for the worst channel condition of interest by transmitting quaternary symbols of each Class 2 codeword c 0 , c 1 , c 2 in one time slot and the remaining c 3 , c 4 , c 5 , c 6 in the other time slot.

Thus, the c 0 bits occupy rows 1 and 3, the c 1 bits occupy rows 5 and 7, the c 2 bits occupy rows 9 and 11, the c 3 bits occupy rows 2 and 4, the c 4 bits occupy rows 6 and 8, the c 5 bits occupy rows 10 and 12, and the c 6 bits occupy rows 14 and The Class 3 bits typically consist of codebook indices and least significant bits of other parameter types.

The bits corresponding to these codebook indices are distributed in such a way that a given codebook index is completely transmitted in one time slot, but the codebook index corresponding to the adjacent subframe or subblock of speech is transmitted in the other time slot. The compressed speech bits are extracted into Class 1, Class 2 and Class 3 bits.

The channel decoder shown in FIG. These soft decision values typically are related to the quantized value of the square of the differentially demodulated fade amplitude. In the TIA half rate codec test, fourteen bits of precision were used to represent the magnitude of the soft decision value, but it must be understood that the channel decoder described below could be used with any soft decision or hard decision representation.