1.3.3 Soft output Viterbi algorithm

A decoder with a soft decision makes decision not only about binary value “1” or “0”, but also trust value related to this bit. If demodulator decides, then trust value is 1, the degree of trust to it is high. If it is less certain, then it has less trust value. A decoder with a soft input can produce data with a hard decision or data with a soft decision. For example, Viterbi decoder accepts soft information from a demodulator and produces data with a hard decision. A decoder can use soft information for determination of hard equality of the bit to “0” or “1”, and on the output we will get such hard decision.

The primary difference between hard-decision and soft-decision Viterbi decoding, is that the soft-decision algorithm cannot use a Hamming distance metric because of its limited resolution. A distance metric with the needed resolution is Euclidean distance, and to facilitate its use, the binary numbers of “1” and “0” are transformed to the octal numbers “7” and “0”, respectively. Soft-decision Viterbi decoding, for the most part, proceeds in the same way as hard-decision. Consider how soft-decision decoding is performed with the use of Euclidean distances, i.e. BM_t =  . Suppose that a pair of soft-decision code symbols with values (5, 4) arrives at a decoder during the first transition interval. The metric BM (0, 0) = and the metric BM (7, 7) = . The rest of the task, pruning the trellis in search of a common stem, proceeds in the same way as hard-decision decoding.

1.4 Concatenated codes

1.4.1 Serial concatenated encoding fundamentals

The important stage in development of encoding and decoding devices for reliable information protection from noise is research and development of concatenated codes. Using together two or more correction codes is the concatenated encoding. The example of such encoding with using of two codes with the serial including of coders and decoders is shown in a fig. 1.11.

Figure 1.11 – Block diagram of a concatenated code system

Block (n, k) codes are used more frequent as outer coders, and convolutional – as inner codes. The concatenated methods of encoding possess substantial advantages in comparison to many known methods of encoding in the case when in a telecommunication channel there are impulse noise, resulting in bursts of errors. A fight against burst of errors is carried out with transposition of output bits of outer coder with reverse operation at the input of outer decoder. Devices, executing these operations, are called interleaver, i.e. resorting of code symbols, and deinterleaver, i.e. restoration the order of their following.

In the real communication networks for data transmission as outer code is used Reed-Solomon (RS) code, which have maximal correcting ability with d_min = n – r + 1. For example, the RS (255, 223) code has minimum code distance d_min = 255 – 223 + 1 = 33, i.e. in code combination ща 255 bits this code is able to correct t_c (33 – 1)/2 = 16 bits, received with errors. At the choice of the inner code, a preference to convolution codes with decoding using Viterbi algorithm is given.

If information bits are coded by an outer code with d_min1, and inner – with d_min2, minimum code distance of the formed concatenated code is determined as:

d_min1,2 = d_min1 × d_min2 (1.30)

That’s why concatenated codes have high correction ability.