1.4.4 Perforation of output sequences

The two components of turbo code encoder can be replaced by the code and change their relative information transfer rates. Different code rates R₂, such as 1/2, 2/3, 3/4, etc. can be obtained from the code with a relative rate R₁ = 1/3 through the perforations. For others relative information transfer rates of the encoder can contain more than two encode components.

Perforation is deletion of some elements from the output of the encoder to increase of the code rate.

For the codes with code rate R₁ = 1/n we can obtain the rate R₂ = k/n_p, where n_p = k*n – l, using the matrix of perforations. The matrix of perforations is a matrix of size k*n containing l zeros. Zero indicates that the bit in the output sequence is not transmitted. The informative sequence a should be not perforated, i.e., in the first row of perforation matrix zeros can not be.

For example, R₁ = 1/3 and it is required R₂ = 2/5. So, n = 3, k = 2, n_p = 5. Let’s calculate l = 3*2 – 5 = 1. So, matrix of perforations can be:

		k columns
n rows	a	1	1
	b	1	0
		1	1

The realization of perforation for the code combination of turbo code 010.110.111.011 will be 010.1X0.111.0X1. Note that for each two input bits the amount of output bits is 5, and the rate of the code is 2/5.

With the perforator, deleting of different number of the bits we can control the code rate. That is, we can construct a coder, adapting to the communication channel. For very noisy channels perforator deletes fewer bits, the code rate decreases and the noise immunity of encoder growth. If the communication channel of good quality, we can perforate a large number of bits, causing the information transfer rate growth.

1.5 Frames structure on hdlc procedure

1.5.1 Types of frames according to hdlc procedure

The HDLC (High Level Data Link Control) protocol is defined by ISO for use on both point-to-point and multipoint data links. It supports full duplex transparent-mode operation and is now extensively used in both multipoint and computer networks.

In HDLC protocol frames can be of three types: I, S, U.

I-frame is called information frame,

S-frame –supervisor frame,

U-frame –unnumbered frame.

The I-frame is used only for data (information) transmission from users or higher levels.

The S-frame provides transfer of the special support information on a condition of transferred I-frames. They are used for transfer of receipts on confirmation or request, readiness or unavailability to reception of the next I-frame.

For struggle against "losses" and "inserts", which are characteristic for automatic repeat request systems in I-frames and S-frames, numbers of corresponding frames are transferred. Therefore I-frames and S-frames are "numbered".

The U-frame also is necessary for support information transfer. But this information serves basically as management of a data link (channel). With the help of U-frame takes place a link initialization, a connection establishment/disconnection, change of an operating mode and other service functions. In this frame numbers of information frames are not transferred, whence and the name – «unnumbered frame».

1.5.2 I-frame structure

Each frame consists of fields. The I-frame has 6 fields, and S - and U-frames have 5 fields. The I-frame structure is shown in fig. 1.17.

Opening flag	Address	Control	Information	Control sequence	Closing flag
8 bits	8 (16) bits	8 (16) bits	N bits	16 bits	8 bits

Figure 1.17 – I-frame structure

Let's consider frames fields construction.

Frame beginning and end fields. For the frame beginning and end detection the principle of the start-stop cyclic synchronisation is used. As a starting combination the sequence of a kind 01111110 is applied. The similar sequence is used for a detection of the frame end. This sequence is called as «opening flag» or «closing flag» accordingly.

Address field. In this field the address (number) of corresponding station in the binary form is transferred. Each station has the unique address. In a frame containing commands, the address of remote station is transferred, and in a frame-answer the local address is transferred.

Address field expansion on 8 bits (1 byte) is supposed. The index that the following byte of a frame is included into address area is presence of zero in the first bit of the previous byte of an address field, excepting byte of a kind 00000000. Thus, the younger bit of the usual (not expanded) address should be equal 1.

Control field. It contains identifiers of a frame type and operations of HDLC protocol. The basic (8-bit) format of the control field is resulted in fig. 1.18. The order of bits transfer in the channel begins with bits of younger categories.

Order of bits transfer of control field in the channel
8	7	6	5	4	3	2	1
	NR		P/F		NS		0
Identification of the frame type ↑.

Figure 1.18 – The basic format of the control field of I-frame

N_S – bits of a serial number of the given (sent) I-frame (modulo 8).

N_R – bits of a serial number of an expected (received) frame (modulo 8), i.e. correct reception of I-frames to number N_R ‑ 1 inclusive proves to be true.

P/F – bit of interrogation/termination of interrogation. In a command frame this bit is interpreted as bit of "interrogation" P (poll). If on a sent frame it is necessary to receive the answer it is exposed P = 1; if the answer is not necessary, P = 0. In an answer frame this bit is interpreted as bit of "the interrogation termination» F (finish). If the frame with P = 1 earlier has been correctly accepted, in reciprocal frame F = 1, otherwise F = 0.

Except the basic (8-bit) format of the control field there is also an expanded format (16 bits). The term "expanded" means expansion of a range of serial numbers of sent and received frames to 127. For operations with expansion by a serial number the sizes of fields N_S and N_R increase from 3 bits (modulo 8) to 7 bits (modulo 128). Thus, the size of the control field increases from one byte to two bytes. The expanded format of the control field is resulted in fig. 1.19.

Order of bits transfer of management field in the channel
16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1
			NR				P/F				NS				0

Figure 1.19 – The expanded format of the control field of I-frame

Check field. In the check field the control sequence (CS), received as a result of coding by a cyclic code with generator polynomial P(x) = x¹⁶ + x¹² + x⁵ + 1 is located. As k information categories which will be protected by a correcting code, categories of fields undertake: address, control and information. Thus, contents between opening and closing flags are a code combination of a cyclic code. For definition CS usual procedure of construction of the allowed cyclic code combination by formula (1.4) is used