# M-PSK TCM Encoder

Convolutionally encode binary data and modulate using PSK method

## Library

TCM, in Digital Baseband sublibrary of Modulation

## Description

The M-PSK TCM Encoder block implements trellis-coded modulation (TCM) by convolutionally encoding the binary input signal and mapping the result to a PSK signal constellation.

The **M-ary number** parameter is the number of points in the signal
constellation, which also equals the number of possible output symbols from the
convolutional encoder. (That is, log_{2}(**M-ary
number**) is equal to n for a rate k/n convolutional code.)

### Input Signals and Output Signals

If the convolutional encoder described by the trellis structure represents a rate
*k*/*n* code, then the block input signal must
be a binary column vector with a length of *L***k*
for some positive integer *L*.

This block accepts a binary-valued input signal. The output signal is a complex
column vector of length *L*.

### Specifying the Encoder

To define the convolutional encoder, use the **Trellis
structure** parameter. This parameter is a MATLAB^{®} structure whose format is described in Trellis Description of a Convolutional Code. You can use this
parameter field in two ways:

If you want to specify the encoder using its constraint length, generator polynomials, and possibly feedback connection polynomials, then use a

`poly2trellis`

command within the**Trellis structure**field. For example, to use an encoder with a constraint length of 7, code generator polynomials of 171 and 133 (in octal numbers), and a feedback connection of 171 (in octal), set the**Trellis structure**parameter to`poly2trellis(7,[171 133],171)`

If you have a variable in the MATLAB workspace that contains the trellis structure, then enter its name as the

**Trellis structure**parameter. This way is faster because it causes Simulink^{®}software to spend less time updating the diagram at the beginning of each simulation, compared to the usage in the previous bulleted item.

The encoder registers begin in the all-zeros state. You can configure the encoder
so that it resets its registers to the all-zeros state during the course of the
simulation. To do this, set the `Operation mode`

to **Reset
on nonzero input via port**. The block then opens a second input port,
labeled `Rst`

. The signal at the `Rst`

port is a
scalar signal. When it is nonzero, the encoder resets before processing the data at
the first input port.

### Signal Constellations

The trellis-coded modulation technique partitions the constellation into subsets
called cosets, so as to maximize the minimum distance between pairs of points in
each coset. This block internally forms a valid partition based on the value you
choose for the **M-ary number** parameter.

The figure below shows the labeled set-partitioned signal constellation that the
block uses when **M-ary number** is 8. For constellations of other
sizes, see [1].

### Coding Gains

Coding gains of 3 to 6 decibels, relative to the uncoded case can be achieved in the presence of AWGN with multiphase trellis codes [3].

## Parameters

**Trellis structure**MATLAB structure that contains the trellis description of the convolutional encoder.

**Operation mode**In

`Continuous`

mode (default setting), the block retains the encoder states at the end of each frame, for use with the next frame.In

`Truncated (reset every frame)`

mode, the block treats each frame independently. I.e., the encoder states are reset to all-zeros state at the start of each frame.In

`Terminate trellis by appending bits`

mode, the block treats each frame independently. For each input frame, extra bits are used to set the encoder states to all-zeros state at the end of the frame. The output length is given by $$y=n\cdot (x+s)/k$$, where*x*is the number of input bits, and $$s=\text{constraintlength}-1$$ (or, in the case of multiple constraint lengths,*s*=`sum(ConstraintLength(i)-1)`

). The block supports this mode for column vector input signals.In

`Reset on nonzero input via port`

mode, the block has an additional input port, labeled`Rst`

. When the`Rst`

input is nonzero, the encoder resets to the all-zeros state.**M-ary number**The number of points in the signal constellation.

**Output data type**The output type of the block can be specified as a

`single`

or`double`

. By default, the block sets this to`double`

.

## Pair Block

## References

[1] Biglieri, E., D. Divsalar, P. J. McLane and M. K. Simon,
*Introduction to Trellis-Coded Modulation with
Applications*, New York, Macmillan, 1991.

[2] Proakis, John G., Digital Communications, Fourth edition, New York, McGraw-Hill, 2001

[3] Ungerboeck, G., “Channel Coding with
Multilevel/Phase Signals”, *IEEE Trans. on Information
Theory*, Vol IT28, Jan. 1982, pp. 55–67.

## Extended Capabilities

## Version History

**Introduced before R2006a**