US 7,010,052 B2 · Apparatus and method of CTCM encoding and decoding for a digital communication system

Abstract

A method of building systematically a multi-dimensional (n, D, L) circular trellis coded modulation (CTCM) encoder with properties of optimal energy efficiency, strong tail biting and maximum minimum distance (dmin) of trellis paths is disclosed. In addition, a communication system for use in a power limited channel application is disclosed comprising a circular trellis coded modulation (CTCM) encoder with permuted state structure for encoding based on a circular trellis path associated with a sequence of digital information bits and a set of simplexes identified for the path from a multi-dimensional signal constellation; a transmitter coupled to said CTCM encoder for transmitting said sequence of channel symbols over said channel; a receiver for receiving a transmission from said transmitter including said sequence of channel symbols and any noise induced therein; and a CTCM decoder coupled to said receiver for decoding the received transmission without knowledge of the starting state of the circular trellis path of the CTCM encoder to recover the sequence of information bits. Apparatus and methods of encoding and decoding are also disclosed utilizing a combination of circular trellis-coded modulation with permuted state structure and simplex signal constellation techniques for use in the digital communication system.

Claims38

Dependent claims

Method of building systematically a multi-dimensional (n, D, L) circular trellis coded modulation (CTCM) encoder with properties of optimal energy efficiency, strong tail biting and maximum minimum distance (dmin) of trellis paths, where n is the size of the symbol alphabet, D is the depth of the trellis, and L is the length of the information symbol sequence, said method comprising the steps of:

a) identifying simplex-transition sets of originating and next states for each stage i of a circular trellis;
wherein a simplex is a set of M signals in an N-dimensional space with N≧M−1, satisfying that for all I, j∈{1, 2, . . . , M}, the cross-correlation between signals si and sj is
s
i
·
s
j
=
{
1
,
i
=
j
-
1
⁢
/
⁢
(
M
-
1
)
,
i
≠
j
⁢
for normalized signal energy. The M signals have equal distance from each other;
b) determining butterfly structures (butterflies) associated with the identified simplex-transition sets wherein the originating and next states of said simplex-transition sets are arranged in an internal order within said butterfly structures;
c) aligning said butterfly structures into a multi-dimensional state transition matrix (STM) in a predetermined order;
d) constructing a simplex of channel symbols from a multi-dimensional signal constellation space for each of said identified simplex-transition sets;
e) aligning each simplex of channel symbols into a multi-dimensional initial input simplex (IIS) matrix in an order in relation to said predetermined order of butterfly structures in said STM;
and
f) assigning channel symbols to state transitions of a trellis path by mapping between said simplex-transition sets of the STM and said simplexes of symbols of said IIS matrix.

33 more elements

A communication system for use in a power limited channel application, said system comprising:

a circular trellis coded modulation (CTCM) encoder for converting a sequence of digital information bits of a predetermined length into a corresponding sequence of channel symbols based on a circular trellis path associated with the sequence of digital information bits and a set of simplexes identified for said path from a multi-dimensional signal constellation, said CTCM encoder including means for determining an initial starting state of the circular trellis path which renders said path circular without the addition of redundant bits to the sequence of digital information bits;
first storing means for storing a representation of a multi-dimensional matrix of simplexes of channel symbols, said simplexes being arranged in said matrix in an ordered relationship to identified state transitions of the circular trellis path;
and means for converting the sequence of digital information bits into the corresponding sequence of channel symbols of the circular trellis path by operating on the sequence of digital information bits in accordance with said stored matrix representation;
wherein a simplex is a set of M signals in an N-dimensional space with N≧M−1, satisfying that for all I, j∈{1, 2, . . . , M}, the cross-correlation between signals si and sj is
s
i
·
s
j
=
{
1
,
i
=
j
-
1
⁢
/
⁢
(
M
-
1
)
,
i
≠
j
⁢
for normalized signal energy. The M signals have equal distance from each other,
a transmitter coupled to said CTCM encoder for transmitting said sequence of channel symbols over said channel;
a receiver for receiving a transmission from said transmitter including said sequence of channel symbols and any noise induced therein;
a CTCM decoder coupled to said receiver for decoding received transmission without knowledge of the starting state of the circular trellis path of the CTCM encoder to recover the sequence of information bits.

32 more elements

A circular trellis coded modulation (CTCM) encoder for converting a sequence of digital information bits of a predetermined length into a corresponding sequence of channel symbols based on a circular trellis path associated with the sequence of digital information bits and a set of simplexes identified for said path from a multi-dimensional signal constellation, said CTCM encoder comprising:

means for determining an initial starting state of the circular trellis path which renders said path circular without the addition of redundant bits to the sequence of digital information bits;
first storing means for storing a representation of a multi-dimensional matrix of simplexes of channel symbols, said simplexes being arranged in said matrix in an ordered relationship to identified state transitions of the circular trellis path;
and
wherein a simplex is a set of M signals in an N-dimensional space with N≧M−1, satisfying that for all I, j∈{1, 2, . . . , M}, the cross-correlation between signals si and sj is
s
i
·
s
j
=
{
1
,
i
=
j
-
1
⁢
/
⁢
(
M
-
1
)
,
i
≠
j
⁢
for normalized signal energy. The M signals have equal distance from each other,
means for converting the sequence of digital information bits into the corresponding sequence of channel symbols of the circular trellis path by operating on the sequence of digital information bits in accordance with said stored matrix representation.

30 more elements

A method of circular trellis coded modulation (CTCM) encoding comprising the step of:

converting a sequence of digital information bits of a predetermined length into a corresponding sequence of channel symbols based on a circular trellis path associated with the sequence of digital information bits and a set of simplexes identified for said path from a multi-dimensional signal constellation, said step of converting including:
determining an initial starting state of the circular trellis path which renders said path circular without the addition of redundant bits to the sequence of digital information bits;
storing a representation of a multi-dimensional matrix of simplexes of channel symbols arranged in an ordered relationship to identified state transitions of the circular trellis path;
and converting the sequence of digital information bits into the corresponding sequence of channel symbols of the circular trellis path by operating on the sequence of digital
wherein a simplex is a set of M signals in an N-dimensional space with N≧M−1, satisfying that for all I, j∈{1, 2, . . . , M}, the cross-correlation between signals Si and sj is
s
i
·
s
j
=
{
1
,
i
=
j
-
1
⁢
/
⁢
(
M
-
1
)
,
i
≠
j
⁢
for normalized signal energy. The M signals have equal distance from each other.