Systematic punctured convolutional encoding method

Claim 7

The method of claim 3 , wherein a convolutional code generated according to the predetermined puncturing matrix is non-catastrophic.

Claim 8

The method of claim 4 , wherein the generated convolutional code according to the predetermined puncturing matrix has a largest value of minimum free distance (d-free) and a minimum information code error after decoding.

Claim 9

The method of claim 5 , wherein the puncturing matrix is selected from given matrices according to a corresponding code rate, and the convolutional code is punctured according to a weight spectrum corresponding to the selected puncturing matrix.

Claim 10

The method of claim 6 , wherein the given puncturing matrix and corresponding weight spectrum are selected from one of a following puncturing matrices: [ 1 0 1 1 ]  where a constraint length (k) is 3, a first generating polynomial (G 1 ) is 101, a second generating polynomial (G 2 ) is 111, and d-free is 5; [ 1 1 0 1 ]  where a constraint length (k) is 4, a first generating polynomial (G 1 ) is 1101, a second generating polynomial (G 2 ) is 1111, and d-free is 6; [ 1 1 0 1 ]  where a constraint length (k) is 5, a first generating polynomial (G 1 ) is 10011, a second generating polynomial (G 2 ) is 11101, and d-free is 7; [ 1 0 1 1 ]  where a constraint length (k) is 6, a first generating polynomial (G 1 ) is 101011, a second generating polynomial (G 2 ) is 111101, and d-free is 8; and [ 1 1 1 0 ]  where a constraint length (k) is 7, a first generating polynomial (G 1 ) is 1011011, a second generating polynomial (G 2 ) is 1111001, and d-free is 10 input information constraint first generating second generating puncturing length (k) polynomial (G 1 ) polynomial (G 2 ) d-free matrix 3 101 111 5 [ 1 0 1 1 ]  4 1101 1111 6 [ 1 1 0 1 ]  5 10011 11101 7 [ 1 1 0 1 ]  6 101011 111101 8 [ 1 0 1 1 ]  7 1011011 1111001 10 [ 1 1 0 1 ] 

Claim 11

A rate-1/2 convolutional encoding system for a digital communication system, comprising: means for obtaining first and second block code words by multiplying an input information word by first and second convolutional code generating polynomials, respectively; and means for generating a convolutional code word by interleaving the first and second code words with an interleaving depth (λ) of n; wherein the input information word exists in a systematic form in the second block code word C 2 (x) expressed as C 2 ( x )= r 2 ( x )+ x m I ( x ) = I n ( x ) g 2 ( x ) = C s ( x ) where I(x) is the input word, r 2 (x) is a remainder after dividing x m I(x) by g 2 (x), m is the number of shifters, I n (x) is an information word polynomial, g 2 (x) is a code word generating polynomial for the second block code word, and C s (x) is a systematic code word.

Claim 12

A rate-1/2 convolutional encoding system for a digital communication system, comprising: means for obtaining first and second block code words by multiplying an input information word by first and second convolutional code generating polynomials, respectively; and means for generating a convolutional code word by interleaving the first and second code words with an interleaving depth (λ) of n; wherein the input information word exists in a systematic form in the second block code word C 2 (x) expressed as C 2 ( x )= r 2 ( x )+ x m I ( x ) = I n ( x ) g 2 ( x ) = C s ( x ) where I(x) is the input word, r 2 (x) is a remainder after dividing x m I(x) by g 2 (x), m is the number of shifters, I n (x) is an information word polynomial, g 2 (x) is a code word generating polynomial for the second block code word, and C s (x) is a systematic code word.

Claim 13

A rate-1/n convolutional encoding system for a digital communication system having a non-systematic convolutional encoder, comprising: (a) means for obtaining first to n-th block code words by multiplying first to n convolutional code generating polynomials by an information polynomial upon input of an information word; (b) means for converting one of the first to n-th block code words to a systematic code word and obtaining a new information word, I n (x), corresponding to the systematic code word; and (c) means for generating a convolutional code by encoding the new information code in the non-systematic convolutional encoder; wherein one of the first to n-th block code words is selected and converted to the systematic code word using equation (1), and the new information word corresponding to the systematic code word is obtained using equation (2), in the converting means (b): C s ( x )= r q ( x )+x m I ( x )  (1) I n ( x )= C s ( x )/ g s ( x )  (2) where C s (x) is a code word of the sth block (s being one of 1, . . . , n), I(x) is an input information word, r q (x) is a remainder after dividing x m I(x) by g s (x), g s (x) being an sth code word generating polynomial, and m is the number of shifters.

Claim 14

A rate-1/n convolutional encoding system for a digital communication system having a non-systematic convolutional encoder, comprising: (a) means for obtaining first to n-th block code words by multiplying first to n convolutional code generating polynomials by an information polynomial upon input of an information word; (b) means for converting one of the first to n-th block code words to a systematic code word and obtaining a new information word, I n (x), corresponding to the systematic code word; and (c) means for generating a convolutional code by encoding the new information code in the non-systematic convolutional encoder; wherein one of the first to n-th block code words is selected and converted to the systematic code word using equation (1), and the new information word corresponding to the systematic code word is obtained using equation (2), in the converting means (b): C s ( x )= r q ( x )+x m I ( x )  (1) I n ( x )= C s ( x )/ g s ( x )  (2) where C s (x) is a code word of the sth block (s being one of 1, . . . , n), I(x) is an input information word, r q (x) is a remainder after dividing x m I(x) by g s (x), g s (x) being an sth code word generating polynomial, and m is the number of shifters.

Claim 15

A rate-k/n convolutional encoding system for a digital communication system having a non-systematic convolutional encoder, comprising: means for obtaining first to n-th block code words by multiplying first to n convolutional code generating polynomials by an information polynomial upon input of an information word; means for converting one of the first to n-th block code words to a systematic code word and obtaining a new information word corresponding to the systematic code word; means for generating a convolutional code by encoding the new information code in the non-systematic convolutional encoder; and means for systematically puncturing the convolutional code using a predetermined puncturing matrix wherein the predetermined puncturing matrix satisfies the condition that all elements of one row vector are 1s.

Claim 16

A rate-k/n convolutional encoding system for a digital communication system having a non-systematic convolutional encoder, comprising: means for obtaining first to n-th block code words by multiplying first to n convolutional code generating polynomials by an information polynomial upon input of an information word; means for converting one of the first to n-th block code words to a systematic code word and obtaining a new information word corresponding to the systematic code word; means for generating a convolutional code by encoding the new information code in the non-systematic convolutional encoder; and means for systematically puncturing the convolutional code using a predetermined puncturing matrix wherein the predetermined puncturing matrix satisfies the condition that all elements of one row vector are 1s.

Claim 17

A system as claimed in claim 10 , wherein the predetermined puncturing matrix further satisfies the following conditions: a convolutional code generated is non-catastrophic; and the generated convolutional code has the largest value of minimum free distance (d-free) and a minimum information code error after decoding.

Claim 18

A system as claimed in claim 11 , wherein the puncturing matrix is selected from given matrices according to a corresponding code rate, and the convolutional code is punctured according to a weight spectrum corresponding to the selected puncturing matrix.

Claim 21

A rate-k/n convolutional encoding system for a digital communication system having a non-systematic convolutional encoder, comprising: (a) means for obtaining first to n-th block code words by multiplying first to n convolutional code generating polynomials by an information polynomial upon input of an information word; (b) means for converting one of the first to n-th block code words to a systematic code word and obtaining a new information word, I n (x), corresponding to the systematic code word; and (c) means for generating a convolutional code by encoding the new information code in the non-systematic convolutional encoder; wherein one of the first to n-th block code words is selected and converted to the systematic code word using equation (1), and the new information word corresponding to the systematic code word is obtained using equation (2), in the converting means (b): C s ( x )= r q ( x )+x m I ( x )  (1) I n ( x )= C s ( x )/ g s ( x )  (2) where C s (x) is a code word of the sth block (s being one of 1, . . . , n), I(x) is an input information word, r q (x) is a remainder after dividing x m I(x) by g s (x), g s (x) being an sth code word generating polynomial, and m is the number of shifters.

Claim 22

A rate-k/n convolutional encoding system for a digital communication system having a non-systematic convolutional encoder, comprising: (a) means for obtaining first to n-th block code words by multiplying first to n convolutional code generating polynomials by an information polynomial upon input of an information word; (b) means for converting one of the first to n-th block code words to a systematic code word and obtaining a new information word, I n (x), corresponding to the systematic code word; and (c) means for generating a convolutional code by encoding the new information code in the non-systematic convolutional encoder; wherein one of the first to n-th block code words is selected and converted to the systematic code word using equation (1), and the new information word corresponding to the systematic code word is obtained using equation (2), in the converting means (b): C s ( x )= r q ( x )+x m I ( x )  (1) I n ( x )= C s ( x )/ g s ( x )  (2) where C s (x) is a code word of the sth block (s being one of 1, . . . , n), I(x) is an input information word, r q (x) is a remainder after dividing x m I(x) by g s (x), g s (x) being an sth code word generating polynomial, and m is the number of shifters.