# US 8,751,907 B2 · Joint encoding and decoding methods for improving the error rate performance

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- Number: US 8,751,907 B2
- Document ID: US8751907B2
- Status: Granted
- Kind: B2
- Application number: 13/822,631
- Filed: 2011-02-14
- Published: 2013-07-18
- Granted: 2014-06-10
- Earliest claimed: 2011-02-14
- Assignees: King Saud University
- Applicants: Youssouf Ould-Cheikh-Mouhamedou
- Inventors: Youssouf Ould-Cheikh-Mouhamedou
- Web page: https://patentgrep.com/patent/US8751907B2

## CPC

- H03M 13/05: using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits {(H03M13/2906 takes precedence)}
- H03M 13/1102: {Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes}
- H03M 13/2957: {Turbo codes and decoding}
- H03M 13/2963: {Turbo-block codes, i.e. turbo codes based on block codes, e.g. turbo decoding of product codes}
- H03M 13/3994: {using state pinning or decision forcing, i.e. the decoded sequence is forced through a particular trellis state or a particular set of trellis states or a particular decoded symbol}
- H03M 13/6362: {by puncturing}
- H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C)

## Abstract

Joint encoding and decoding methods for improving the error rate performance are described. In one aspect, the systems and methods determine values and positions of L desired symbols. In encoding unit receives data symbols for encoding. The encoding unit calculates, responsive to receiving the data symbols, values and positions of H help symbols. The encoding unit inserts the help symbols into the data symbols at respective help symbols positions, thereby generating new data symbols. Encoding unit encodes the new data symbols to produce a codeword C′ that contains the L desired symbols. The codeword C′ is communicated to a decoder that is instructed to explore some or all L desired symbols in C′.

## Claims

### Claim 1

A computer-implemented data encoding method comprising the steps of:
receiving data symbols U consisting of Z symbols (where, Z=K+T data symbols, K information symbols and T overhead symbols for error detection and/or trellis termination for convolutional and turbo codes);
determining size of the data symbols U;
communicating said size of the data symbols U as input to a tuner;
wherein said tuner performs the steps of:
(a) outputting a priori a size of L desired symbols to a decoder;
(b) outputting a priori values of the L desired symbols to the decoder;
(c) outputting a priori positions j1, j2, . . . jL of the L desired symbols to the decoder, the size, values and positions of the L desired symbols being alternatively determined by distance measurement methods and by error rate performance results;
communicating the data symbols U, and the size, values and positions of the L desired symbols to the input of an encoder insertion unit;
wherein said encoder insertion unit performs the steps of:
forming new data symbols U′ at its output, said U′ consisting of Z′=Z+H symbols, said H symbols being inserted into U′ at positions i1, i2, . . . iH, and wherein the size, values, and positions of the L desired symbols determining said H symbols and positions i1, i2, . . . iH;
encoding the new data symbols U′ to form a codeword C′; and
transmitting over a communications channel the codeword C′.

### Claim 2 (depends on 1)

The computer-implemented data encoding method, according to claim 1 further comprising the step of choosing the quantities of (a) (b) (c) of claim 1 such that Hamming distance spectra of a new code with the codeword C′ are better than Hamming distance spectra of a standard code C.

### Claim 3 (depends on 2)

The computer-implemented data encoding method, according to claim 2 further comprising the step of puncturing the codeword C′ by removing some symbols in C′ thereby achieving a target rate of C′.

### Claim 4 (depends on 2)

The computer-implemented data encoding method, according to claim 2 further comprising the step of data decoding, wherein the data decoding comprising the steps of:
receiving from an encoder as a priori information A, size, values and positions of L desired symbols determined at the encoder;
communicating the a priori information A to a first input of a decoder instruction unit;
communicating recorded values V, from a codeword C′ transmitted by the encoder, to a second input of the decoder instruction unit;
wherein the decoder instruction unit performs the steps of:
outputting an adjusted recorded values V′; and
outputting an adjusted a priori information A′; and
wherein a SISO (Soft Input Soft Output) decoder performs the steps of:
accepting V′ and A′ as inputs; and
outputting Decision information and Reliability information about the codeword C′.