In this paper time-invariant spatially coupled low-density parity-check convolutional codes (SC-LDPC-CCs) are considered, and the connections existing between their low-weight codewords and cycles in their Tanner graphs are studied. Using the polynomial representation of these codes, we show that parity-check matrices having columns with weight ≥ 2 can be analyzed considering a certain number of parity-check sub-matrices having regular columns with weight 2. These sub-matrices are associated to cycles in the code Tanner graph and define as many codes we denote as component codes. Based on this observation, we find that codewords of the main code can be expressed as a combination of codewords of the component codes. The design of codes free of codewords up to a certain weight is also addressed. We show that low-weight codewords in the main code can be avoided by removing some types of cycles in its Tanner graph. Our design approach is applied to some well known ensembles of SC-LDPC-CCs to prove its effectiveness.
Connections between low-weight codewords and cycles in spatially coupled LDPC convolutional codes / Battaglioni, Massimo; Baldi, Marco; Cancellieri, Giovanni. - In: IEEE TRANSACTIONS ON COMMUNICATIONS. - ISSN 0090-6778. - ELETTRONICO. - 66:8(2018), pp. 3268-3280. [10.1109/TCOMM.2018.2820702]
Connections between low-weight codewords and cycles in spatially coupled LDPC convolutional codes
Battaglioni, Massimo
;Baldi, Marco
;Cancellieri, Giovanni
2018-01-01
Abstract
In this paper time-invariant spatially coupled low-density parity-check convolutional codes (SC-LDPC-CCs) are considered, and the connections existing between their low-weight codewords and cycles in their Tanner graphs are studied. Using the polynomial representation of these codes, we show that parity-check matrices having columns with weight ≥ 2 can be analyzed considering a certain number of parity-check sub-matrices having regular columns with weight 2. These sub-matrices are associated to cycles in the code Tanner graph and define as many codes we denote as component codes. Based on this observation, we find that codewords of the main code can be expressed as a combination of codewords of the component codes. The design of codes free of codewords up to a certain weight is also addressed. We show that low-weight codewords in the main code can be avoided by removing some types of cycles in its Tanner graph. Our design approach is applied to some well known ensembles of SC-LDPC-CCs to prove its effectiveness.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.