ICTACT Journal on Communication Technology

H. Prashantha Kumar ¹, U. Sripati ¹, K. Rajesh Shetty ¹, B. Shankarananda ²

Affiliations
1 Department of Electronics and Communication Engineering, National Institute of Technology, Karnataka, IN
2 Vivekananda Institute of Technology, IN

Abstract

The boundaries between block and convolutional codes have become diffused after recent advances in the understanding of the trellis structure of block codes and the tail-biting structure of some convolutional codes. Therefore, decoding algorithms traditionally proposed for decoding convolutional codes have been applied for decoding certain classes of block codes. This paper presents the decoding of block codes using tree structure. Many good block codes are presently known. Several of them have been used in applications ranging from deep space communication to error control in storage systems. But the primary difficulty with applying Viterbi or BCJR algorithms to decode of block codes is that, even though they are optimum decoding methods, the promised bit error rates are not achieved in practice at data rates close to capacity. This is because the decoding effort is fixed and grows with block length, and thus only short block length codes can be used. Therefore, an important practical question is whether a suboptimal realizable soft decision decoding method can be found for block codes. A noteworthy result which provides a partial answer to this question is described in the following sections. This result of near optimum decoding will be used as motivation for the investigation of different soft decision decoding methods for linear block codes which can lead to the development of efficient decoding algorithms. The code tree can be treated as an expanded version of the trellis, where every path is totally distinct from every other path. We have derived the tree structure for (8, 4) and (16, 11) extended Hamming codes and have succeeded in implementing the soft decision stack algorithm to decode them. For the discrete memoryless channel, gains in excess of 1.5dB at a bit error rate of 10-5 with respect to conventional hard decision decoding are demonstrated for these codes.

Keywords

Extended Hamming Codes, Tree Diagram, Soft Decision Decoding, Discrete Memoryless Channel, Fano Metric.

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H. Prashantha Kumar ¹, U. Sripati ¹, K. Rajesh Shetty ¹

Affiliations
1 Department of Electronics and Communication Engineering, National Institute of Technology Karnataka, IN

Abstract

Low density parity check (LDPC) codes are capacity-approaching codes, which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical Shannon limit for a memory less channel. LDPC codes are finding increasing use in applications like LTE-Networks, digital television, high density data storage systems, deep space communication systems etc. Several algebraic and combinatorial methods are available for constructing LDPC codes. In this paper we discuss a novel low complexity algebraic method for constructing regular LDPC like codes derived from full rank codes. We demonstrate that by employing these codes over AWGN channels, coding gains in excess of 2dB over un-coded systems can be realized when soft iterative decoding using a parity check tree is employed.

Keywords

LDPC Codes, Full Rank Codes, Conjugacy Class, Transform Domain Components Parity Check Tree, Soft Iterative Decoding.

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