Abstract
We compare LDPC block and LDPC convolutional codes with respect to their decoding performance under low decoding latencies. Protograph based regular LDPC codes are considered with rather small lifting factors. LDPC block and convolutional codes are decoded using belief propagation. For LDPC convolutional codes, a sliding window decoder with different window sizes is applied to continuously decode the input symbols. We show the required E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</inf> /N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> to achieve a bit error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−5</sup> for the LDPC block and LDPC convolutional codes for the decoding latency of up to approximately 550 information bits. It has been observed that LDPC convolutional codes perform better than the block codes from which they are derived even at low latency. We demonstrate the trade off between complexity and performance in terms of lifting factor and window size for a fixed value of latency. Furthermore, the two codes are also compared in terms of their complexity as a function of E <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</inf> /N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> . Convolutional codes with Viterbi decoding are also compared with the two above mentioned codes.
Highlights
Shannon in his famous article in 1948: “A mathematical theory of communication” [1] has proved that a coded transmission with rates close to capacity is possible with arbitrarily low error rate given long codes
Convolutional codes have been considered as a good choice for applications with strong latency constraints [2], whereas LDPC block codes (LDPC-BCs) perform better than convolutional codes when the requirements on latency are rather permissive
Stopping Rule: We introduce a simple, yet effective stopping rule based on the estimates of bit error rate (BER) using the log likelihood ratios (LLR) of the target symbols within a window
Summary
Shannon in his famous article in 1948: “A mathematical theory of communication” [1] has proved that a coded transmission with rates close to capacity is possible with arbitrarily low error rate given long codes. Convolutional codes have been considered as a good choice for applications with strong latency constraints [2], whereas LDPC block codes (LDPC-BCs) perform better than convolutional codes when the requirements on latency are rather permissive. An investigation in terms of decoding latency is carried out in [2], where convolutional codes and LDPC-BCs are compared under equal structural latency. We consider the convolutional counter part of LDPC-BCs, termed as LDPC convolutional codes (LDPCCCs). We compare the performance of LDPC-BCs and LDPC-CCs over a range of latencies. We compare the performance of such a suboptimal decoding scheme with LDPC-BCs under low latency over additive white Gaussian noise (AWGN) channel. The paper is organized as follows; Section II introduces the system model used throughout the paper to compare the codes on the basis of their decoding latency.
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