CRC-Aided Belief Propagation List Decoding of Polar Codes

Although iterative decoding of polar codes has recently made huge progress based on the idea of permuted factor graphs, it still suffers from a non-negligible performance degradation when compared to state-of-the-art CRC-aided successive cancellation list (CA-SCL) decoding. In this work, we show that iterative decoding of polar codes based on the belief propagation list (BPL) algorithm can approach the error-rate performance of CA-SCL decoding and, thus, can be efficiently used for decoding the standardized 5G polar codes. Rather than only utilizing the cyclic redundancy check (CRC) as a stopping condition (i.e., for error-detection), we also aim to benefit from the error-correction capabilities of the outer CRC code. For this, we develop two distinct soft-decision CRC decoding algorithms: a Bahl-Cocke-Jelinek-Raviv (BCJR)-based approach and a sum product algorithm (SPA)-based approach. Further, an optimized selection of permuted factor graphs is analyzed and shown to reduce the decoding complexity significantly. Finally, we benchmark the proposed CRC-aided belief propagation list (CA-BPL) to state-of-the-art 5G polar codes under CA-SCL decoding and, thereby, showcase an error-rate performance not just close to the CA-SCL but also close to the maximum likelihood (ML) bound as estimated by ordered statistic decoding (OSD).Comment: Submitted to IEEE for possible publicatio

Partially permuted multi-trellis belief propagation for polar codes

Abstract Belief propagation (BP) is an iterative decoding algorithm for polar codes which can be parallelized effectively to achieve higher throughput. However, because of the presence of error floor due to cycles and stopping sets in the factor graph, the performance of the BP decoder is far from the performance of state of the art cyclic redundancy check (CRC) aided successive cancellation list (CA-SCL) decoders. It has been shown that successive BP decoding on multiple permuted factor graphs, which is called the multi-trellis BP decoder, can improve the error performance. However, when permuting the entire factor graph, since the decoder dismisses the information from the previous permutation, the number of iterations required is significantly larger than that of the standard BP decoder. In this work, we propose a new variant of the multi-trellis BP decoder which permutes only a subgraph of the original factor graph. This enables the decoder to retain information of variable nodes in the subgraphs, which are not permuted, reducing the required number of iterations needed in-between the permutations. As a result, the proposed decoder can perform permutations more frequently, hence being more effective in mitigating the effect of cycles which cause oscillation errors. Experimental results show that for a polar code with block length 1024 and rate 0.5 the error performance gain of the proposed decoder at the frame error rate of 10−6 is 0.25 dB compared to multi-trellis decoder based on full permutations. This performance gain is achieved along with reduced latency in terms of the number of iterations

A White Paper on Broadband Connectivity in 6G

Executive Summary This white paper explores the road to implementing broadband connectivity in future 6G wireless systems. Different categories of use cases are considered, from extreme capacity with peak data rates up to 1 Tbps, to raising the typical data rates by orders-of-magnitude, to support broadband connectivity at railway speeds up to 1000 km/h. To achieve these goals, not only the terrestrial networks will be evolved but they will also be integrated with satellite networks, all facilitating autonomous systems and various interconnected structures. We believe that several categories of enablers at the infrastructure, spectrum, and protocol/algorithmic levels are required to realize the intended broadband connectivity goals in 6G. At the infrastructure level, we consider ultra-massive MIMO technology (possibly implemented using holographic radio), intelligent reflecting surfaces, user-centric and scalable cell-free networking, integrated access and backhaul, and integrated space and terrestrial networks. At the spectrum level, the network must seamlessly utilize sub-6 GHz bands for coverage and spatial multiplexing of many devices, while higher bands will be used for pushing the peak rates of point-to-point links. The latter path will lead to THz communications complemented by visible light communications in specific scenarios. At the protocol/algorithmic level, the enablers include improved coding, modulation, and waveforms to achieve lower latencies, higher reliability, and reduced complexity. Different options will be needed to optimally support different use cases. The resource efficiency can be further improved by using various combinations of full-duplex radios, interference management based on rate-splitting, machine-learning-based optimization, coded caching, and broadcasting. Finally, the three levels of enablers must be utilized not only to deliver better broadband services in urban areas, but also to provide full-coverage broadband connectivity must be one of the key outcomes of 6G